332 The Physics Teacher ◆ Vol. 50, September 2012 DOI: 10.1119/1.4745683

Each of these forces is mediated by bosons. The strong nuclear force is mediated by the gluon, while the electromag-netic force is governed by the photon. The weak nuclear force, which is responsible for beta decay, is caused by the exchange of three bosons: the neutral Z boson and the charged W+ and W– bosons.

While there is much more one can say about the Stan-dard Model,3 the story of the Higgs boson is intimately tied to work in the early 1960s, during which physicists Sheldon Glashow, Stephen Weinberg, and Abdus Salam attempted to unify the weak and electromagnetic forces.4 Building on earlier work by Yang and Mills, it was possible to express the electromagnetic and weak nuclear forces in a common theoretical formalism. This success came with a price, spe-cifically that the force-carrying bosons for the weak nuclear force were massless. This claim was obviously nonsense as the behavior of the weak force was inconsistent with that conjec-ture. However, the unification was sufficiently elegant so as to be of interest even in light of this obvious failure.

What is now called the Higgs mechanism resolved the problem. While the Higgs mechanism has an explicit math-ematical formulation in which the addition of the Higgs field minimizes the energy of the situation, the effect of the Higgs field is often described in terms of analogies. For instance, like how a barracuda experiences less friction in water than a sumo wrestler and can thus move more quickly in that medium, some particles experience greater interactions with the Higgs field and thus have a larger mass. Another popular

The Higgs Boson: Is the End in Sight?Don Lincoln, Fermi National Accelerator Laboratory, Batavia, IL

This summer, perhaps while you were lounging around the pool in the blistering heat, the blogosphere was buzzing about data taken at the Large Hadron

Collider1 at CERN. The buzz reached a crescendo in the first week of July when both Fermilab and CERN announced the results of their searches for the Higgs boson. Hard data confronted a theory nearly half a century old and the theory survived.

The Higgs boson is the missing piece of the Standard Model of particle physics. The boson was proposed in 1964 by Peter Higgs, although Higgs cannot (and does not) take all of the credit. Nearly simultaneous ideas by many gifted theorists means that the model governing the behavior of this boson could fairly be called the Anderson-Englert-Brout-Higgs-Guralnik–Hagen-Kibble theory,2 but luckily for journalists and students the world over, we just call it the Higgs boson. To understand the significance of the announcements of July 2012, we need to know some back story.

The late 1940s and 1950s were the heyday of the “particle zoo,” in which physicists discovered myriad particles with all sorts of properties: different masses, lifetimes, charges, inter-actions, spin, and so on. While it was a delightfully confusing era, it was really a time for some simplifying ideas that could consolidate the observations as being different manifestations of a few underlying principles. The 1960s brought with them the unifying ideas of quarks, quantum chromodynamics, and the unification of the weak and electromagnetic forces. The modern Standard Model was born.

The Standard ModelThe Standard Model (see Fig. 1) postulates that the fermi-

on quarks and leptons are the particles of matter, while several bosons mediate the forces that hold them together. Quarks are found inside the protons and neutrons (collectively called nucleons). Physicists have discovered six different “flavors” of quarks, with the names up, down, charm, strange, top, and bottom. Only up and down quarks are found inside the nucle-ons, while the others are more massive and unstable. The most massive quark is the top quark; with a mass of 173.5 GeV, it weighs about as much as an entire atom of gold.

The most familiar lepton is the electron, although there ex-ist two other charged leptons (the muon and the tau), as well as three neutral leptons called neutrinos. These 12 quarks and leptons are the complete set of known fundamental fermions.

These building blocks of matter are insufficient to describe our universe. After all, without some forces to hold them to-gether, the particles would wander around without interacting with one another, and matter as we understand it wouldn’t exist. The forces that are relevant in the quantum realm are electromagnetism and the strong and weak nuclear forces. We have no quantum theory of gravity.

Fig. 1. The Standard Model is the most successful description of the behavior of matter ever devised. The quark and lepton fermions, combined with the force-carrying bosons, can explain all data taken to date. The ghostly Higgs boson is the final piece remaining to be discovered. (Figure courtesy of Fermilab.)

The Physics Teacher ◆ Vol. 50, September 2012 333

quark/antiquark pair that can annihilate and make a Higgs boson, which then decays.

While this production mechanism is the dominant one, it is not the only one (see Fig. 2). Further, the contribution from other sources of Higgs boson production depends on the beam energy. At the lower energy accessible using the Fermilab Tevatron, another production mechanism is signifi-cant. At a rate of approximately a third that of the production of Higgs boson through virtual quarks, Higgs bosons can be produced in association with a W or Z boson. Investigat-ing this “associated production” is favored at the Tevatron because the backgrounds (i.e., events indistinguishable from Higgs boson production, but from more ordinary sources) are much smaller.

When a Higgs boson is produced, it exists for on order 10-22 seconds if its mass is low (i.e., on the order of 120 GeV). Thus we never observe the Higgs boson directly, but rather need to look for its decay products. Prior to 2010, it was nec-essary to look for the Higgs boson over a large mass range, from 114 GeV to about 600 GeV. Because of the Higgs boson’s affinity for particles of heavy mass, it preferentially decays into the heaviest particles it can, again consistent with energy conservation. The heavier denizens of the subatomic realm are the charm quark (1.3 GeV), tau lepton (1.8 GeV), bot-tom quark (4.5 GeV), W boson (80 GeV), Z boson (91 GeV), and top quark (173.5 GeV). In order to conserve energy and momentum, the Higgs boson must decay into at least two daughter particles, one matter and one antimatter. If the Higgs boson had a mass near 114 GeV, it would decay about 70% of the time into a bottom quark/antiquark pair, with the remainder of the decays into gluons, charm quarks, and tau leptons. In the mass range of 114–160 GeV, these fractions drop quasi-linearly as it becomes possible to make a W+/W– pair. At a mass of about 160–165 GeV (twice the mass of the W boson), Higgs bosons decay more than 95% of the time into pairs of W bosons. Above that mass, it becomes possible for the Higgs boson to decay into pairs of Z bosons, and from a mass of about 200–350 GeV, Higgs bosons decay into pairs of W bosons 70% of the time and pairs of Z bosons about 30% of the time. Above that mass, it becomes possible to decay

analogy invokes two people, a celebrity and a nobody, try-ing to walk through a crowd. Because of the crowd’s desire to interact with the well-known person, the celebrity has a more difficult time moving and can be imagined to have more iner-tia and to have effectively gained more mass.

Returning to a more technical description, while the theoretical electroweak bosons were massless, the Higgs mechanism “broke the symmetry” between the photon and the weak bosons, resulting in the following physical particles: a massless photon, a massive neutral weak boson (Z), two massive charged weak bosons (W±), and a new particle, now called the Higgs boson. The photon has long been known and was understood to be a quantized particle with Einstein’s pro-posal of the photoelectric effect, and the weak bosons were discovered in 1983 at the CERN laboratory in Switzerland. However, the existence of the Higgs boson remains to be es-tablished. That’s what this summer’s news was about.

The Higgs boson was originally postulated to break the theoretical symmetry between the electromagnetic and weak forces, by giving mass to the weak bosons. This mechanism is called electroweak symmetry breaking or EWSB. While the scope of the original proposal of the Higgs boson was limited to EWSB, it turned out to be easy to extend the theory to the fermion sector and to give mass to the quarks and leptons. Within this theoretical paradigm, there is only one unknown and that is the mass of the Higgs boson. Once the mass of the Higgs boson is determined, one can precisely calculate the production rates for it and its various decay modes. Because of this theoretical certainty, it is possible to optimize detectors and search strategies to maximize the chances for discovery. Additional firm predictions for the Higgs boson are that it is electrically neutral, is fundamental (i.e., contains no constitu-ents), its quantum mechanical spin is zero, and its parity is positive.

ProductionHiggs bosons are created inside particle accelerators from

the transformation of beam kinetic energy into the mass en-ergy of the boson. For recent searches, the Tevatron, located at Fermilab just outside Chicago, collided a beam of protons with a beam of antiprotons at a center of mass energy of 1.96 TeV, and the LHC collided two beams of protons at a center of mass energy of 8 (7) TeV in 2012 (2011). Because the Higgs boson generates the mass of fundamental particles, it preferentially interacts with the most massive particles it can, consistent with energy conservation. Since the heaviest known particle is the top quark, it is this particle that inter-acts most strongly with the Higgs boson. Since the top quark has a mass of 173.5 GeV, and the mass of the proton is 0.938 GeV, top quarks are not generally found inside the beam particles. However, it is possible to make “virtual” top quarks in the proton. These quarks do not have the “right” mass and can only exist because of the Heisenberg uncer-tainty principle. In order to generate the requisite interac-tion, gluons from the two colliding beam protons make a top

Fig. 2. While the production of Higgs boson is dominated by vir-tual top quarks originating from gluons in the beams, there are other ways in which it can be created. In this example, two vir-tual electroweak bosons are initially produced, which annihilate and create a Higgs boson.

334 The Physics Teacher ◆ Vol. 50, September 2012

photons precisely enough, this decay chain becomes attrac-tive due to its relatively small backgrounds.

BackgroundsOne of the greatest challenges in finding the Higgs boson

is the backgrounds. For instance, if the mass of the Higgs boson is low (say, 125 GeV), it preferentially decays into a bottom quark/antiquark pair. The problem is that producing bottom quarks/antiquarks via more ordinary physical pro-cesses totally swamps the Higgs boson signal by a huge factor. It is literally impossible to find the Higgs boson via this decay pattern. However the background for decays into pairs of Z bosons is much lower, as is the diphoton decay mode. The background for decay into W boson pairs is also relatively low, but to identify the W boson involves decays into unde-tectable neutrinos. Further, the ability of detectors to identify photons and the decay products of Z bosons is excellent. For these reasons, the Z and photon decay chains are the most powerful methods to identify events in which Higgs bosons are created.

Higgs hunting historyIn 1989, the Large Electron Positron (LEP) accelerator be-

gan operations at the CERN laboratory by circulating beams under the French and Swiss countryside. This accelerator collided electrons and positrons at an energy precisely tuned to copiously produce Z bosons. By 1994, the CERN Council decided that the LEP tunnel would ultimately house the LHC. In 1995, the LEP accelerator physicists raised the collision energy to 140 GeV. Further improvements culminated in a collision energy of 208 GeV, when the LEP accelerator was turned off for good in 2000 to make way for the LHC.

The LEP data were studied for hints of the Higgs boson, and, after an exciting false lead or two, the physicists finally concluded that they had not observed it and set a lower limit on the mass of the boson of 114.4 GeV. This was the state of affairs when the Fermilab Tevatron turned on in 2001 with a refurbished accelerator that raised the collision energy from 1.8 to 1.96 TeV and increased the instantaneous beam lumi-nosity by a factor of 10. After accumulating data for nearly a decade, the two Tevatron collaborations (DZero and CDF)5

made our first announcement restricting the allowed mass of the Higgs boson in July of 2010, when we had excluded the mass range of 158–175 GeV.

In September of 2008, the LHC began operations in front of the world, only just a few days later to have an improperly soldered electrical connection fail, which caused the cryo-genic system to release a vast amount of liquid helium. The resultant damage took about a year and a half to repair and the LHC began running again in March of 2010 at half the design energy (e.g., 7 TeV as opposed to 14 TeV). Even with this reduced capacity, the writing was on the wall for the Fer-milab Tevatron. By July of 2011, the LHC experiments were able to rule out the range of about 150–200 GeV as a possible

into pairs of top quarks. For masses above about 400 GeV, the Higgs boson decays into pairs of (W/Z/top) particles about (54/25/20)% of the time (see Fig. 3).

Given the expected Higgs boson decay modes, it is im-perative that any detector have excellent capabilities to detect bottom quarks and W and Z bosons. Good ability to identify tau leptons and top quarks is also beneficial.

There is one decay mode of the Higgs boson that is ex-tremely powerful and entirely counterintuitive. This is its de-cay into two photons (see Fig. 4). Because photons are mass-less, they do not interact with the Higgs boson directly, but occur in instances when the Higgs boson decays into an inter-mediate state of a pair of top quark/antiquarks that have tem-porary masses which are far from their “right” mass. (Again, this is possible under the aegis of the Heisenberg uncertainty principle.) This quark pair then annihilates into a pair of pho-tons. This process is rather rare, occurring about 0.1% of the time. However if the detector is able to measure the energy of

Fig. 3. The decay fractions of the Higgs boson are completely specified by the theory for each value of the mass of the Higgs boson. This plot shows the range of possible decay modes.

Fig. 4. While the Higgs boson preferentially decays into the heaviest particles consistent with energy conservation, through the intermediate decay into top quarks or W bosons, the Higgs can convert into two photons. This is an especially clear pro-duction mechanism and is therefore a dominant method to search for Higgs bosons at the LHC. The decay percentages for this mechanism are too small to show up in Fig. 3.

The Physics Teacher ◆ Vol. 50, September 2012 335

their excluded mass range (this extended region had already been ruled out by the LHC) but, more interestingly, an-nounced a two standard deviation excess in their data that suggested the existence of a particle in the mass range of 115–135 GeV.

Higgs physics heats upThis was the state of affairs as we entered July 2012. As

a collaborator on both the Fermilab DZero and the CERN CMS experiment, I was able to see the scientific process that precedes a big announcement. Physicists involved in smaller scientific groups may not appreciate the magnitude of how these measurements were vetted prior to being made public. Each of the Tevatron experiments were conducted by about

range for the Higgs boson. While the Tevatron experiments announced an update at the same conference, those results were no longer competitive. Other announcements of prog-ress were made in a seminar at CERN on Dec. 13, 2011, at which the two large LHC experiments (ATLAS and CMS, see sidebar) ruled out all masses outside the mass range of about 116–127 GeV (and with both experiments setting similar limits). More interestingly, both experiments found small sta-tistical excesses of order two standard deviations at a mass of about 125 GeV. A statistical excess of two standard deviations is not enough to be of real interest, although the fact that both experiments found an excess in the same region certainly did add some spice to the announcements.

In March of 2012, the Tevatron experiments extended

The detectors at the LHCThe detectors at the LHC are immense and must work under incredible conditions. When the LHC is operating at full capacity, the beams will

cross in the center of the detectors about 40 million times a second. During each crossing, 20 pairs of protons will collide on average. Thus each

detector must inspect of order a billion collisions per second, with the traces of those collisions often occurring in the equipment at the same

time. At most, a few hundred beam crossings can be recorded to computer tape each second. Selecting which ones are recorded is the job of

very fast custom electronics that we call a trigger.

The two large detectors at the LHC are CMS (Compact Muon Solenoid) and ATLAS (A Toroidal Large ApparatuS). See Figs. 5 and 6. Both de-

tectors can be thought of as approximate cylinders, with the symmetry axis along the beam line. CMS is about 50 feet wide, 70 feet long, and

weighs about 14,000 tons, while ATLAS is much larger and lighter at 70 feet wide, 140 feet long, and about 8000 tons. Both detectors consist of

about 100,000,000 individual detector elements, with the majority of these elements occurring in the finely grained silicon detectors at the heart

of the experiment. Like most particle physics detectors, they contain layers of subdetectors nested like Russian matryoshka dolls. The center

of the detectors is a huge array of silicon pixels a few tens of microns across. Surrounding the precision central tracker are trackers of larger

granularity. Following the tracking detectors are first calorimeters that measure electromagnetic energy (photons and electrons) and a second

set of calorimeters that measure hadronic energy (pions and protons). The outer detectors are designed to measure muons, which are the one

electrically charged particle that can penetrate that far. Mind you, each experiment uses different technology for each layer of the detector and

the curious reader can see Ref. 1 for details. Both detectors have similar capabilities, as they are studying the same phenomena, under the same

conditions. As they say, time will tell which design choices were good and which were bad.

Both ATLAS and CMS have a solenoidal magnetic field in their tracking volume, although the CMS solenoid actually surrounds the calorim-

eters as well. This is an uncommon choice in particle physics. Also, both detectors have a second set of magnets for the muon detector region,

with ATLAS having a series of eight distinctive large toroidal magnets that give the detector its name.

Fig. 6. The ATLAS detector is the largest particle detector at a particle collider. If you look closely, you see a person standing near the center of the detector. (Figure courtesy of CERN.)

Fig. 5. The CMS detector is the most massive particle detector at a particle collider. The white dots in the yel-low region (center bottom) are hard hats worn by people. (Figure courtesy of CERN.)

336 The Physics Teacher ◆ Vol. 50, September 2012

sentations focused on specific analyses and many presenta-tions occurred simultaneously), followed by a couple of days of plenary meetings (which were overview talks with no other simultaneous presentations). This format guaranteed that the Higgs boson plenary session would be anticlimactic because the measurements would have been already announced.

In addition, important experimental particle physics results are generally announced in a seminar at the hosting laboratory before being released more generally. In order to accommodate these various considerations, the CERN man-agement decided to have a seminar at 9:00 in the morning on July 4th. This would kick off the ICHEP conference but had the unfortunate consequence of occurring on a major holiday at 3:00 a.m. in the Eastern U.S. The CMS and ATLAS Higgs results were described first in a joint seminar, followed by a press conference that included the CERN director and leaders

400-500 physicists, while each of the LHC collaborations in-volve on the order of 3000 physicists. With those numbers of personnel, every conceivable effect was checked and double checked. Peer review has an entirely different meaning under these conditions.

When the LHC resumed operations in March of 2012 (af-ter the scheduled winter shutdown), the energy of the accel-erator was raised to 8 TeV. This increase resulted in a 20-30% increase in the Higgs production cross section. Further, the LHC is running superbly. By late June of 2012, the LHC had delivered as much integrated luminosity to the experiments as it had in all of 2011. With June came the moment when the LHC’s accumulated luminosity surpassed the Tevatron’s inte-grated luminosity that took a decade to record.

In order to make the best measurement possible, the LHC experimenters deliberately blinded themselves to data in those mass regions in which the Higgs boson could still exist. Because there were those earlier hints of an excess at 125 GeV, we didn’t want to bias our event selection criteria to either amplify or suppress a similar excess in the 2012 col-lision data. It was equally important that both the CMS and ATLAS experiments work independently. If the data taken in both experiments tell the same story, we are much more likely to believe that something has been discovered.

The initial unblinding for the data in both experiments was done in mid-June. For this first look at the new data, all of the 2011 data and about half of the 2012 data taken to that point were included. It was at this time that the blogosphere started heating up. To understand precisely what was be-ing observed, we must define the term Standard Model Lite (SML), which is the Standard Model but with the Higgs boson removed from the theory. According to the blogs, both exper-iments were seeing more events in which two photons or two Z bosons were produced than could be accounted for by SML. In addition, the blogs reported that the 2011 and 2012 data were telling a common story. Neither experiment confirmed the rumors, as there were cross-checks that remained to be done. Further, both experiments needed to include the entire set of data collected in 2012, a step that was not performed until the last days of June.

On July 2, the Tevatron experimenters (DZero and CDF) announced in a seminar held at Fermilab our nearly final results in our searches for the Higgs boson. By combining dozens of analyses and both experiments’ data sets, we found an excess of 2.9 sigma, indicating the existence of a particle not predicted by the Standard Model Lite. The mass range for this possible particle was in the range of 115–135 GeV. This announcement was a delightful aperitif for the LHC results released but two days later.

Both LHC experimental teams (ATLAS and CMS) expect-ed to present their measurements at the International Confer-ence on High Energy Physics (ICHEP) held in Melbourne this year. This particular conference was organized so that the first few days were parallel meetings (meaning that the pre-

Fig. 8. This data distribution shows the ATLAS collaboration’s study of diphoton production. The small bump at a mass of near 125 GeV indicates the observation of a new boson that is consistent with being the Higgs boson. (Figure courtesy of CERN and the ATLAS collaboration.)

Fig. 7. The announcement of evidence of a new boson was fol-lowed by a press conference, attended by international media. L to r: Fabiola Gianotti (leader of ATLAS), Rolf-Dieter Heuer (CERN director), and Joe Incandela (leader of CMS). (Figure courtesy of CERN.)

The Physics Teacher ◆ Vol. 50, September 2012 337

References1. Don Lincoln, The Quantum Frontier: The Large Hadron Col-

lider (Johns Hopkins University Press, Baltimore, 2009).2. Ian Sample, Massive: The Hunt for the God Particle (Virgin

Books, Ireland, 2010).3. Don Lincoln, Understanding the Universe: From Quarks to the

Cosmos (Revised) (World Scientific Press, Singapore, 2012).4. Bruce Schumm, Deep Down Things: The Breathtaking Beauty

of Particle Physics (Johns Hopkins University Press, Baltimore, 2004).

5. Ref. 3, pp. 306–312.

Don Lincoln is a senior researcher at Fermilab and member of both of the Fermilab DZero and CERN CMS collaborations, and has co-authored over 500 papers. He is also an avid popularizer of frontier physics and has written two books on science for the public: The Quantum Frontier: The Large Hadron Collider and Understanding the Universe: From Quarks to the Cosmos.lincoln@fnal.gov; http:/www.facebook.com/pages/Don-Lincoln/100958137881

of the two big LHC experiments (Fig. 7). The results were si-mulcast and I watched them with about 250 people who came to Fermilab in the middle of the night to see the announce-ment, including an inspiring number of physics undergradu-ate students.

So what, exactly, was announced? Both CMS and ATLAS independently claimed that they had “5 sigma” evidence for the existence of a new boson. “5 sigma” means that there is only about one chance in 3.5 million of seeing what was ob-served if the universe were governed by the Standard Model without the Higgs boson. This level of improbability is the standard in particle physics to declare that something new has been observed. Both experimental teams announced measurements in the photon and Z boson decay channels, and the CMS group also announced the outcome of studies in the W boson, bottom quark, and tau lepton decay channels. These three additional channels told a story that was consis-tent with the more powerful search modes, but will require more data before they can contribute strongly to the study of Higgs bosons. Both experiment groups announced a mass of the new boson of about 125 GeV (see Fig. 8).

What was discovered?So, was the discovery of the Higgs boson announced? No.

The reason is that the Higgs boson is a theoretically very well described particle, with specific couplings to fermions and bosons, a completely determined range of decay modes, as well as a specific value for its spin and parity. The amount of data announced on July 4th was insufficient to establish that the newly discovered boson had the required properties. Thus the announcement was that we found something and that it will require some work to establish precisely what it is. The measurements reported thus far are consistent with the Standard Model Higgs boson, but proving that it is the Stan-dard Model Higgs boson will take some additional time and data. The CERN management has instituted an operational plan designed to allow the two LHC experiments to accumu-late enough data in 2012 to independently verify these impor-tant properties. The observations of July are not the end of the story, but merely a new beginning.

As I am writing this, just a few days after the announce-ment, here is the status. The LHC will continue to collide beams of protons until December of 2012. After a short winter break, the LHC will collide beams of lead ions for the first part of 2013 and then shut down for repairs and up-grades. While the date at which the accelerator will resume operations is not yet specified, it is expected to be about the beginning of 2015. The LHC will then be able to safely collide beams at 13 or 14 TeV, opening yet another energy frontier. The next few years promise exciting possibilities.

PT 09.12 EI ad.indd 1 6/27/12 5:29 PM

GUEST COMMENT

Fireworks on the 4th of July

The February editions of The Physics Teacher and Ameri-can Journal of Physics include a poster by the ContemporaryPhysics Education Project with the title: “The Higgs Boson– Born on the 4th of July,” covering the Higgs boson newsreported on July 4, 2012. For an extensive description of thediscovery of the Higgs-like particle, see Don Lincoln’s arti-cle in The Physics Teacher.1

After half a century of waiting, the drama was intense.

Physicists slept overnight outside the auditorium to get seats

for the seminar at the CERN lab in Geneva, Switzerland. Ten

thousand miles away on the other side of the planet, at the

world’s most prestigious international particle physics confer-

ence, hundreds of physicists from every corner of the globe

lined up to hear the seminar streamed live from Geneva (see

Fig. 1). And in universities from North America to Asia physi-

cists and students gathered to watch the streaming talks.

In 1964, six theoretical physicists hypothesized a new field

(like an electromagnetic field) that would permeate all of

space and solve a critical problem for our understanding of

the universe. Independently, other physicists were construct-

ing a theory of the fundamental particles, eventually called

the “Standard Model,” that would prove to be phenomenally

accurate. These otherwise unrelated efforts turned out to be

intimately interconnected. The Standard Model needed a

mechanism to give fundamental particles mass. The field

theory devised by Peter Higgs, Robert Brout, Francois Eng-

lert, Gerald Guralnik, Carl Hagen, and Thomas Kibble did

just that.

Peter Higgs realized that, in analogy with other quantum

fields, there would have to be a particle associated with this

new field. It would have intrinsic spin of zero and therefore

be a boson, a particle with integer spin (unlike fermions,

which have half-integer spin: 1/2, 3/2, etc.), and indeed it

soon became known as the Higgs boson. The only drawback

was that no one had seen it.

Unfortunately, the theory that predicted its existence

didn’t specify the mass of the Higgs boson. Everyone hoped

it would be fairly light so that existing accelerators could dis-

cover it. But as the years went by it became clear that the

Higgs boson would be extremely massive, and most likely

beyond the reach of all machines built prior to the Large

Hadron Collider (LHC).

By the time the LHC started collecting data in 2010,

experiments at other accelerators had shown that the mass of

a Higgs boson had to be greater than about 115 GeV. The

LHC experiments planned to search for evidence anywhere

in the mass range 115–600 GeV or even up to 1,000 GeV.

On July 4, the leaders of the ATLAS2 and CMS3 experi-

ments were presenting their latest results on the search for

the Higgs boson. Rumors were flying that they were going to

report more than search results, but what was it? Indeed,

when the talks were presented, both experiments reported

that they had evidence for a “Higgs-like” boson with a mass

around 125 GeV. There was definitely a particle there, and if

it wasn’t the Higgs it was a very good mimic. The evidence

was far from weak; they were five sigma results, meaning

less than one chance in a million of the data being only a sta-

tistical fluctuation.

The data were convincing but not perfect, and there were

significant shortcomings. For one thing, the limited statistics

collected by July 4 couldn’t establish if the rate at which this

Higgs candidate decays to various collections of less massive

particles (the “branching ratios”) are those predicted by the

Standard Model.4

How does one know when one sees a collision event if it

is a candidate for a Higgs boson? There are unique character-

istics that make these events stand out.

Higgs bosons decay into other particles almost instantly

after they are produced, so we only see the products of the

decay. The most common decays (among those we are capa-

ble of seeing) are those to:

• a b-quark and its antiquark (b�b),• a tau lepton and its antiparticle (sþs�),• two photons (cc),• two W bosons (WþW�),• two Z bosons (Z0Z0).

A technicality: For a 125-GeV Higgs boson, the decay to

two Z bosons is not possible because Z bosons have a mass

of 91 GeV so the pair has a mass of 182 GeV, which is more

than 125 GeV. However, what we do observe is the decay to

a Z boson and a virtual Z boson (Z�) whose effective mass is

much less.

This Z Z� decay mode is quite easy for the ATLAS and

CMS experiments to detect because the Z boson sometimes

decays into an electron/antielectron pair or a muon/antimuon

pair. So in the collision of two protons, one of the manyFig. 1. Physicists applaud the Higgs boson news at the International Confer-

ence on High Energy Physics in Melbourne (July 4, 2012).

85 Am. J. Phys. 81 (2), February 2013 http://aapt.org/ajp VC 2013 American Association of Physics Teachers 85

particles produced on rare occasions is a Higgs boson H,

which occasionally decays as H ! Z þ Z�. Each of these Zbosons then (occasionally) decays as either Z ! e� þ eþ

or Z ! l� þ lþ. The end result is that we will sometimes

see (in addition to some unrelated particles) four muons, or

four electrons, or two muons and two electrons.

Figure 2 shows a neon sign of an actual event recorded by

ATLAS in which four muons (shown in neon) were pro-

duced. The other particles are shown in the background.

While decays of this kind had been observed for the new

particle by July 4, the rates at which they occur were still

uncertain. It was not even known if the newly discovered

particle has the right quantum numbers—that is, whether it

has the spin and parity required of a Higgs boson.

In other words, the July 4 particle looks like a duck, but

we need to make sure it swims like a duck and quacks like a

duck. This work is continuing. There is a major conference

in March 2013, which comes after the conclusion of this

year’s proton-proton collision run at the LHC. Physicists

look forward with great anticipation to seeing what the

experiments report about branching ratios, spin, and parity,

the properties essential to confirm that this really is the Higgs

boson.

Most physicists believe it is; it is difficult to create a

theory with a massive particle having significantly different

properties. However, the confirmation—or not—will eventu-

ally come from the data.

The discovery of the Higgs boson is an enormous clue

about the mechanism for giving mass to fundamental par-

ticles, as conceived by Higgs, Brout, Englert, Guralnik,

Hagen, and Kibble. What is this mechanism? It is a mathe-

matical theory for which an overly simplified cartoon (see

Fig. 3) can be used to demonstrate its essential nature.

Fundamental particles get their masses from the Higgs

mechanism. However, most of the ordinary mass of the

Fig. 2. A neon sign showing an actual event recorded by ATLAS, which

might reflect the decay of a Higgs boson into four muons, shown in neon.

The other particles are shown in the background.

Fig. 3. A cartoon helps to understand the Higgs mechanism. (a) Imagine that a room full of physicists chattering quietly is like space filled with the Higgs field

(top left). A well-known scientist walks in (top center), creating a disturbance as he moves across the room and attracting a cluster of admirers with each step

(top right). This cluster of admirers increases his resistance to movement; in other words, he acquires mass, just like a particle moving through the Higgs field.

(b) On the other hand, if a rumor crosses the room (bottom left), it creates the same kind of clustering, but this time among the scientists themselves (bottom

right). In this analogy, these clusters are the Higgs particles. # 1996 CERN. We thank CERN for the use of these images and text; the concept was inspired by

Professor David J. Miller of University College London.

86 Am. J. Phys., Vol. 81, No. 2, February 2013 86

universe does not come from this mechanism. Ordinary mass

comes mostly from the masses of protons and neutrons,

which are not fundamental particles, but particles made of

quarks.

Only a small part of the masses of neutrons and protons

comes from the mass of their constituents, the quarks. Most

of the mass comes from the kinetic energy of the quarks, via

E ¼ mc2. So the Higgs is not the source of most of the mass

of protons and neutrons.

The universe would be dramatically different if fundamen-

tal particles had no mass. There might be particles somewhat

similar to protons and neutrons, but there would be no atoms.

There would be no significant brightness. It would be a dark

universe with no people…and no fun. Whatever else it

teaches us, discovering the Higgs boson assures us of fun.

Certainly watching these grand experiments is amazing fun.

R. Michael BarnettLawrence Berkeley National Laboratory

ACKNOWLEDGMENTS

The author greatly appreciates valuable input from PaulPreuss (LBNL), Howard Haber (UC Santa Cruz), and mem-bers of the Contemporary Physics Education Project.

1Don Lincoln, “The Higgs Boson: Is the End in Sight?” Phys. Teach. 50,

332–337 (2012).2The ATLAS experiment, <www/atlas.ch/news/2012/atlas-and-the-higgs.

html>.3The CMS experiment, <cms.web.cern.ch/news/observation-new-particle-

mass-125-gev>.4Additional information on the Standard Model can be found online at The

Particle Adventure, <ParticleAdventure.org>.

87 Am. J. Phys., Vol. 81, No. 2, February 2013 87

A question of massJeremy Bernsteina�

�Received 7 May 2010; accepted 17 August 2010�

We present a pedagogical discussion of spontaneous symmetry breaking, the Goldstone theorem,and the Higgs mechanism. If the Higgs boson is found, it might provide an explanation of the originof mass. © 2011 American Association of Physics Teachers.

�DOI: 10.1119/1.3487939�

“The quantity of any matter is the measure of it by itsdensity and volume conjointly…. This quantity is what Ishall understand by the term mass or body in the discussionsto follow. It is ascertainable from the weight of the body inquestion. For I have found by pendulum experiments of highprecision, that the mass of a body is proportional to itsweight; as will hereafter be shown.” Isaac Newton1

When I took freshman physics as a sophomore at Harvardin 1948, this definition of mass was still used in our text-book. As it happens, the previous year I had taken a philo-sophically oriented course in modern physics given by thephilosopher-physicist Philipp Frank. He introduced us to thework of his fellow Austrian philosopher-physicist ErnstMach. Therefore I knew of Mach’s devastating critique in hisbook, The Science of Mechanics,1 and how it had influencedEinstein. Newton’s definition of mass is circular. What isdensity? How does it is apply to the photon, which has nomass?

When I began writing my Ph.D. thesis in the early 1950s,I would have described myself as an “elementary particle”theorist rather than as a nuclear theorist. Elementary particleswere considered to not consist of anything else, whereas theatomic nucleus consists of neutrons and protons, which weretaken to be elementary particles. There were not that manyelementary particles known at the time. In addition to theneutron and the proton, there was the photon, the electron,and the neutrinos. The positron was known, and most physi-cists, Feynman being a notable exception, believed that theantiproton would be found once accelerators were suffi-ciently energetic. A few years earlier, a “heavy electron” hadbeen discovered that had some of the properties of the elec-tron, including its weak and electromagnetic interactions, ex-cept that it was about two hundred times more massive andunstable. For various reasons that no longer make any sense,it was first called the mu meson and then eventually themuon. It seemed to serve no purpose and when I. I. Rabiheard of it, he asked, “Who ordered that?”

Rabi’s pique was understandable. In the 1930s, a theory ofthe nuclear force had been proposed. It had to account forsatisfying two conditions. First, the nuclear force was veryshort ranged and acted only when the neutrons and protonswere practically on top of each other. Second, it had to bemuch stronger than the electrical force; otherwise, the posi-tively charged protons, which repel each other, would tearthe nucleus apart. As it is, heavy nuclei with many protonstend to fission spontaneously. Both of these conditions couldbe satisfied if a fairly massive particle was exchanged be-tween the neutrons and protons and among themselves. The

strength of this interaction was postulated to be large com-pared to the electrostatic force. It was also shown that therange r of this force was related to the mass m of the particlebeing exchanged. From the uncertainty principle for energyand time, with the energy uncertainty equal to mc2, we havemc2��c /r, and thus its mass was predicted to be about 400times larger than that of the electron. This mass, unlike themass of the muon, seemed to have a connection to the dy-namics. The muon had something like the correct mass, but itonly interacted electrically and weakly, and thus it was thewrong particle. The right particle was called the pi-meson orthe pion. Why did it not show up in cosmic rays rather thanthe muon? The answer turned out to be very simple. Thepion, when it was not absorbed in the atmosphere, decayedinto a muon and neutrinos. When accelerators became suffi-ciently powerful, they produced pions in droves. At the timeI was writing my thesis, pion physics was flourishing. Butthen, the roof fell in.

Particles that no one anticipated also began to show up indroves in cosmic rays. They became known as “strange par-ticles” because they were. There was the K meson, whichcame in a charged and neutral variety, and hyperons, whichhad masses greater than the proton or neutron. The lattercategory includes a lambda particle, which is neutral, asigma particle with charges plus, minus, and zero, and a xiparticle with charges zero and minus. These were the lowestmass particles, which were repeated in higher mass replicas.In short, it was a particle zoo. It took strong nerves to see anypattern, a pattern that might reflect an underlying symmetry.

At the time, there was a clear idea of how such a symme-try might appear. The neutron and proton were prime ex-amples. They had many properties in common includingtheir spins, which were identical, and their masses, which didnot differ by much. The neutron was a bit heavier and de-cayed into a proton, an electron, and an antineutrino. Sup-pose we imagined a world in which electromagnetism wasswitched off. In this world, the neutron and proton wouldhave the same mass and would collapse into a doublet. Thethree pi mesons, plus, minus, and zero charge, would col-lapse into a triplet. A symmetry would emerge, which wascalled “isotopic spin,” which is invariance under the groupSU�2�. The predictions were reasonable, and hence isotopicspin was a useful approximate symmetry. Maybe somethinganalogous could be found for the strange particles.

The trouble was that the mass differences were too great.Although the mass difference of the neutron and proton wasonly a fraction of a percent of the mass of either particle, theK mesons had nearly four times the mass of the pions. It took

25 25Am. J. Phys. 79 �1�, January 2011 http://aapt.org/ajp © 2011 American Association of Physics Teachers

an act of faith to see how these objects fitted into some kindof symmetric structure. But Murray Gell-Mann took the leap.He proposed a symmetry that was a generalization of isoto-pic spin, SU�3�, and suggested that if the various mass dif-ferences were neglected, the known particles could be orga-nized in multiplet structures. For example, the known scalarmesons, including a newly discovered particle that wascalled the eta, fitted into an octet. The known hyperons fittedinto a tenfold decuplet, but there was one missing. It wasgiven the name �− and its properties were predicted. When itshowed up with these properties, the lingering doubts aboutthis scheme vanished and Gell-Mann was awarded a well-deserved Nobel Prize. It was a textbook example of a sym-metry and its breaking.

This kind of symmetry breaking is nearly as old as thequantum theory itself. Eugene Wigner and Herman Weyl, forexample, studied the role of group theory in quantum me-chanics. The idea was that the description of a quantum me-chanical system could be split into two contributions—aHamiltonian that exhibits the symmetries of the group plus asecond Hamiltonian that did not. If the later is “small,” thensome aspects of the original symmetry would still be appar-ent.

As an example, consider the group of rotations in three-dimensional space called SO�3�. These rotations are gener-ated by the orbital angular momentum. Suppose one part ofthe Hamiltonian contains only a central force. This part isinvariant under rotations, which means that the angular mo-mentum operators commute with this part of the Hamil-tonian. The eigenstates are both eigenstates of the energy andthe angular momentum. If, for example, the nuclear forcethat binds the neutron and proton together is represented by acentral force, then the ground state of the deuteron would bean S-state. But it isn’t. It has a small percentage of the Dstate, which manifests itself in the fact that the deuteron hasa quadrupole moment. The rotational symmetry is broken inthis case by adding a tensor force. The total angular momen-tum, which includes the spin, is conserved, but the purelyorbital part is not. Nonetheless, it is still useful to expand thewave functions in eigenfunctions of the angular momentum.

In the isotopic spin example, the neutron-proton system inthe absence of electromagnetism shows symmetries underthe group of special unitary transformations SU�2�. Onceelectromagnetism is included, the symmetry is broken, butnonetheless, there are still some useful manifestations. Like-wise, the elementary particles in the absence of symmetrybreaking are invariant under the special unitary group SU�3�.If this symmetry is broken, it is still possible to derive rela-tions among the masses, but their origin was still unex-plained. However, in the early 1960s, Yoichiro Nambu andothers showed that a second kind of symmetry breaking waspossible in quantum mechanics, which was called spontane-ous symmetry breaking. To see what it means, we consideran example that has nothing to do with quantum mechanics.

Consider the equation

d2f�x�/dx2 = x2 + cx . �1�

If c=0, Eq. �1� is symmetric under x inversion: x→−x. Wedrop the integration constants and obtain

f�x� = 1/12x4 + c/6x3. �2�

The solution with c�0 is not x inversion symmetric. This,lack of symmetry is in the spirit of Wigner-Weyl symmetrybreaking. But consider

d2f�x�/dx2 = x2. �3�

Equation �3� is x-inversion symmetric. The solution is

f�x� = 1/12x4 + Bx + C . �4�

Unless B is zero, the solution does not have the same sym-metry as Eq. �3�. The symmetry has been “spontaneouslybroken” by the choice of solution, determined by the initialconditions.

To see how spontaneous symmetry breaking works inquantum mechanics and to understand the consequences, weconsider an example, the self-interactions of a complex sca-lar field, ��x , t�=�1�x , t�+ i�2�x , t�, where �1,2 are realfields. This field describes a charged spinless particle. It isthe simplest example that I know, and it is the one that wasfirst considered historically. See, for example, Ref. 2. It willlead us to the Higgs mechanism.

We begin by exhibiting the Lagrangian of a free complexscalar classical field, which corresponds to a particle with amass m. To make the notation more compact, I will employthe usual convention of setting c=1. Thus

L = ����x�†����x� − m2��x�†��x�

= ���/�t�†���/�t� − ����†���� − m2�†� , �5a�

and the corresponding Hamiltonian is

H = ���/�t�† � �/�t + ����† • ���� + m2�†� . �5b�

We shall be interested in minimizing the energy. The kineticterms are always positive definite, and therefore to minimizethe energy associated with H, we must take the fields to beconstants in spacetime.

The Lagrangian in Eq. �5a� yields the field equation

��2t − �2 − m2���x� = 0, �6�

where I have simplified the notation by using x for �x , t�. Thesolutions of the field equations for individual particle andantiparticle states with momentum p have energies �p2+m2,which establishes the interpretation of m as a particle mass.

The Lagrangian is invariant under the global gauge trans-formation �→exp�i���, where � is a real number. It is notinvariant under the spacetime dependent or local gaugetransformation �→exp�i��x���. Under an infinitesimaltransformation, a term is added to the Lagrangian of theform, with �,� standing for the derivative with respect to the�th coordinate

�L = i�,�����†� − �†���� �,�J�. �7�

If we think of � as a dynamical variable, then we can writedown the Euler–Lagrange equation for � as

���L/��,� = �L/�� . �8�

The term on the left is the divergence of the current gener-ated by the local gauge transformation, and the term on the

26 26Am. J. Phys., Vol. 79, No. 1, January 2011 Jeremy Bernstein

right vanishes, and hence the current generated this way isconserved. This argument is a variant of what is known as aNoether theorem.

From the Noether theorem, we have

��J� = � · J�x,t� + �/�tJ0�x,t� = 0, �9a�

0 = d3x��J�. �9b�

If nothing strange happens at the boundary in space, Eq. �9b�reduces to

0 = �/�t d3xJ�x,t�0 Q , �10�

where Q is the spatial integral of the charge density Jo�x , t�.We now want to quantize this theory. Thus we write

��x� = d3k�b†k�k

�−��x� + ak�k�+��x�� . �11�

Here, � in the integral can be taken as a shorthand for theFourier transform coefficients, say, exp�ikx�, with some suit-able normalization. The a and b coefficients are annihilationoperators, and their conjugates are creation operators. Theonly nonvanishing commutators of the a and b operators are

�ak,ak�†� = �3�k − k�� = �bk,bk�

†� . �12�

The momentum ��x� conjugate to � is given by

��x� = ��t��†�x��

= − i� d3kk�bk�k�−���x� − ak

†�k�+���x�� . �13�

Equation �13� yields the commutation relation

���x�,�y�� = i���x − y� . �14�

The charge can be written in terms of the a and b operatorsas

Q = d3p�ap†ap − bp

†bp� . �15�

From Eq. �15�, it follows that

�Q,�� = � �16�

so that

exp�i�Q�� exp�− i�Q� = exp�i��� . �17�

Thus the charge generates the global gauge transformation,that is, � transforms under unitary transformations generatedby the operator exp�i�Q�.

The Hamiltonian in normal ordered form with a† and b† tothe left of a and b is given by

H = d3kk�ak†ak + bk

†bk� . �18�

We have dropped an additive constant. Additive constants tothe Hamiltonian do not change the physics because we areconcerned with energy differences and not with absolute en-

ergies. �In contrast, an additive constant to the Lagrangianchanges the action, and thus the transition amplitudes thatare calculated with path integrals. We must make sure thatadditive constants do not change the physics by eliminatingany constants.�

The vacuum state �0� is that state for which the energy isminimum. If it has the property that 0�H�0�=0, it followsthat from equations such as 0�ak

†ak�0�=0 that

ak�0� = bk�0� = 0, �19�

and thus both the Hamiltonian and the charge operators act-ing on this state are zero. We also have the obvious property

0���0� = 0. �20�

So far the particle mass has been specified without anyexplanation for its origin. We now want to introduce massgeneration through spontaneous symmetry breaking. We in-troduce a new Lagrangian

L = 1/2����x�†����x� + m2/2��x�†��x�

− �/4��†�x���x��2. �21�

Several properties of this Lagrangian are evident. First, theterm proportional to m2 is not a mass term. Compare the signto the sign in the mass term in Eq. �5a�. Instead, it is aself-interaction term. Second, the Lagrangian is invariant un-der global gauge transformations but not local ones. There isa conserved current as before and a conserved charge. Butdoes this charge annihilate the vacuum, that is, Q�0�=0 asbefore, and if not what does this mean? Here we run into thequestion of what is the vacuum.

We recall the equation

�Q,�� = � , �22�

which also holds here. Equation �22� implies that if Q doesnot annihilate the vacuum, then it must be that

0���0� � 0. �23�

Equation �23� means that � cannot have a particle interpre-tation because we cannot build up the single particle statesby the creation operators acting on the zero particle vacuumstate.

We recall from the discussion following Eq. �5a� that theenergy is minimized for constant fields, and it is thereforedetermined by minimizing the potential. Let us consider theclassical potential

V = − m2/2��†�� + �/4��†��2. �24�

Clearly one extremal is when �=0. Quantum mechanicallywe want to replace this condition by the condition that thevacuum expectation value of the potential is a minimum. Weshall see that in this case, there is no unique answer.

Let us warm up with a simpler case, which will illustratethe issues. We consider a real field � and the potential

V = − m2/2�2 + �/4�4. �25�

The potential and � are all functions of the spacetime pointx. At the minima of the vacuum expectation value of theenergy, they are constants, and hence we can find a condition

27 27Am. J. Phys., Vol. 79, No. 1, January 2011 Jeremy Bernstein

on � that minimizes the potential for all x. We take thederivative with respect to � and set it equal to zero. Thus

��m2 − ��2� = 0. �26�

Equation �26� has three solutions,

� = 0, � �m2/� . �27�

Equation �27� corresponds to the values of the potential at 0,which is a local maximum and �1 /4 m2 /�, two distinctminima with the same energy. If we pick the one with thepositive minimum for �, then for this vacuum

0���0� = �m2/� v . �28�

Equation �28� shows that � does not have the usual particleinterpretation and suggests that we introduce a new field todescribe the fluctuations of � away from its constant vacuumvalue v. We have

= � − v . �29�

In terms of , the Lagrangian becomes

L = 1/2�� �� − m 2 2 − �v 3 − 1/4� 4 + m4/4� , �30�

where

m = �2m2. �31�

This choice of vacuum has produced an , a particle witha nonzero mass and some peculiar self interactions. But notethat the �→−� symmetry of the original Lagrangian in Eq.�21� has been broken spontaneously. There is no trace of it inthe transformed Lagrangian. The last term, which is a con-stant, also deserves further comment. If we were consideringa Hamiltonian, we could add a constant term with no mis-givings. But as I have mentioned, the Lagrangian is different.

From it, we define the action �tt�Ldt. If we add a constant to

the Lagrangian, it adds a term proportional to the time dif-ference in the action. We had better eliminate this term if wewant a sensible theory.

With this example in mind, we now return to the complexfields with the continuous global gauge transformation in-variance. As we shall see, this invariance brings in somethingnew. The way to deal with this case is to write

� = 1/�2��1 + i�2� , �32�

where �1,2 are real fields. In terms of these fields, the La-grangian becomes

L = 1/2����1�2 + 1/2����2�2 + 1/2m2��12 + �2

2�

− 1/4���12 + �2

2�2. �33�

The minima are given by the condition that

�12 + �2

2 = m2/� v2. �34�

The phase is undetermined. We choose the phase so that atthe minimum,

�1 = �m2/�, �2 = 0. �35�

We can then displace �1 by its vacuum expectation value inthe vacuum defined by this choice of phase and thus write

��x� = �1/ � 2��v + �x� + i��x�� . �36�

We can rewrite the Lagrangian in terms of these fields.There will be self-interaction terms of � ,�� as well as inter-actions between them and the additive constant. What inter-ests us is the “kinetic” term LK,

Lk = 1/2�����2 + 1/2��� �2 − m2 2, �37�

which shows that the new � field is massless and the fieldhas mass m.

Let us review what we have done. We began with a La-grangian for a complex field of zero mass, which was glo-bally gauge invariant. We broke this gauge invariance spon-taneously and found two interacting real scalar fields. One ofthese fields has mass zero, and the other has acquired a mass.Is this result some freakish artifact of this Lagrangian, or arewe in the presence of a more general phenomenon? The an-swer is the latter. We have found a realization of what isknown as the Goldstone theorem.

I will not try to give a detailed proof of this theorem herebut only state what it is. There are fine points that I willdiscuss shortly. Suppose you have a theory with a certainnumber of conserved currents, and these currents give rise toconserved charges that generate some set of gauge transfor-mations. If one of these charges has a nonvanishing expec-tation value so that the gauge symmetry is broken spontane-ously, then necessarily it will give rise to a mass zero, spinzero particle—the � in the example we have discussed. On itsface, this result would appear to rule out theories of this kindin elementary particle physics because there are no such par-ticles. However, there is a loophole, and through it we willdrive a truck. The loop hole is Lorentz invariance.

Needless to say, we want all our theories to be Lorentzinvariant, but they need not be “manifestly” Lorentz invari-ant. A case in point is electrodynamics. This theory is cer-tainly Lorentz invariant. When Einstein had to choose be-tween Newtonian mechanics and electromagnetism, he chosethe latter precisely because it was relativistic. But electro-magnetism is not manifestly Lorentz invariant in the follow-ing sense. The photon field A� is not well-defined. Thetheory is invariant under gauge transformations of the formA�→A�+���, where � is a function of the spacetime pointx. This invariance precludes terms such as A�A� in the La-grangian, and thus the photon has no mass.

To define the theory, we must select a gauge. Two populargauges are the Lorenz gauge,3 with ��A�=0, and the Cou-lomb gauge with � ·A=0. The Lorenz gauge condition ismanifestly Lorentz invariant, and the Coulomb gauge is not.You can use either gauge to carry out calculations. You willget the same answers for any physical quantity, and theseanswers will be Lorentz covariant.

The proof of the Goldstone theorem that most clearlymakes use of the manifest Lorentz covariance is due toWalter Gilbert.4 Gilbert has an interesting history. He got hisPh.D. in physics from Abdus Salam and then switched intobiology. In 1980, he won the Nobel Prize for chemistry. Itwas during his physics period when he published this proof.For details, an interested reader can read my 1974 reviewarticle.5

28 28Am. J. Phys., Vol. 79, No. 1, January 2011 Jeremy Bernstein

The first people to use the gauge loophole were PeterHiggs,2 Francois Englert, and Robert Brout.6 Many of thepoints were later clarified by G. S. Guralnik, C. R. Hagen,and T. W. B. Kibble.7 I will stay within the confines of theelectrodynamics of charged scalar particles for the momentso as to use the work we have already done.

We can write the Lagrangian as

L = − 1/4��/�x�Av�x�� − ��/�xvA��x��2

− ���/�x� + ieA��x���†�x����/�x� − ieA��x���x��

+ m2�†�x���x� − 1/2��†�x���x��2. �38�

The first part of the Lagrangian is the free electromagneticpart, and the last part is the bosonic part we have alreadyseen. The middle part is the coupling term.

As before, it is convenient to split � into its real andimaginary parts and use the two-dimensional notation

� = ��1,�2� . �39�

To simplify the notation, we shall introduce the 2�2 matrixq,

q = �0 − i

i 0� . �40�

By using the Noether techniques I described earlier, we findthe conserved current,

J� = i���/�x����x�q��x� + e��x� · ��x�A��x�� , �41�

whose charges generate global gauge transformations. Wecan now break this invariance spontaneously and make thesame choice of vacuums as before. That is, we minimize thescalar boson potential as we have done in our previous ex-amples. What is new here is the vector potential, which didnot enter our previous discussion. The result is

�/�xv��/x�Av�x�� − ��/xvA��x��

= m2��1/m� � /�x���x� − A��x�� . �42�

By this point, the reader may wonder where is all thisformalism leading? Behold, you are about to witness amiracle.

It is at this point we must choose a gauge for A��x�. It isconvenient to use the Lorenz gauge � /�x�A��x�=0. Equation�42� can then be written as

�/�xv��/�xvA��x�� = m2�A��x� − �1/m� � /�x���x�� . �43�

We define a new field B��x� by

B� = A��x� − �1/m� � /�x���x� . �44�

From the field equations, this ��x�, unlike the previous ex-ample beginning with Eq. �33�, obeys the equation of anuncoupled zero mass boson—the Goldstone boson,

�/�xv � /�xv��x� = 0. �45�

If we make the substitution of Eq. �44� into Eq. �43� and useEq. �45�, we obtain

�/�xv � /�xvB� = m2B�. �46�

The “photon” has morphed into a vector meson with mass.

Let us summarize what we have done. The electrodynam-ics of a charged boson with a spontaneously broken gaugesymmetry in the manifestly covariant Lorenz gauge yieldsresults consistent with a Goldstone theorem. We obtain anuncoupled massless Goldstone scalar boson �, a massive sca-lar boson , and a massive vector meson B�. Because thesemasses have the same origin, there is a relation betweenthem. Because the Goldstone particle is uncoupled, it is alsounobservable and can be ignored.

What happens in the Coulomb gauge where � ·A=0? Iwon’t go though the steps but summarize the results. There isno Goldstone theorem because the gauge is not explicitlycovariant and no Goldstone boson. There is a massive scalarboson and a massive vector meson B�.

The first person to make full use of these ideas was StevenWeinberg in 1967.8 To appreciate what he did, we must setthe context. In 1934, Fermi produced the first modern theoryof �-decay. He was an expert in quantum electrodynamics,and hence it was natural for him to use it as a template. Inquantum electrodynamics the current of charged particles J�

interacts with the electric field A� with a coupling of theform J�A�. Thus charged currents do not act directly witheach other but only by the exchange of photons. Becausethere was apparently no equivalent of the photon for theweak interactions such as �-decay, Fermi directly coupled acurrent J�

N for the “nucleons,” the neutron and proton, witha current J�

L for the “leptons,” the electron and neutrino, thatis, J�

NJ�L. This phenomenological theory worked very well.

One could use it to calculate, for example, the energy spec-trum of the electrons emitted in �-decay. But it came to seemanomalous. The “strong” interaction between nucleons, asYukawa proposed in the prequark days, took place with theexchange of mesons, the electromagnetic interactions withphotons, and presumably gravitation with gravitons. Therewas a suggestion of using the same meson that produced thestrong interactions to produce the weak ones. This idea wasabandoned. But in the 1950s, it was suggested that one ormore weak heavy photons might do the trick. There weretwo problems. None had been observed, and the theory thatwas being proposed did not make any sense.

The former difficulty was easily disposed of. Because thecontact theory with the currents coupled directly to eachother worked well phenomenologically, it had to be thatthese weak mesons were very massive—too massive, it wasargued, for the generation of accelerators that then existed toproduce them. When they finally were produced, it turnedout that their masses were about a hundred times greater thanthe nucleon masses. The second difficulty was qualitativelydifferent. In the theories that were then being proposed, theweak mesons were being put in “by hand.” They were justmassive particles whose masses had no particular origin. Ifone tried to calculate anything beyond the lowest order phe-nomenology, we obtained terrible infinities. These infinitieswere much worse than those in quantum electrodynamics,which could be swept under the rug by renormalization. Inshort, the theory did not make any sense. Theorists were leftgrasping for straws. Then came Weinberg.

29 29Am. J. Phys., Vol. 79, No. 1, January 2011 Jeremy Bernstein

The “electroweak” theory of Weinberg plays on thethemes we have discussed but at a higher register. The un-derlying Lagrangian consists of massless vector mesons,three of which—the two charged ones and the neutral one—are coupled to the scalar bosons. In addition, there is thephoton, which is not coupled to these bosons. Then there arethe bosons themselves, which are self-coupled as well. ThisLagrangian has a global gauge symmetry, but the symmetrygroup is non-Abelian. In the examples that I have discussed,the effect of the global gauge transformation is to multiplythe fields by a numerical phase. These examples are Abelian,and therefore it does not matter in which order two of thesetransformations are performed. In the non-Abelian case, itdoes matter. The latter case complicates the formalism butdoes not change the underlying methodology. Once again thegauge symmetry is broken spontaneously. The coupled vec-tor mesons acquire masses, while the photon remains mass-less and there are massive scalar bosons. Apart from the factthat this method unifies two otherwise disparate interactions,it also cures the nonrenormalization issue.

There was always a sort of canary in the mineshaft inter-action. It was the v reaction �+�� →W++W−. A neutrino andan antineutrino interact and produce a pair of weak vectormesons. No one proposed to measure this reaction, but itscalculation should nonetheless make sense. When this calcu-lation is done in the conventional theory with no scalarbosons and the masses being put in by hand, the cross sec-tion increases without limit as the neutrino momentum ap-proaches infinity. Here there are no issues of infinities causedby going to higher order, but rather there is a violation in thelimit that quantum mechanics imposes on the magnitude ofsuch cross sections due to the conservation of probability.

Weinberg observed that there is a contribution in the elec-troweak theory from the scalar bosons to this process, whichcancels the terms that violated the quantum limit and rendersthe cross sections reasonable. He conjectured that the theorywas renormalizable, which was proven in detail by MartinusVeltman and his student Gerhard t’Hooft.

The alert reader will notice that something is missing inthis discussion. All the leptons have mass including the neu-trinos, to say nothing of the masses of the neutrons and pro-tons. What is the origin of their masses? Hopefully, thereader will indulge me in a bit of personal reminiscence. Fortwo years in the late 1950s I was a postdoc at Harvard. JulianSchwinger was the leading light in theoretical physics at thetime. We, the postdocs and junior faculty, audited whatevercourse he happened to be teaching. The material was alwaysoriginal. The lectures were on Wednesdays, and afterwardthe small group of us would have lunch with Schwinger atChez Dreyfus in Cambridge. We would be joined by anothersmall group from MIT that included Vikki Weisskopf. IfSchwinger had any new ideas, he would try them out onWiesskopf. As it happened on this occasion, he had devel-oped a “theory of everything.” Some of this theory survivesin the work of other people. In 1962, he published a paper on“Gauge invariance and mass.”9 In it he raised the question ofwhether one could have a massive vector meson in a theorythat had an underlying gauge invariance. This possibility is

not exactly what we have been discussing, but it inspired P.W. Anderson to use these ideas in condensed matterphysics.10 Anderson used language in a nonrelativistic con-text, which is very similar to what we have been discussing.

I remember a lunch in which Schwinger began by sayingto Weisskopf, “Now I will make you a world.” The “world”was written down on a few paper napkins, one of which Isaved. In any event, one of the things that he said, which hasstuck with me ever since, was that scalar particles were theonly ones that could have nonvanishing vacuum expectationvalues. He then went on to say that if you couple one of

these to a fermion � by a coupling of the form ��� �, thenthis vacuum expectation value would act like a fermionmass. This sort of coupling is how mass generation is done inprinciple for the fermions. All particles in this picture wouldacquire their masses from the vacuum. We are a long wayfrom Newton.

I have avoided so far the use of the term Higgs boson—theanalog in the electroweak theory of the . Certainly, Higgsdeserves the credit for first exhibiting the mechanism in thecontext of scalar electrodynamics. But as I have tried toshow, it took other people to make it work. The Higgs bosonis what is being looked for at CERN. If they find it, we shallall be happy and relieved. And if not? I am reminded of astory about Einstein. He had just received a telegram withthe news that the eclipse expeditions had confirmed his gen-eral relativity prediction about the Sun bending starlight. Hewas very pleased with himself and showed the telegram toone of his students, Ilse Rosenthal-Schneider. She asked himwhat he would have done if the telegram had contained thenews that the experiments disagreed with the theory. He re-plied, “Da könt mir halt der lieber Gott leid tun-die theoriestimmt doch. �Then I would have been sorry for the dearLord. The theory is right�.”

ACKNOWLEDGMENTS

The author is grateful to Elihu Abrahams and RomanJackiw for helpful communications and to an anonymousreferee for a very careful reading of the paper.

a�Electronic mail: jbernste@earthlink.net1This translation from the Latin can be found in Ernst Mach, The Scienceof Mechanics �Open Court, LaSalle, IL, 1960�, p. 298.

2P. W. Higgs, “Broken symmetries and the masses of gauge bosons,” Phys.Rev. Lett. 13, 508–509 �1964�.

3This is not a misprint. Ludvig Valentin Lorenz was a 19th century Danishphysicist to whom we owe this choice of gauge. I am grateful to Wolf-gang Rindler for making the fact that this choice is the Lorenz gauge andnot the Lorentz gauge clear so the use of “Lorenz” and not “Lorentz” isnot a misprint. See J. D. Jackson, “Examples of the zeroth theorem of thehistory of science,” Am. J. Phys. 76, 704–729 �2008� for a brief biogra-phy of Lorenz.

4W. Gilbert, “Broken symmetries and massless particles,” Phys. Rev. Lett.12, 713–714 �1964�.

5For a discussion of the boundary question see Jeremy Bernstein, “Spon-taneous, symmetry breaking, gauge theories, the Higgs mechanism andall that,” Rev. Mod. Phys. 46, 1–48 �1974�.

6F. Englert and R. Brout, “Broken symmetries and the mass of gaugevector mesons,” Phys. Rev. Lett. 13, 321–323 �1964�.

30 30Am. J. Phys., Vol. 79, No. 1, January 2011 Jeremy Bernstein

7G. S. Guralnik, C. R. Hagen, and T. W. B. Kibble, “Global conservationlaws and massless particles,” Phys. Rev. Lett. 13, 585–587 �1964�.

8S. Weinberg, “A model of leptons,” Phys. Rev. Lett. 19, 1264–1266�1967�.

9J. Schwinger, “Gauge invariance and mass,” Phys. Rev. 125, 397–398�1962�.

10P. W. Anderson, “Plasmons, gauge invariance and mass,” Phys. Rev. 130,439–442 �1963�.

Gravitational Lensing

This sculpture depicts gravitational lensing by dark matter. The cause of lensing is represented here by a cluster ofMöbius strips, the subtle aspects of which allude to not-yet-understood properties of dark matter. Installed at theEast Lansing �MI� High School, the sculpture honors the sustained achievements in physics education by JohnPlough and colleagues. It is intended to remind students of the many unsolved problems in astrophysics andcosmology that remain to be attacked by new generations of scientists. This sculpture was created by Jens Zorn,Professor of Physics at the University of Michigan.

31 31Am. J. Phys., Vol. 79, No. 1, January 2011 Jeremy Bernstein

Resource Letter: SM-1: The standard model and beyondJonathan L. RosnerEnrico Fermi Institute and Department of Physics, University of Chicago, 5640 South Ellis Avenue,Chicago, Illinois 60637

~Received 22 July 2002; accepted 22 November 2002!

This Resource Letter provides a guide to literature on the standard model of elementary particles andpossible extensions. In the successful theory of quarks and leptons and their interactions, importantquestions remain, such as the mechanism of electroweak symmetry breaking, the origin of quark andlepton masses, the source of the baryon asymmetry of the Universe, and the makeup of its matterand energy density. References are cited for quarks and leptons, gauge theories, color andchromodynamics, weak interactions, electroweak unification, CP violation, dynamics of heavyquarks, Higgs bosons, precision electroweak measurements, supersymmetry, dynamical electroweaksymmetry breaking, composite quarks and leptons, grand unification and extended gauge groups,string theories, large extra dimensions, neutrino masses, cosmic microwave background radiation,dark matter, dark energy, accelerator facilities, and non-accelerator experiments. ©2003 American

Association of Physics Teachers.

@DOI: 10.1119/1.1539087#

I. INTRODUCTION

The ‘‘Standard Model’’ of elementary particle physics en-compasses the progress of the past half-century in under-standing the weak, electromagnetic, and strong interactions.During this period tremendous strides were made in bringingquantum field theory to bear upon a wide variety of phenom-ena.

The arsenal of techniques for understanding the strong in-teractions in the 1960s included principles based on analyt-icity, unitarity, and symmetry. The successes of the emergingquark model often seemed mysterious. The ensuing decadeyielded a theory of strong interactions, quantum chromody-namics ~QCD!, permitting calculations of a wide range ofproperties of thehadrons, or strongly interacting particles,and has been validated by the discovery of its force-carrier,the gluon.

In the 1960s the weak interactions were represented by aphenomenological four-fermion theory of no use for higher-order calculations. Attempts to describe weak interactionswith heavy boson exchange bore fruit when these interac-tions were unified with electromagnetism and a suitablemechanism for generation of heavy boson mass was found.This electroweak theoryhas been spectacularly successful,

leading to the prediction and observation of theW and Zbosons and to precision tests confirming the theory’s validityin higher-order calculations.

This Resource Letter begins with sections devoted to theresources available for study of the standard model of par-ticle physics and its extensions: periodicals~Sec. II!, confer-ence proceedings~Sec. III!, texts and reviews~Sec. IV!, his-torical references~Sec. V!, popular literature~Sec. VI!,Internet resources~Sec. VII!, and a guide to Nobel prizesrelated to the subject~Sec. VIII!.

A description of Standard Model research literature fol-lows. In Sec. IX, based in part on Ref. 1, the ingredients ofthe standard model—the quarks and leptons and theirinteractions—are introduced, and QCD is discussed briefly.The unified theory of weak and electromagnetic interactionsis described, its role in explaining CP violation is explained,and its missing piece—the Higgs boson—is mentioned.

Important questions remain that are not addressed in thestandard model. These include the unification of the elec-troweak and strong interactions~possibly including gravity!,the origin of quark and lepton masses, the source of thebaryon asymmetry of the Universe, and the nature of its un-seen matter and energy density. Some proposed standard

RESOURCE LETTER

Roger H. Stuewer,EditorSchool of Physics and Astronomy, 116 Church Street SE,University of Minnesota, Minneapolis, Minnesota 55455

This is one of a series of Resource Letters on different topics intended to guide college physicists,astronomers, and other scientists to some of the literature and other teaching aids that may helpimprove course content in specified fields.@The letter E after an item indicates elementary level ormaterial of general interest to persons becoming informed in the field. The letter I, for intermediatelevel, indicates material of somewhat more specialized nature; and the letter A indicates ratherspecialized or advanced material.# No Resource Letter is meant to be exhaustive and complete; in timethere may be more than one letter on some of the main subjects of interest. Comments on thesematerials as well as suggestions for future topics will be welcomed. Please send such communicationsto Professor Roger H. Stuewer, Editor, AAPT Resource Letters, School of Physics and Astronomy,University of Minnesota, 116 Church Street SE, Minneapolis, MN 55455; e-mail:rstuewer@physics.spa.umn.edu.

302 302Am. J. Phys.71 ~4!, April 2003 http://ojps.aip.org/ajp/ © 2003 American Association of Physics Teachers

model extensions devoted to these problems are noted inSec. X. Concrete evidence for physics beyond the standardmodel, including neutrino masses, cosmic microwave back-ground radiation, dark matter, and ‘‘dark energy,’’ is de-scribed in Sec. XI. A variety of experimental methods areappropriate for probing these phenomena~Sec. XII!. A briefsummary~Sec. XIII! concludes.

1. ‘‘The Standard Model in 2001,’’ J. L. Rosner, based on five lectures atthe 55th Scottish Universities’ Summer School in Particle Physics, St.Andrews, Scotland, August 7–23, 2001. Published inHeavy FlavourPhysics„Theory and Experimental Results on Heavy Quark Phys-ics and CP Violation…, edited by C. T. H. Davies and S. M. Playfer~Institute of Physics, Bristol and Philadelphia, 2002!, pp. 1–56.~I!

II. PERIODICALS

The literature on the standard model of particle physicsand its extensions is extensive and international, but a goodsense of the field can be gained by perusing about a dozenmain journals. Subsequent sections are devoted to othermeans of gaining information about this rapidly changingsubject.

Instrumentation journals with some articles on elementaryparticle physics:

IEEE Transactions on Nuclear ScienceNuclear Instruments and Methods AReview of Scientific Instruments

Journals devoted primarily or largely to elementary particlephysics

European Journal of Physics CFizika Elementarnykh Chastits i Atomnogo Yadra~SovietJournal of Particles and Nuclei!International Journal of Modern Physics AJournal of High Energy Physics~‘‘JHEP;’’ electronic!Journal of Physics GModern Physics Letters ANuclear Physics BNuovo Cimento APhysical Review DPhysics Letters BProgress of Theoretical Physics (Kyoto)Yadernaya Fizika~Soviet Journal of Nuclear Physics—1992; Physics of Atomic Nuclei 1993–!.Zeitschrift fur Physik C, now absorbed into EuropeanJournal of Physics C

Zhurnal Eksperimental’nyi i Teoreticheskii Fizika (SovietPhysics—JETP)

Laboratory newslettersCERN Courier~European Center for Nuclear Research!;web address:http://www.cerncourier.com/FermiNews ~Fermilab, USA!; web address:http://www.fnal.gov/pub/ferminews/SLAC Beam Line~Stanford Linear Accelerator Center!;web address:http://www.slac.stanford.edu/pubs/beamline/

Rapid publication journals with section devoted to particlephysics

Chinese Physics LettersEurophysics LettersPhysical Review LettersPis’ma v Zhurnal Eksperimental’nyi i Teoreticheskii Fiz-ika (JETP Letters)

Review journalsAnnals of Physics (N.Y.)Annual Review of Nuclear and Particle SciencePhysics ReportsReports on Progress in PhysicsReviews of Modern Physics

Other journals with frequent articles on particle physics orrelated subjects

Acta Physica PolonicaAmerican Journal of PhysicsAstroparticle PhysicsAstrophysical JournalNatureNew ScientistPhysics Today (AIP)Physics World (IOP)Progress of Theoretical Physics (Japan)ScienceScience NewsScientific American

III. CONFERENCE PROCEEDINGS

The latest biennial ‘‘Rochester’’ Conference in High En-ergy Physics was held in Amsterdam in July 2002; the pre-vious one was in Osaka in 2000.2 In odd-numbered yearsthere occur both the International Symposium on Lepton andPhoton Interactions at High Energies, of which the most re-cent was in Rome,3 and the International Europhysics Con-ference on High Energy Physics, most recently held inBudapest.4 The locations of each of these conferences since1990 are summarized in Table I. A search of the SPIRESlisting at the SLAC Library~see Sec. VII!is the easiest wayto find the corresponding Proceedings.

2. XXX International Conference on High Energy Physics„ICHEP2000…, Osaka, Japan, 27 July–2 August 2000, edited by C. S. Lim andT. Yamanaka~World Scientific, Singapore, 2001!. ~I!

3. 20th International Symposium on Lepton and Photon Interactionsat High Energies ~Lepton Photon 01!, Rome, Italy, 23–28 July 2001,edited by J. Lee-Franzini, P. Franzini, and F. Bossi~World Scientific,Singapore, 2002!. ~I!

4. International Europhysics Conference on High Energy Physics„High Energy Physics 2001: Proceedings…, Budapest, Hungary, July2001, edited by D. Horvath, P. Levai, and A. Patkos~JHEP, 2001!.~I!

Table I. Locales of major high energy physics conferences since 1990.~1!International Conference on High Energy Physics~‘‘Rochester’’ Confer-ence!;~2! International Symposium on Lepton and Photon Interactions atHigh Energies;~3! International Europhysics Conference on High EnergyPhysics.

~1! ~2! ~3!

Year Location Year Location Year Location

1990 Singapore 1991 Geneva 1991 Geneva1992 Dallas, TX 1993 Ithaca, NY 1993 Marseille1994 Glasgow 1995 Beijing 1995 Brussels1996 Warsaw 1997 Hamburg 1997 Jerusalem1998 Vancouver 1999 Stanford 1999 Tampere, Finl.2000 Osaka 2001 Rome 2001 Budapest2002 Amsterdam 2003 Fermilab 2003 Aachen

303 303Am. J. Phys., Vol. 71, No. 4, April 2003 Jonathan L. Rosner

IV. TEXTBOOKS, EXPOSITIONS, AND REVIEWARTICLES

This section indicates textbooks and articles at the inter-mediate or advanced level. For popularizations at the non-specialist’s level, see Sec. VI.

A. Textbooks

1. Quantum field theory

5. Quantum Field Theory, C. Itzykson and J. B. Zuber~McGraw-Hill,New York, 1980!. ~A!

6. Gauge Theory of Elementary Particle Physics, T. P. Cheng and L. F.Li ~Clarendon, Oxford, 1984!. ~A!

7. Field Theory: A Modern Primer , 2nd ed., P. Ramond, Frontiers ofPhysics74, 1–329~1989!.~A!

8. Quantum Field Theory, L. S. Brown ~Cambridge U. P., Cambridge,MA, 1992!. ~A!

9. Quantum Field Theory, F. Mandl and G. Shaw, Revised edition~Wiley-Interscience, Chichester, UK, 1993!. ~I!

10. An Introduction to Quantum Field Theory , M. E. Peskin and D. V.Schroeder~Addison-Wesley, Reading, MA, 1995!. ~A!

11. The Quantum Theory of Fields. Vol. 1: Foundations, S. Weinberg~Cambridge U. P., Cambridge, MA, 1995!. ~A!

12. The Quantum Theory of Fields. Vol. 2: Modern Applications, S.Weinberg~Cambridge U. P., Cambridge, MA, 1996!. ~A!

13. Quantum Field Theory, 2nd ed., L. H. Ryder~Cambridge U. P., Cam-bridge, MA, 1996!. ~I!

2. Standard model (electroweak and strong interactions)

14. Leptons and Quarks, L. B. Okun’ ~North-Holland, Amsterdam,1982!.~I!

15. Quarks and Leptons: An Introductory Course in Modern ParticlePhysics, F. Halzen and A. D. Martin~Wiley, New York, 1984!.~I!

16. Weak Interactions and Modern Particle Theory, H. Georgi~Benjamin/Cummings, Menlo Park, CA, 1985!. ~I!

17. Dynamics of the Standard Model, J. F. Donoghue, E. Golowich, andB. R. Holstein, Cambridge Monogr. Part. Phys. Nucl. Phys. Cosmol.2,1–540~1992!.~I!

18. Gauge Theories of the Strong, Weak, and Electromagnetic Inter-actions, C. Quigg ~Addison-Wesley, New York, 1997!. ~I!

19. An Introduction to the Standard Model of Particle Physics, W. N.Cottingham and D. A. Greenwood~Cambridge U. P., Cambridge, MA,1998!.~I!

3. CP violation

20. CP Violation, edited by C. Jarlskog~World Scientific, Singapore,1989!.~I!

21. CP Violation, I. I. Y. Bigi and A. I. Sanda, Cambridge Monogr. Part.Phys. Nucl. Phys. Cosmol.9, 1–382~2000!.~I!

22. CP Violation, G. C. Branco, L. Lavoura, and J. P. Silva~ClarendonPress, Oxford, 1999!. ~I!

4. Elementary particle phenomenology

23. An Introduction to Quarks and Partons, F. E. Close~AcademicPress, London, 1979!. ~I!

24. Concepts of Particle Physics, K. Gottfried and V. F. Weisskopf~Ox-ford U. P., Cambridge, MA, Oxford, 1984!, Vol. 1; ~1986!Vol. 2!. ~I!

25. The Experimental Foundations of Particle Physics, R. N. Cahn andG. Goldhaber~Cambridge U. P., Cambridge, MA, 1989!. ~I!

26. Collider Physics, V. D. Barger and R. J. N. Phillips, updated edition~Addison-Wesley, Redwood City, CA, 1997!. ~I!

27. Introduction to High-Energy Physics, 4th ed., D. H. Perkins~Cam-bridge U. P., Cambridge, MA, 2000!. ~I!

5. Symmetries

28. The Eightfold Way, M. Gell-Mann and Y. Ne’eman~Benjamin, NewYork, 1964!.~I!

29. Lie Groups, Lie Algebras, and Some of Their Applications, R.Gilmore ~Wiley-Interscience, New York, 1974!. ~I!

30. Semi-Simple Lie Algebras and Their Representations, R. N. Cahn~Benjamin/Cummings, New York, 1984!. ~I! See also:http://phyweb.lbl.gov/ ;rncahn/www/liealgebras/book.html.

31. Lie Algebras in Particle Physics, 2nd ed., H. Georgi~Perseus Books,1999!.~I!

6. Higgs boson(s)

32. The Higgs Hunter’s Guide, J. F. Gunion, H. E. Haber, G. Kane, andS. Dawson~Addison-Wesley, Redwood City, CA, 1990!. ~I!

33. Perspectives on Higgs Physics, edited by G. L. Kane~World Scien-tific, Singapore, 1993!. ~I!

34. Perspectives on Higgs Physics II, edited by G. L. Kane~World Sci-entific, Singapore, 1997!. ~I!

7. Neutrinos

35. Solar Neutrinos: The First Thirty Years, edited by J. N. Bahcallet al. ~Frontiers in Physics, 2002!. ~I!

8. Supersymmetry

36. Supersymmetry and Supergravity, 2nd ed., J. Wess and J. Bagger~Princeton U. P., Cambridge, MA, Princeton, NJ, 1992!. ~A!

37. Perspectives on Supersymmetry, edited by G. L. Kane~World Sci-entific, Singapore, 1998!. ~I!

38. The Quantum Theory of Fields. Vol. 3: Supersymmetry, S. Wein-berg ~Cambridge U. P., Cambridge, MA, 2000!. ~A!

9. Beyond the standard model

39. Electroweak Symmetry Breaking and New Physics at the TeVScale, edited by T. Barklowet al. ~World Scientific, Singapore, 1996!.~A!

40. Journeys Beyond the Standard Model, P. Ramond~Perseus Books,Reading, MA, 1999!. ~I!

10. String theory

41. Superstring Theory. Vol. 1: Introduction, M. B. Green, J. H.Schwarz, and E. Witten~Cambridge U. P., Cambridge, MA, 1987!. ~A!

42. Superstring Theory. Vol. 2: Loop Amplitudes, Anomalies, and Phe-nomenology, M. B. Green, J. H. Schwarz, and E. Witten~CambridgeU. P., Cambridge, MA, 1987!. ~A!

43. String Theory. Vol. 1: An Introduction to the Bosonic String, J.Polchinski~Cambridge U. P., Cambridge, MA, 1998!. ~A!

44. String Theory. Vol. 2: Superstring Theory and Beyond, J. Polchin-ski ~Cambridge U. P., Cambridge, MA, 1998!. ~A!

B. Expositions „summer school lectures, collections ofarticles…

A conference on kaon physics was held at the Universityof Chicago in 1999 as part of a series. A volume of articlesbased on the conference gives an overview of the field.45

Regular summer schools in particle physics are organizedin several locales, including Boulder~Colorado!, Carge`se~Corsica!, CERN, Erice~Sicily!, and SLAC~Stanford!. Thetopics typically vary from year to year but there are fre-quently lectures on various aspects of the Standard Model~see, e.g., the lectures on CP violation by Nir46 and the over-view by Rosner1!.

304 304Am. J. Phys., Vol. 71, No. 4, April 2003 Jonathan L. Rosner

The Theoretical Advanced Study Institute~TASI! at theUniversity of Colorado was devoted in June of 2000 to flavorphysics, a major aspect of the standard model, and the pro-ceedings also contain various aspects of proposed physicsbeyond the standard model.47 For specific reviews given atsummer schools, see the section on Reviews, below.

45. Kaon Physics, edited by J. L. Rosner and B. Winstein~University ofChicago Press, Chicago, 2001!. ~I!

46. ‘‘CP violation in and Beyond the Standard Model,’’ Y. Nir, Lecturesgiven at 27th SLAC Summer Institute on Particle Physics: CP Viola-tion in and Beyond the Standard Model~SSI 99!, Stanford, California,7–16 July 1999, Institute for Advanced Study report IASSNS-HEP-99-96, hep-ph/9911321.~A!

47. TASI-2000: Flavor Physics for the Millennium, edited by J. L. Ros-ner ~World Scientific, Singapore, 2001!. ~I!

C. Review articles

A number of review articles will be referred to in the nar-rative of the Standard Model and its extensions~Secs.X–XIII!. These include the following:

1. Gauge theories

48. ‘‘Gauge Theories,’’ E. S. Abers and B. W. Lee, Phys. Rep.9, 1–141~1973!.~I!

2. Standard Model

In addition to Rosner~2001!,1 see

49. ‘‘The Electroweak Theory,’’ C. Quigg, in Ref. 47, pp. 3–67.

3. Hadron spectra and quarks

50. ‘‘Charm and Beyond,’’ T. Appelquist, R. M. Barnett, and K. D. Lane,Annu. Rev. Nucl. Part. Sci.28, 387~1978!.~I!

51. ‘‘Charmonium and Gluons: Basic Experimental Facts and TheoreticalIntroduction,’’ V. A. Novikov et al., Phys. Rep.41, 1–133~1978!.~I!

52. ‘‘Hadron Spectra and Quarks,’’ S. Gasiorowicz and J. L. Rosner, Am.J. Phys.49, 954–984~1981!.~I!

53. ‘‘Heavy Quark Systems,’’ W. Kwong, C. Quigg, and J. L. Rosner,Annu. Rev. Nucl. Part. Sci.37, 325–382~1987!.~I!

54. ‘‘Upsilon Spectroscopy,’’ W. Buchmu¨ller and S. Cooper, Adv. Ser. Di-rect. High Energy Phys.1, 412–487~1988!.~I!

55. ‘‘Heavy Quark Symmetry,’’ N. Isgur and M. B. Wise, Adv. Ser. Direct.High Energy Phys.10, 549–572~1992!.~I!

4. Group theory

56. ‘‘Group Theory for Unified Model Building,’’ R. Slansky, Phys. Rep.79, 1–128~1981!.~I!

5. Neutrino physics

Massive neutrinos and neutrino oscillations:

57. ‘‘Massive Neutrinos and Neutrino Oscillations,’’ S. M. Bilenky and S.T. Petcov, Rev. Mod. Phys.59, 671–754~1987!.~I!

58. ‘‘Neutrino Mass, Mixing, and Oscillation,’’ B. Kayser, in Ref. 47, pp.625–650; ‘‘Neutrino Mass, Mixing, and Flavor Change,’’ B. Kayser,hep-ph/0211134, to appear inNeutrino Mass, edited by G. Altarelliand K. Winter~Springer Tracts in Modern Physics, 2002!. ~I!

59. ‘‘Oscillations of Atmospheric Neutrinos,’’ C. K. Jung, T. Kajita, T.Mann, and C. McGrew, Annu. Rev. Nucl. Part. Sci.51, 451–488~2001!.~I!

60. See the web page of John N. Bahcall:http://www.sns.ias.edu/ ;jnb/ for a list of review articles as well asup-to-the-minute information on neutrino oscillation parameters.

Precision electroweak measurements using neutrinos:

61. ‘‘Precision Measurements with High Energy Neutrino Beams,’’ J. M.Conrad, M. H. Shaevitz, and T. Bolton, Rev. Mod. Phys.70, 1341–1392 ~1998!.~I!

6. Supersymmetry

62. ‘‘A Supersymmetry Primer,’’ S. P. Martin, inPerspectives on Super-symmetry II, edited by G. L. Kane~World Scientific, Singapore,1997!, pp. 1–98.~I! A current version may be found athttp://zippy.physics.niu.edu/primer.shtml

63. ‘‘Report of the Beyond the MSSM Subgroup for the Tevatron Run IISUSY / Higgs Workshop,’’ to be published in the proceedings of Phys-ics at Run II: Workshop on Supersymmetry/Higgs~Summary Meeting,Batavia, IL, 19–21 Nov. 1998!, preprint hep-ph/0006162~unpub-lished!.~A!

64. ‘‘Report of the SUGRA Working Group for Run II of the Tevatron,’’ S.Abel et al., to be published in the proceedings of Physics at Run II:Workshop on Supersymmetry / Higgs~Summary Meeting, Batavia, IL,19–21 Nov. 1998!, preprint hep-ph/0003154~unpublished!. ~A!

65. ‘‘Low-Scale and Gauge-Mediated Supersymmetry Breaking at the Fer-milab Tevatron Run II,’’ R. Culbertsonet al., Fermilab reportFERMILAB-PUB-00-251-T, hep-ph/0008070~unpublished!. ~A!

66. ‘‘The Snowmass Points and Slopes: Benchmarks for SUSY Searches,’’B. C. Allanachet al., presented at APS/DPF/DPB Summer Study onthe Future of Particle Physics~Snowmass 2001!, Snowmass, Colorado,30 June–21 July 2001, Eur. Phys. J. C25, 113–123~2002!.~A!

67. ‘‘TASI Lectures: Weak Scale Supersymmetry—a Top-MotivatedBottom-Up Approach,’’ G. L. Kane, preprint hep-ph/0202185~unpub-lished!.~I!

68. ‘‘Supersymmetry, Supergravity, and Particle Physics,’’ H. P. Nilles,Phys. Rep.110, 1–162~1984!.~I!

69. ‘‘The Search for Supersymmetry: Probing Physics Beyond the Stan-dard Model,’’ H. E. Haber and G. L. Kane, Phys. Rep.117, 75–263~1985!.~I!

70. ‘‘Introducing Supersymmetry,’’ M. F. Sohnius, Phys. Rep.128, 39–204 ~1986!.~I!

7. Extended gauge theories

71. ‘‘Low-Energy Phenomenology of Superstring Inspired E6 Models,’’ J.L. Hewett and T. G. Rizzo, Phys. Rep.183, 193–381~1989!.~A!

8. Atomic parity violation

72. ‘‘A Bibliography of Atomic Parity Violation and Electric Dipole Mo-ment Experiments,’’ C. E. Wieman, in Ref. 47, pp. 373–375.~I!

9. Particle properties and general lore

A wide variety of mini-reviews of various aspects of theStandard Model may be found in the Review of ParticlePhysics published by the Particle Data Group:

73. ‘‘Review of Particle Physics,’’ K. Hagiwaraet al. ~Particle DataGroup!, Phys. Rev. D66, 010001~2002!.~I!

D. Other Resource Letters

74. ‘‘Resource Letter WI-1: Weak Interactions,’’ B. R. Holstein, Am. J.Phys.45, 1033–1039~1977!.~E–A!

75. ‘‘Resource Letter NP-1: New Particles,’’ Jonathan L. Rosner, Am. J.Phys.48, 90–103~1980!.~Particles with charmed and beauty quarks.!~E–A!

76. ‘‘Resource Letter SP-2: Symmetry and Group Theory in Physics,’’ J.Rosen, Am. J. Phys.49, 304–319~1981!.~E–A!

77. ‘‘Resource Letter Q-1: Quarks,’’ O. W. Greenberg, Am. J. Phys.50,1074– 1089~1982!.~E–A!

78. ‘‘Resource Letter CPP-1: Cosmology and Particle Physics,’’ D. Lind-ley, E. W. Kolb, and D. N. Schramm, Am. J. Phys.56, 492–501~1988!.~E–A!

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79. ‘‘Resource Letter GI-1: Gauge Invariance,’’ T. P. Cheng and L. F. Li,Am. J. Phys.56, 586–600~1988!.~E–A!

80. ‘‘Resource Letter HEPP-1: History of Elementary Particle Physics,’’ R.C. Hovis and H. Kragh, Am. J. Phys.59, 779–807~1991!.~E–A!

81. ‘‘Quantum Chromodynamics,’’ A. S. Kronfeld and C. Quigg, in prepa-ration. ~E–A!

V. HISTORICAL REFERENCES

A symposium on the history of Symmetries in Physicsfrom 1600 to 198082 contains many informative articles. Fora series of conferences on the history of particle physics,culminating in the rise of the Standard Model, see Refs. 83–85. The history of quantum electrodynamics is detailed inRef. 86, while Pais87 has chronicled the development of par-ticle physics with particular emphasis on its earlier aspects. Areview of some later developments is given in Ref. 88. Per-sonal memoirs include those of a theorist with close ties toexperiment~Sam B. Treiman89! and a Nobel-prize-winningexperimentalist~Jack Steinberger90!. A collection of articleson supersymmetry with a historical flavor is based on a re-cent symposium.91 Two excellent accounts of experimentalhigh energy physics by P. Galison are Refs. 92 and 93.

82. First International Meeting on the History of Scientific Ideas, St.Feliu de Guixols, Catalonia, Spain, Sept. 20–26, 1983, edited by M. G.Doncel, A. Hermann, L. Michel, and A. Pais~Barcelona, AutonomaUniv., Phys. Dept., 1987!. ~I!

83. The Birth of Particle Physics. Proceedings, International Sympo-sium, Batavia, USA, May 28–31, 1980, edited by L. M. Brown andL. Hoddeson~Cambridge U. P., Cambridge, MA, 1983!. ~I!

84. Pions to Quarks: Particle Physics in the 1950s. Proceedings, 2ndInternational Symposium on the History of Particle Physics, Bata-via, USA, May 1–4, 1985, edited by L. M. Brown, L. Hoddeson, andM. Dresden~Cambridge U. P., Cambridge, MA, 1989!. ~I!

85. The Rise of the Standard Model: Particle Physics in the 1960s and1970s, edited by L. Hoddeson, L. Brown, M. Riordan, and M. Dres-den, based on 3rd International Symposium on the History of ParticlePhysics: The Rise of the Standard Model, Stanford, CA, 24–27 June1992 ~Cambridge U. P., Cambridge, MA, 1997!. ~I!

86. QED and the Men Who Made It: Dyson, Feynman, Schwinger,and Tomonaga, S. S. Schweber~Princeton University Press, 1994!. ~I!

87. Inward Bound, A. Pais~Clarendon Press, Oxford, 1986!. ~I!88. ‘‘Elementary Particle Physics in the Second Half of the 20th Century,’’

V. L. Fitch and J. L. Rosner, inTwentieth Century Physics, edited byL. M. Brown, A. Pais, and B. Pippard, Vol. 2, pp. 635–794~IOP,Philadelphia, 1994!. ~I!

89. ‘‘A Life in Particle Physics,’’ S. Treiman, Ann. Rev. Nucl. Part. Sci.46, 1–30~1996!.~E!

90. ‘‘Early Particles,’’ J. Steinberger, Annu. Rev. Nucl. Part. Sci.47, xiii–xlii ~1997!.~E!

91. The Supersymmetric World: The Beginning of the Theory, editedby G. L. Kane and M. Shifman~World Scientific, Singapore, 2000!.~A!

91. How Experiments End, P. Galison~Univ. of Chicago Press, 1987!. ~I!93. Image and Logic: A Material Culture of Microphysics, P. Galison

~Univ. of Chicago Press, Chicago, 1997!. ~I!

VI. POPULAR LITERATURE

A. Books

For descriptions of particle theory in a cosmological con-text see Refs. 94, 95. A well-written account of the experi-ments that led to the idea of quarks being taken seriously isgiven in Ref. 96. The goals of particle theory are described inRefs. 97–99, while Refs. 100, 101 give the case for a fullyunified theory. The ongoing search for the Higgs particle andmany other efforts in particle physics are treated by Ref. 102.Gordon Fraser, the former editor of theCERN Courier, has

written or edited several fine books on particle physics aimedat general audiences.103–106 One recent popular book onquantum mechanics has been written by Sam Treiman.107

Many fine popularizations have been written by Richard P.Feynman, including his book on quantum electrodynamics108

and his Dirac Memorial Lecture, jointly in a volume withthat by Steven Weinberg.109

94. The First Three Minutes: a Modern View of the Origin of theUniverse, S. Weinberg~Basic Books, New York, 1977!. ~I!

95. The Cosmic Code: Quantum Physics as the Language of Nature,H. R. Pagels~Simon and Schuster, New York, 1982!. ~E!

96. The Hunting of the Quark: A True Story of Modern Physics,Michael Riordan~Simon and Schuster, New York, 1987!. ~E!

97. Longing for the Harmonies: Themes and Variations from ModernPhysics, F. Wilczek and B. Devine~Norton, New York, 1988!. ~E!

98. The Particle Garden, G. Kane ~Addison-Wesley, Helix Books, NewYork, 1995!.~E!

99. In Search of the Ultimate Building Blocks, G. ’t Hooft ~CambridgeU. P., Cambridge, MA, 1997!. ~E!

100. The Elegant Universe: Superstrings, Hidden Dimensions, and theQuest of the Ultimate Theory, B. R. Greene~Norton, New York,1999!.~E!

101. Dreams of a Final Theory: The Search for the Fundamental Lawsof Nature, S. Weinberg~Pantheon Books, New York, 1992!. ~E!

102. The God Particle: If the Universe is the Answer, What is theQuestion?, L. M. Lederman and D. Teresi~Houghton Mifflin, Bos-ton, MA, 1993!. ~E!

103. The Search for Infinity: Solving the Mysteries of the Universe, G.Fraser, E. Lillesto” l, and I. Selleva˚g ~Facts on File, New York, 1995!.~E!

104. The Quark Machines: How Europe Fought the Particle PhysicsWar , G. Fraser~Institute of Physics, Bristol and Philadelphia, 1997!.~E!

105. The Particle Century, edited by G. Fraser~Institute of Physics, Bris-tol and Philadelphia, 1998!. ~E!

106. Antimatter: The Ultimate Mirror , G. Fraser~Cambridge Univ.Press, 2000!.~E!

107. The Odd Quantum, S. Treiman~Princeton Univ. Press, Princeton,NJ, 1999!.~E!

108. QED: The Strange Theory of Light and Matter, R. P. Feynman~Princeton Univ. Press, Princeton, NJ, 1985!. ~E!

109. Elementary Particles and the Laws of Physics: The 1986 P. A. M.Dirac Memorial Lectures, R. P. Feynman and S. Weinberg~Cam-bridge U. P., Cambridge, MA, 1987!. ~I!

B. Articles

Instructive popular articles~in more or less chronologicalorder! include ones by Lederman on the discovery of theUpsilon particle ~the first evidence for theb quark!,110

’t Hooft on gauge theories,111 Wilczek112 and Quinn andWitherell113 on matter-antimatter asymmetry, Georgi onquark-lepton and strong-electroweak unification,114

Weinberg,115 Loseccoet al.,116 and Langacker117 on protondecay, Quigg on elementary particles and forces,118 Haberand Kane on supersymmetry,119 Veltman on the Higgsboson,120 Krauss on dark matter in the Universe,121 Green122

and Duff123 on string theory, Rees on the Stanford LinearCollider,124 Bahcall on the solar neutrino problem,125 Myersand Picasso on the LEP Collider at CERN,126 Lederman onthe Fermilab Tevatron,127 Feldman and Steinberger on mea-surements at LEP and SLC suggesting the existence of threefamilies of quarks and leptons,128 Liss and Tipton on thediscovery of the top quark,129 Hogan et al. on supernovasurveys and the accelerating Universe,130 Kearnset al. ondetecting massive neutrinos,131 Weinberg on the goal of atruly unified theory132 ~see below for an Internet link on thisarticle!, Llewellyn Smith on the Large Hadron Collider,133

Caldwell and Kamionkowski,134 and Gibbs135 on the cosmic

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microwave background radiation, Ostriker and Steinhardt on‘‘dark energy,’’136 and Arkani-Hamedet al.137,138 on largeextra dimensions.The Economistcarries frequent and well-informed articles on progress in high energy physics~see,e.g., Ref. 139!. Shorter news articles appear regularly inNa-ture, Science, andScientific American.

110. ‘‘The Upsilon Particle,’’ L. M. Lederman, Sci. Am.239, 72–80~1978!.~E!

111. ‘‘Gauge Theories of the Forces Between Elementary Particles,’’ G.’t Hooft, Sci. Am. 242, 104–138~1980!.~E!

112. ‘‘The Cosmic Asymmetry Between Matter and Antimatter,’’ F. Wilc-zek, Sci. Am.243, 82–90~1980!.~E!

113. ‘‘The Asymmetry Between Matter and Antimatter,’’ H. R. Quinn andM. S. Witherell, Sci. Am.279, 76–81~1998!.~E!

114. ‘‘A Unified Theory of Elementary Particles and Forces,’’ H. Georgi,Sci. Am. 244, 48–63~1981!.~E!

115. ‘‘The Decay of the Proton,’’ S. Weinberg, Sci. Am.244, 64–75~1981!.~E!

116. ‘‘The Search for Proton Decay,’’ J. M. Losecco, F. Reines, and D.Sinclair, Sci. Am.252 ~6!, 54–62 ~1985!.

117. ‘‘Proton Decay,’’ P. Langacker, inProceedings: In celebration of thediscovery of the neutrino ~Benjamin Franklin Symposium, 29Apr–1 May 1992, Philadelphia, Pennsylvania!, edited by C. E. Laneand R. I. Steinberg~World Scientific, River Edge, NJ, 1993!, pp.129–150.~I!

118. ‘‘Elementary Particles and Forces,’’ C. Quigg, Sci. Am.252, 84–95~1985!.~E!

119. ‘‘Is Nature Supersymmetric?,’’ H. E. Haber and G. L. Kane, Sci. Am.254, 52–60 ~1986!.~E!

120. ‘‘The Higgs Boson,’’ M. J. G. Veltman, Sci. Am.255, 76–84~1986!.~E!

121. ‘‘Dark Matter in the Universe,’’ L. M. Krauss, Sci. Am.255, 58–68~1986!.~E!

122. ‘‘Superstrings,’’ M. B. Green, Sci. Am.255, 48–60~1986!.~E!123. ‘‘The Theory Formerly Known as Strings,’’ M. J. Duff, Sci. Am.278,

64–69~1998!.~E!124. ‘‘The Stanford Linear Collider,’’ J. R. Rees, Sci. Am.261, 58–65

~1989!.~E!125. ‘‘The Solar Neutrino Problem,’’ J. N. Bahcall, Sci. Am.262, 54–61

~1990!.~E!126. ‘‘The LEP Collider,’’ S. Myers and E. Picasso, Sci. Am.263, 54–61

~1990!.~E!127. ‘‘The Tevatron,’’ L. M. Lederman, Sci. Am.264, 48–55 ~1991!.~E!128. ‘‘The Number of Families of Matter,’’ G. Feldman and J. Steinberger,

Sci. Am. 264, 70–75~1991!.~E!129. ‘‘The Discovery of the Top Quark,’’ T. M. Liss and P. L. Tipton, Sci.

Am. 277, 54–59 ~1997!.~E! 125.130. ‘‘Surveying Space-Time with Supernovae,’’ C. J. Hogan, R. P. Kirsh-

ner, and N. B. Suntzeff, Sci. Am.280, 28–33 ~1999!.~E!131. ‘‘Detecting Massive Neutrinos,’’ E. Kearns, T. Kajita, and Y. Totsuka,

Sci. Am. 281, 64–71 ~1999!.~E!132. ‘‘A Unified Physics by 2050?,’’ S. Weinberg, Sci. Am.281, 68–75

~1999!.~E!

133. ‘‘The Large Hadron Collider,’’ C. H. Llewellyn Smith, Sci. Am.283,70–77~2000!.~E!

134. ‘‘Echoes from the Big Bang,’’ R. R. Caldwell and M. Kamionkowski,Sci. Am. 284, 38–43~2001!.~E!

135. ‘‘Ripples in Space–Time,’’ W. W. Gibbs, Sci. Am.286, 62–71~2002!.~E!

136. ‘‘The Quintessential Universe,’’ J. P. Ostriker and P. J. Steinhardt,Sci. Am. 284, 46–53 ~2001!.~E!

137. ‘‘The Universe’s Unseen Dimensions,’’ N. Arkani-Hamed, S. Di-mopoulos, and G. R. Dvali, Sci. Am.283, 62–69 ~2000!.~E!

138. ‘‘Large Extra Dimensions: A New Arena for Particle Physics,’’ N.Arkani- Hamed, S. Dimopoulos, and G. R. Dvali, Physics Today55,35–40~2002!.~I!

139. The Economist362 ~8254!, January 5, 2002: ‘‘With All Thy Getting,Get Understanding,’’ p. 12; ‘‘A Survey of the Universe,’’ pp. 47–58.

VII. INTERNET RESOURCES

A. Preprints

A comprehensive repository of preprints on experimentaland theoretical particle physics may be found athttp://arXiv.org/, including experimental papers at http://arXiv.org/archive/hep-ex , phenomenological pa-pers ~theory papers dealing with experiment! at http://arXiv.org/archive/hep-ph , and more abstracttheoretical papers athttp://arXiv.org/archive/hep-th. The SPIRES system at Stanford Linear AcceleratorCenter: http://www.slac.stanford.edu/spires/ lists a number of different categories, includingbooks, conferences, experiments, preprints~SPIRES HEP!,and even names and e-mail addresses of particle physicists.

B. Laboratories and accelerators

National and international high energy physics maintainextensive web pages with vast links to useful information.For a comprehensive listing, see http://www.nevis.columbia.edu/ ;quarknet/high_energy_physics_links.htm . Some examplesare given in Tables II and III.

The site http://physics.web.cern.ch/Physics/HEPWebSites.html contains a number oflinks to further web pages, including the CERN Large Had-ron Collider at http://lhc-new-homepage.web.cern.ch/lhc-new-homepage/ , the‘‘Particle Adventure’’ site http://particleadventure.org/particleadventure ofthe Particle Data Group at Lawrence Berkeley NationalLaboratory, andQuarknet, a network for high school science

Table II. Major accelerator-based HEP laboratories and their public web pages.

Laboratory Location Web address

Brookhaven Upton, New York, USA http://www.bnl.gov/world/Budker Inst. Novosibirsk, Russia http://www.inp.nsk.su/index.en.shtmlCERN Geneva, Switz. http://public.web.cern.ch/Public/Cornell Ithaca, New York, USA http://www.lns.cornell.eduDESY Hamburg, Germany http://www.desy.de/html/home/Fermilab Batavia, IL, USA http://www.fnal.gov/Frascati Frascati, Italy http://www.lnf.infn.it/IHEP Beijing, China http://www.ihep.ac.cn/IHEP Protvino, Russia http://www.ihep.su/KEK Tsukuba, Japan http://www.kek.jp/intra.htmlSLAC Stanford, Calif., USA http://www.slac.stanford.eduTJNAF Newport News, VA, USA http://www.jlab.org/

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teachers to involve them and their students in cutting-edgeresearch in particle physics at http://quarknet.fnal.gov/ . The IHEP laboratory in Russiahosts a chronology of particle physics discoveries:http://ontil.ihep.su/ ;ppds/discovery.html.

C. Popular article with extensive links

The Scientific American article on the future of particlephysics by Steven Weinberg132 appears on the web with avariety of links to other literature: http://www.sciam.com/issue.cfm?issueDate=Dec-99

VIII. NOBEL PRIZES RELATED TO THESTANDARD MODEL

Some contributions in the past 45 years related to the for-mulation of the Standard Model that have been recognizedby Nobel Prizes in Physics are summarized in Table IV.More information may be found on the web siteshttp://www.slac.stanford.edu/library/nobel/ andhttp://www.nobel.se/physics/laureates .Many additional prizes were awarded for instrumentation ordiscoveries crucial to our present understanding of the stan-dard model.

IX. SNAPSHOT OF THE STANDARD MODEL

A. Quarks and leptons

The major ingredients of the standard model have been inplace for some time, and can be gleaned from the populararticle by Quigg.118 The known building blocks of stronglyinteracting particles, thequarks,140–142and the fundamentalfermions lacking strong interactions, theleptons, are summa-rized in Table V. The quark masses quoted there73 are thosefor quarks probed at distances short compared with the char-acteristic size of strongly interacting particles. When re-garded as constituents of strongly interacting particles, how-ever, theu andd quarks act as quasi-particles with masses ofabout 0.3 GeV. The corresponding ‘‘constituent-quark’’masses ofs, c, and b are about 0.5, 1.5, and 4.9 GeV,respectively.52 ~For reviews of the spectroscopy of hadronscontaining the heavy quarksc and b, see Refs. 50, 51, 53,54.! The pattern of charge-changing weak transitions be-tween quarks with chargesQ52/3 and those with chargesQ521/3 is described by the 333 Cabibbo-Kobayashi-Maskawa,143,144or CKM matrix; for a review ofits properties, see Ref. 145.

The quarks and leptons in Table V fall into three ‘‘fami-lies.’’ For evidence that all the existing families~at leastthose containing light neutrinos! may have been discovered,see Ref. 128.

140. ‘‘A Schematic Model of Baryons and Mesons,’’ M. Gell-Mann, Phys.Lett. 8, 214–215~1964!.~I!

141. ‘‘An SU~3! Model for Strong Interaction Symmetry and its Breaking:1,’’ G. Zweig, CERN report 8182/TH 401, 1964~unpublished!. Re-printed inDevelopments in the Quark Theory of Hadrons, editedby D. B. Lichtenberg and S. P. Rosen~Hadronic Press, Nonantum,MA, 1981!, Vol. 1, pp. 22–101.~I!

142. ‘‘An SU~3! Model for Strong Interaction Symmetry and its Breaking:2,’’ G. Zweig, CERN report 8419/TH 412, 1964~unpublished!. Re-printed inDevelopments in the Quark Theory of Hadrons, editedby D. B. Lichtenberg and S. P. Rosen~Hadronic Press, Nonantum,MA, 1980!, Vol. 1, pp. 22–101.~I!

143. ‘‘Unitary Symmetry and Leptonic Decays,’’ N. Cabibbo, Phys. Rev.Lett. 10, 531– 532~1963!.~I!

144. ‘‘CP Violation in the Renormalizable Theory of Weak Interaction,’’M. Kobayashi and T. Maskawa, Prog. Theor. Phys.49, 652–657~1973!.~I!

Table III. Major non-accelerator laboratories and their public web pages.

Laboratory Location Web address

Gran Sasso Central Italy http://www.lngs.infn.it/Kamioka Western Japan http://www-sk.icrr.u-tokyo.ac.jp/Soudan Northern Minn. http://www.hep.umn.edu/soudan/Sudburyn Obs. Ontario http://www.sno.phy.queensu.ca/

Table IV. Nobel prizes in physics since 1957 related to the Standard Model.

Year Recipient~s! Subject

1957 T. D. Lee and C. N. Yang Parity violation1960 D. A. Glaser Bubble chamber1965 R. P. Feynman, J. S. Schwinger,

and S. I. Tomonaga Quantum electrodynamics1968 L. W. Alvarez Discovery of resonances1969 M. Gell-Mann Particle classification1976 B. Richter and S. C. C. Ting J/c discovery1979 S. L. Glashow, A. Salam,

and S. Weinberg Electroweak unification1980 J. W. Cronin and V. L. Fitch CP violation1982 K. G. Wilson Critical phenomena1984 C. Rubbia and W andZ discovery via

S. Van Der Meer SppS collider1988 L. M. Lederman, M. Schwartz, Discovery that

and J. Steinberger nmÞne

1990 J. I. Friedman, H. W. Kendall, Deep inelastic electronand R. E. Taylor scattering

1992 G. Charpak Particle detectors1995 M. L. Perl t lepton

F. Reines Neutrino detection1999 G. ’t Hooft and

M. J. G. Veltman Electroweak interactions2002 R. Davis and M. Koshiba Cosmic neutrinos

R. Giacconi Cosmic x-rays

Table V. The known quarks and leptons. Masses in GeV except whereindicated otherwise. Here and elsewherec51.

Quarks Leptons

Charge 2/3 Charge21/3 Charge21 Charge 0Mass Mass Mass Mass

u 0.0015–0.0045 d 0.005–0.0085 e 0.000511 ne ,3 eVc 1.0–1.4 s 0.085–0.155 m 0.106 nm ,190 keVt 174.365.1 b 4.0–4.5 t 1.777 nt ,18.2 MeV

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145. ‘‘The Cabibbo–Kobayashi–Maskawa Quark-Mixing Matrix,’’ F. J.Gilman, K. Kleinknecht, and B. Renk, inReview of Particle Phys-ics, K. Hagiwaraet al.,73 pp. 113–119.

B. Gauge theories

A theory of particles and their interactions permitting ar-bitrary changes of phase in the particle’s quantum mechani-cal state is anAbelian local gauge theorysuch as electro-magnetism. The term ‘‘Abelian’’ indicates that gauge~phase!transformations at a given space–time point commute withone another, while ‘‘local’’ stands for the freedom to makeseparate gauge transformations at each space–time point.The name ‘‘gauge’’ originated with Hermann Weyl.146

Gauge transformations may be generalized to those that donot commute with one another at a given space–time point.The first suchnon-Abeliangauge theory was proposed by C.N. Yang and R. L. Mills,147 who used it to describe the stronginteractions through self-interacting mesons of spin 1 carry-ing isosopic spin.

The review by Abers and Lee48 helped a generation ofphysicists to apply gauge theories to the electroweak andstrong interactions. An excellent introduction to the subjectat the intermediate graduate level is given by Quigg.18 Anarticle addressed to the lay reader has been written by’t Hooft.111A recent text148 provides a further introduction tothe subject.

146. ‘‘Electron and Gravitation@in German#,’’ H. Weyl, Z. Phys.56, 330–352 ~1929!, partially reprinted in Surveys in High Energy Phys.5,261–267~1986!.~A!

147. ‘‘Conservation of Isotopic Spin and Isotopic Gauge Invariance,’’ C.N. Yang and R. L. Mills, Phys. Rev.96, 191–195~1954!. ~A! Seealso Cambridge University Dissertation, R. Shaw, 1954~unpub-lished!.

148. The Dawning of Gauge Theory, L. O’Raifeartaigh~Princeton Uni-versity Press, Princeton, NJ, 1997!. ~I!

C. Color and quantum chromodynamics

The quarks are distinguished from the leptons by possess-ing a three-fold charge known as ‘‘color’’ that enables themto interact strongly with one another.149–151We also speak ofquark and lepton ‘‘flavor’’ when distinguishing the particlesin Table V from one another. The evidence for color comesfrom several quarters.

1. Quark statistics.TheD11, a low-lying excited state ofthe nucleon, can be represented in the quark model asuuu,so it is totally symmetric in flavor. It has spinJ53/2, atotally symmetric combination of the threeJ51/2 quarkspins. As a ground state, its spatial wave function should besymmetric as well. While a state composed of fermionsshould be totallyantisymmetricunder the interchange of anytwo fermions, the state described so far is totallysymmetricunder the product of flavor, spin, and space interchanges.Color introduces an additional degree of freedom underwhich the interchange of two quarks can produce a minussign.

2. Electron-positron annihilation to hadrons.The chargesof all quarks that can be produced in pairs at a given center-of-mass energy is measured by the ratioR[s(e1e2

→hadrons)/s(e1e2→m1m2)5( iQi2 , where Qi is the

charge of quarki in units of ueu. Measurements73 indicate

values ofR in various energy ranges consistent withNc53~with a small positive correction associated with the stronginteractions of the quarks!.

3. Neutral pion decay.Thep0 decay rate is governed by aquark loop diagram in which two photons are radiated by thequarks in p05(uu2dd)/A2. The predicted rate isG(p0

→gg)57.6S2 eV, whereS5Nc(Qu22Qd

2)5Nc/3. The ex-perimental rate is 7.860.6 eV, in accord with experiment ifS51 andNc53.

4. Triality. Quark composites appear only in multiples ofthree. Baryons are composed ofqqq, while mesons areqq~with total quark number zero!. This is compatible with ourcurrent understanding of QCD, in which only color-singletstates can appear in the spectrum.

A crucial feature of the QCD theory of strong interactionsis its ‘‘asymptotic freedom,’’ a weakening interactionstrength at short distances permitting the interpretation ofdeep inelastic scattering experiments96,152,153 in terms ofquarks. This property was found to be characteristic of non-Abelian gauge theories such as color SU~3! by Gross andWilczek154–156and by Politzer.157,158The result was obtainedearlier for the gauge group SU~2! by Khriplovich159 ~see alsoRef. 160!, but its significance for a strong-interaction theorywas not realized then.

Direct evidence for the quanta of QCD, the gluons, wasfirst presented in 1979 on the basis of extra ‘‘jets’’ of par-ticles produced in electron–positron annihilations to hadrons.Normally one sees two clusters of energy associated with thefragmentation of each quark ine1e2→qq into hadrons.However, in some fraction of events an extra jet was seen,corresponding to the radiation of a gluon by one of thequarks. For a popular history of this discovery, containingfurther references, see Ref. 96.

The transformations that take one color of quark into an-other are those of the group SU~3!. This group is calledSU~3!color to distinguish it from the SU~3!flavor associatedwith the quarksu, d, ands.

149. ‘‘Spin and Unitary Spin Independence in a Paraquark Model of Bary-ons and Mesons,’’ O. W. Greenberg, Phys. Rev. Lett.13, 598–602~1964!.~I!

150. Y. Nambu, ‘‘A Systematics of Hadrons in Subnuclear Physics,’’ inPreludes in Theoretical Physics in Honor of V. F. Weisskopf, ed-ited by A. De-Shalit, H. Feshbach, and L. Van Hove~North-Holland,Amsterdam and Wiley, New York, 1966!, pp. 133–42.~A!

151. ‘‘Advantages of the Color Octet Gluon Picture,’’ H. Fritzsch, M.Gell-Mann, and H. Leutwyler, Phys. Lett.47B, 365–368~1973!.~I!

152. ‘‘High-Energy Inelasticep Scattering at 6° and 10°,’’ E. D. Bloomet al., Phys. Rev. Lett.23, 930–934~1969!.~I!

153. ‘‘Observed Behavior of Highly Inelastic Electron–Proton Scatter-ing,’’ M. Breidenbachet al., Phys. Rev. Lett.23, 935–939~1969!.~I!

154. ‘‘Ultraviolet Behavior of Non-Abelian Gauge Theories,’’ D. J. Grossand F. Wilczek, Phys. Rev. Lett.30, 1343–1346~1973!.~A!

155. ‘‘Asymptotically Free Gauge Theories. I,’’ D. J. Gross and F. Wil-czek, Phys. Rev. D8, 3633–3652~1973!.~A!

156. ‘‘Asymptotically Free Gauge Theories. 2,’’ D. J. Gross and F. Wil-czek, Phys. Rev. D9, 980–993~1974!.~A!

157. ‘‘Reliable Perturbative Results for Strong Interactions?,’’ H. DavidPolitzer, Phys. Rev. Lett.30, 1346–1349~1973!.~A!

158. ‘‘Asymptotic Freedom: An Approach to Strong Interactions,’’ H.David Politzer, Phys. Rep.14, 129–180~1974!.~A!

159. ‘‘Green’s Functions in Theories with Non-Abelian Gauge Group,’’ I.B. Khriplovich, Yad. Fiz.10, 409–424~1969! @Sov. J. Nucl. Phys.10, 235–242~1969!#.~A!

160. ‘‘Renormalization of Gauge Theories,’’ G. ’t Hooft, in Ref. 85, pp.179–198.~A!

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D. Weak interactions

The electromagnetic interaction is described in terms ofphoton exchange. The quantum electrodynamics of photonsand electrons initially encountered divergent quantitiestamed in the 1940s throughrenormalization, leading to suc-cessful estimates of the anomalous magnetic moment of theelectron and the Lamb shift in hydrogen.86 By contrast, theweak interactions as formulated up to the mid-1960s in-volved the pointlike interactions of two currents. This inter-action is very singular and cannot be renormalized. The weakcurrents in this theory were purely charge-changing. As aresult of work by Gershtein and Zel’dovich~who suggestedthat the weak vector current is of universal strength!,161 Leeand Yang,162–164Feynman and Gell-Mann,165 and Sudarshanand Marshak,166 the weak currents were identified as having~vector!–~axial! or ‘‘V –A’’ form.

161. ‘‘Meson Corrections in the Theory of Beta Decay,’’ S. S. Gershteinand Ia. B. Zel’dovich, Zh. E´ ksp. Teor. Fiz.29, 698–699~1955! @Sov.Phys.—JETP2, 576–578~1956!#.~A!

162. ‘‘Question of Parity Conservation in Weak Interactions,’’ T. D. Leeand C. N. Yang, Phys. Rev.104, 254–258~1956!.~A!

163. ‘‘Parity Nonconservation and a Two Component Theory of the Neu-trino,’’ T. D. Lee and C. N. Yang, Phys. Rev.105, 1671–1675~1957!.~A!

164. ‘‘Remarks on Possible Noninvariance Under Time Reversal andCharge Conjugation,’’ T. D. Lee, R. Oehme, and C. N. Yang, Phys.Rev.106, 340– 345~1957!.~A!

165. ‘‘Theory of the Fermi Interaction,’’ R. P. Feynman and M. Gell-Mann, Phys. Rev.109, 193–198~1958!.~I!

166. ‘‘Chirality Invariance and the Universal Fermi Interaction,’’ E. C. G.Sudarshan and R. E. Marshak, Phys. Rev.109, 1860–1862~1958!.~A!

E. Electroweak unification

Yukawa167 and Klein168 proposed early boson-exchangemodels for the charge-changing weak interactions. Klein’smodel had self-interacting bosons, thus anticipating thetheory of Yang and Mills.147 Schwinger and others studiedsuch models in the 1950s, but Glashow169 realized that a newneutral heavy bosonZ, in addition to the massless photonand massive charged bosons, was needed to successfullyunify the weak and electromagnetic interactions. The use ofthe Higgs170–173 mechanism to break the electroweak sym-metry by Weinberg174 and Salam175 converted this phenom-enological theory into one suitable for higher-order calcula-tions.

The charge-changing weak currents could be viewed asmembers of an SU~2!algebra.176,143 However, the neutralmember of this multiplet could not be identified with electriccharge. ChargedW6 bosons couple only to left-handed fer-mions, while the photon couples to both left and right-handed fermions. Moreover, a theory with only photons andcharged weak bosons leads to unacceptable divergences inhigher-order processes.18 The neutral heavyZ boson can bearranged to cancel these divergences. It leads toneutral cur-rent interactions, in which~for example!an incident neutrinoscatters inelastically on a hadronic target without changingits charge. The discovery of neutral-current interactions ofneutrinos177–180and other manifestations of theZ strikinglyconfirmed the new theory.

A key stumbling block to the construction of an elec-troweak theory applying to the quarks known at the time (u,d, ands) was the presence offlavor-changing neutral cur-

rents. The hypothesis of a fourth ‘‘charmed’’ quarkc was anelegant way to avoid this problem.181 The charmed quarkalso was crucial in avoiding ‘‘anomalies,’’ effects due to tri-angle diagrams involving internal fermions and three exter-nal gauge bosons.182–184Evidence for charm was first foundin 1974 in the form of theJ/c particle,185,186a bound state of

c andc. An earlier Resource Letter75 deals with events lead-ing up to this discovery, as well as early evidence for the fifth(b) quark to be mentioned below. The whole topic of elec-troweak unification is dealt with at an intermediate level inseveral references mentioned earlier~e.g., Refs. 14, 18, 24!.

167. ‘‘On the Interaction of Elementary Particles,’’ H. Yukawa, Proc. Phys.Math. Soc. Japan17, 48– 57 ~1935!.~A!

168. ‘‘Sur la Theorie des Champs Associe´s ades Particules Charge´es,’’ O.Klein, in Les Nouvelles The´ories de la Physique, Paris, Inst. deCooperation Intellectuelle~1939!, pp. 81–98, translation ‘‘On theTheory of Charged Fields,’’ reprinted inOskar Klein MemorialLectures, Vol. 1, edited by G. Ekspong~World Scientific, Singapore,1991!, and in Surveys in High Energy Phys.5, 269–285~1986!.~A!

169. ‘‘Partial Symmetries of Weak Interactions,’’ S. L. Glashow, Nucl.Phys.22, 579–588~1961!.~A!

170. ‘‘Broken Symmetries, Massless Particles, and Gauge Fields,’’ P. W.Higgs, Phys. Lett.12, 132–133~1964!.~A!

171. ‘‘Broken Symmetries and the Masses of Gauge Bosons,’’ P. W. Higgs,Phys. Rev. Lett.13, 508–509~1964!.~A!

172. ‘‘Broken Symmetry and the Mass of Gauge Vector Mesons,’’ F. En-glert and R. Brout, Phys. Rev. Lett.13, 321–322~1964!.~A!

173. ‘‘Global Conservation Laws and Massless Particles,’’ G. S. Guralnik,C. R. Hagen, and T. W. B. Kibble, Phys. Rev. Lett.13, 585–587~1964!.~A!

174. ‘‘A Model of Leptons,’’ S. Weinberg, Phys. Rev. Lett.19, 1264–1266~1967!.~A!

175. ‘‘Weak and Electromagnetic Interactions,’’ A. Salam, inProceedingsof the Eighth Nobel Symposium, edited by N. Svartholm~Almqvistand Wiksell, Stockholm, 1968; Wiley, New York, 1978!, pp. 367–377. ~A!

176. ‘‘The Axial Vector Current in Beta Decay,’’ M. Gell-Mann and M.Levy, Nuovo Cim.16, 705–726~1960!.~I!

177. ‘‘Search for Elastic Muon Neutrino Electron Scattering,’’ F. J. Hasertet al., Phys. Lett.46B, 121–124~1973!.~I!

178. ‘‘Observation of Neutrino-Like Interactions Without Muon or Elec-tron in the Gargamelle Neutrino Experiment,’’ F. J. Hasertet al.,Phys. Lett.46B, 138–140~1973!.~I!

179. ‘‘Observation of Neutrino-Like Interactions Without Muon or Elec-tron in the Gargamelle Neutrino Experiment,’’ F. J. Hasertet al.,Nucl. Phys.B73, 1–22~1974!.~I!

180. ‘‘Observation of Muonless Neutrino Induced Inelastic Interactions,’’A. C. Benvenutiet al., Phys. Rev. Lett.32, 800–803~1974!.~I!

181. ‘‘Weak Interactions with Lepton–Hadron Symmetry,’’ S. L. Glashow,J. Ilipoulos, and L. Maiani, Phys. Rev. D2, 1285–1292~1970!.~I!

182. ‘‘An Anomaly Free Version of Weinberg’s Model,’’ C. Bouchiat, J.Iliopoulos, and P. Meyer, Phys. Lett.38B, 519–523~1972!.~I!

183. ‘‘Gauge Theories Without Anomalies,’’ H. Georgi and S. L. Glashow,Phys. Rev. D6, 429–431~1972!.~I!

184. ‘‘Effect of Anomalies on Quasi-Renormalizable Theories,’’ D. J.Gross and R. Jackiw, Phys. Rev. D6, 477–493~1972!.~A!

185. ‘‘Experimental Observation of a Heavy ParticleJ,’’ J. J. Aubertet al.,Phys. Rev. Lett.33, 1404–1406~1974!.~I!

186. ‘‘Discovery of a Narrow Resonance ine1e2 Annihilation,’’ J. E.Augustinet al., Phys. Rev. Lett.33, 1406–1408~1974!.~I!

F. CP violation

The symmetries of time reversal~T!, charge conjugation~C!, and space inversion or parity~P! have provided bothclues and puzzles in our understanding of the fundamentalinteractions. The realization that the charge-changing weakinteractions violated P andC maximally was central to theformulation of theV–A theory. The theory was constructedin 1957 to conserve the productCP, but the discovery in

310 310Am. J. Phys., Vol. 71, No. 4, April 2003 Jonathan L. Rosner

1964 of the long-lived neutral kaon’s decay to two pions(KL→pp)187 showed that evenCP was not conserved. In1973, Kobayashi and Maskawa~KM!144 proposed thatCPviolation in the neutral kaon system could be explained in amodel with three families of quarks. The quarks of the thirdfamily, now denoted byb for bottom andt for top, weresubsequently discovered in 1977188,189 and 1994,190–195 re-spectively. Popular articles on these discoveries include oneby Lederman110 and Liss and Tipton.129

An alternative theory ofCP violation in the kaon system,proposed by Wolfenstein,196 involved a ‘‘superweak’’CP-violating interaction mixingK0 andK0, which would lead toidentical CP violation inKL→p1p2 and KL→p0p0. Thediscovery that this was not so~see Refs. 197, 198 for themost recent published results, which are continually beingupdated in conference reports! disproved the superweaktheory and displayed a ‘‘direct’’ form of CP violation withmagnitude consistent with that predicted by the KM theory.

Decays of hadrons containingb quarks are further groundfor testing the KM hypothesis and for displaying evidencefor new physics beyond this ‘‘standard model’’ ofCP viola-tion. A meson containing ab quark will be known generi-cally as aB meson. Electron-positron colliders have beenconstructed at SLAC~Stanford, CA!199 and KEK ~Tsukuba,Japan!200 expressly to studyB mesons; others at DESY~Hamburg, Germany!and Cornell~Ithaca, NY!201 were for-tunate in having just the right energy to produceB mesons inpairs. The BaBar detector at SLAC and the Belle detector atKEK have already produced a series of major results onBdecays andCP violation.202,203 Studies of particles contain-ing b quarks also are expected to be an important part of thephysics program at the Fermilab Tevatron204 and the CERNLarge Hadron Collider~LHC!.205

187. ‘‘Evidence for the 2p Decay of theK20 Meson,’’ J. H. Christenson, J.

W. Cronin, V. L. Fitch, and R. Turlay, Phys. Rev. Lett.13, 138–140~1964!.~I!

188. ‘‘Observation of a Dimuon Resonance at 9.5 GeV in 400-GeVProton–Nucleus Collisions,’’ S. W. Herbet al., Phys. Rev. Lett.39,252–255~1977!.~I!

189. ‘‘Observation of Structure in theY Region,’’ W. R. Inneset al., Phys.Rev. Lett.39, 1240–1242, 1640~E! ~1977!.~I!

190. ‘‘Evidence for Top Quark Production inpp Collisions atAs51.8TeV,’’ CDF Collaboration, F. Abeet al., Phys. Rev. D50, 2966–3026~1994!.~I!

191. ‘‘Evidence for Top Quark Production inpp Collisions atAs51.8TeV,’’ CDF Collaboration, F. Abeet al., Phys. Rev. Lett.73, 225–231~1994!.~I!

192. ‘‘Observation of Top Quark Production inpp Collisions,’’ CDF Col-laboration, F. Abeet al., Phys. Rev. Lett.74, 2626–2631~1995!.~I!

193. ‘‘Search for the Top Quark inpp Collisions atAs51.8 TeV,’’ D0Collaboration, S. Abachiet al., Phys. Rev. Lett.72, 2138–2142~1994!.~I!

194. ‘‘Search for High Mass Top Quark Production inpp Collisions atAs51.8 TeV,’’ D0 Collaboration, S. Abachiet al., Phys. Rev. Lett.74, 2422–2426~1995!.~I!

195. ‘‘Observation of the Top Quark,’’ D0 Collaboration, S. Abachiet al.,Phys. Rev. Lett.74, 2632–2637~1995!.~I!

196. ‘‘Violation of CP Invariance and the Possibility of Very Weak Inter-actions,’’ L. Wolfenstein, Phys. Rev. Lett.13, 562–564~1964!.~I!

197. ‘‘Observation of Direct CP Violation inKS,L→pp Decays,’’ Fermi-lab KTeV Collaboration, A. Alavi-Haratiet al., Phys. Rev. Lett.83,22–27~1999!.~I! For a more recent reference see ‘‘Measurements ofDirect CP Violation, CPT Symmetry, and Other Parameters in theNeutral Kaon System,’’ A. Alavi-Haratiet al., preprint hep-ex/0208007, submitted to Phys. Rev. D.~I!

198. ‘‘A Precise Measurement of the Direct CP Violation Parameter Re

(e8/e), ’’ CERN NA48 Collaboration, A. Laiet al., Eur. Phys. J. C

22, 231–254~2001!.~I! For a more recent reference see ‘‘A PrecisionMeasurement of Direct CP Violation in the Decay of Neutral KaonsInto Two Pions,’’ J. R. Batleyet al., Phys. Lett. B544, 97–112~2002!.~I!

199. ‘‘The First Year of the BaBar Experiment at PEP-II,’’ BaBar Collabo-ration, B. Aubertet al., SLAC report SLAC-PUB-8539, contributedto 30th International Conference on High-Energy Physics~ICHEP2000!, Osaka, Japan, 27 Jul–2 Aug 2000, e-Print Archive: hep-ex/0012042.~I!

200. ‘‘KEKB Performance,’’ Belle Collaboration, presented by A. E.Bondar at Beauty-2000: 7th International Conference on B-Physics atHadron Machines, Sea of Galilee, Kibbutz Maagan, Israel, 13–18Sept. 2000, Nucl. Instr. Meth. A462, 139–145~2001!.~I!

201. ‘‘Review of Results from CESR and DORIS,’’ E. I. Shibata, inBe-yond the Standard Model: Proceedings, Ames, IA, Nov. 18–22,1988, edited by B.-L. Young~World Scientific, Singapore, 1988!, pp.38–59.~I!

202. ‘‘Measurement of the CP-violating Asymmetry Amplitude sin(2b),’’BaBar Collaboration, B. Aubertet al., Phys. Rev. Lett.89, 201802~2002!.~I!

203. ‘‘An Improved Measurement of Mixing-Induced CP Violation in theNeutralB Meson System,’’ Belle Collaboration, K. Abeet al., Phys.Rev. D66, 071102~R! ~2002!.~I!

204. ‘‘ B physics at the Tevatron: Run II and Beyond,’’ K. Anikeevet al.,proceedings of workshops at Fermilab, 23–25 Sept. 1999 and 24–26Feb. 2000, Fermilab preprint FERMILAB-PUB-01-197, hep-ph/0201071~unpublished!. ~I!

205. ‘‘The LHCb Project,’’ A. Schopper, Acta Phys. Pol.B32, 1769–1775~2001!.~I!’’

G. Dynamics of heavy quarks

With the discovery of the charmed~Sec. IX E!and beauty~Sec. IX F!quarks, a whole new laboratory emerged for thestudy of QCD. A bound state of a heavy quark and its anti-quark,cc or bb, is known asquarkonium, in analogy withpositronium, the bound state of a positron and an electron.~The top quark lives too short a time fort t bound states to beof much interest, though one can study some effects of thebinding.! Quarkonium states have been extensivelystudied,50,51,53,54with their spectroscopy and decays provid-ing useful information on QCD at various distance scales.

The states of light quarks bound to a single heavy quarkhave their own regularities. They are analogous to atoms inwhich the light quarks and gluons represent the ‘‘electronic’’degrees of freedom, while the heavy quarks represent thenuclei. Thus, certain properties of these states are related inthe same way that, for example, properties of hydrogen anddeuterium are related. This ‘‘heavy quark symmetry’’55 hasprovided very useful guides to the properties of hadrons con-taining charm and beauty quarks, and permits more precisedeterminations of underlying weak couplings~such as ele-ments of the Cabibbo–Koyayashi–Maskawa@CKM# matrix!.

H. Higgs boson„s…

An unbroken SU~2! U~1! theory involving the photonwould requireall fields to have zero mass, whereas theW6

andZ are massive. The symmetry-breaking that generatesWand Z masses must not destroy the renormalizability of thetheory. TheHiggs mechanismachieves this goal at the priceof introducing an additional degree of freedom correpondingto a physical particle, theHiggs particle, which is the subjectof intense searches.32,120,206,207Current 95% c.l. limits on a

311 311Am. J. Phys., Vol. 71, No. 4, April 2003 Jonathan L. Rosner

standard-model Higgs boson areMH.114 GeV/c2 via directsearches208 and MH,193 GeV/c2 from fits to precise elec-troweak data.209

Discovering the nature of the Higgs boson is a key tofurther progress in understanding what may lie beyond thestandard model. There may exist one Higgs boson or morethan one. There may exist other particles in the spectrumrelated to it. The Higgs boson may be elementary or com-posite. If composite, it points to a new level of substructureof the elementary particles.

I. Precision electroweak measurements

Precision electroweak measurements can yield informa-tion on many new-physics possibilities in addition to theHiggs boson. The seminal paper of Veltman210 showed howthe ratio of W and Z masses could shed light on the topquark’s mass. A systematic study of electroweak radiativecorrections within the standard model was performed byMarciano and Sirlin211 and used to analyze a wide variety ofelectroweak data, initially in Ref. 212 and most recently inRef. 209. Widely-used parametrizations of deviations fromStandard-Model predictions213–215 have been used to con-strain new particles in higher-order loop diagrams associatedwith W, Z, and photon self-energies. Some reviews includeRefs. 216–219.

206. ‘‘Report of the Tevatron Higgs Working Group,’’ M. Carenaet al.,Fermilab report FERMILAB-CONF-00-279-T, hep-ph/0010338~un-published!.~A!

207. ‘‘The Higgs Working Group: Summary Report,’’ D. Cavalliet al., inProceedings of Workshop on Physics at TeV Colliders, Les Houches,France, 21 May–1 June 2001, edited by P. Aurencheet al. ~Paris,IN2P3, 2001!, pp. 1–120.~A!

208. LEP Higgs Working Group, results quoted in web page of LEP Elec-troweak Working Group,http://lepewwg.web.cern.ch/LEPEWWG/.~I!

209. LEP Electroweak Working Group, http://lepewwg.web.cern.ch/LEPEWWG/ . ~I!

210. ‘‘Limit on Mass Differences in the Weinberg Model,’’ M. Veltman,Nucl. Phys.B123, 89 ~1977!.~A!

211. ‘‘Radiative Corrections to Neutrino Induced Neutral Current Phenom-ena in the SU~2!L3U~1! Theory,’’ W. J. Marciano and A. Sirlin, Phys.Rev. D22, 2695~1980!;31, 213~1985!.~A!

212. ‘‘A Comprehensive Analysis of Data Pertaining to the Weak NeutralCurrent and the Intermediate Vector Boson Masses,’’ U. Amaldiet al., Phys. Rev. D36, 1385~1987!.~I!

213. ‘‘A New Constraint on a Strongly Interacting Higgs Sector,’’ M. E.Peskin and T. Takeuchi, Phys. Rev. Lett.65, 964–967~1990!.~A!

214. ‘‘Estimation of Oblique Electroweak Corrections,’’ M. E. Peskin andT. Takeuchi, Phys. Rev. D46, 381–409~1992!.~A!

215. ‘‘Vacuum Polarization Effects of New Physics on Electroweak Pro-cesses,’’ G. Altarelli and R. Barbieri, Phys. Lett. B253, 161–167~1991!.~A!

216. ‘‘Electroweak Theory. Framework of On-Shell Renormalization andStudy of Higher-Order Effects,’’ K. I. Aokiet al., Prog. Theor. Phys.Suppl.73, 1–225~1982!.~A!

217. ‘‘Electroweak Radiative Corrections,MZ , MW , and the Heavy Top,’’W. Hollik, Adv. Ser. Direct. High Energy Phys.10, 1–57~1992!.~A!

218. The Standard Model in the Making: Precision Study of the Elec-troweak Interactions, D. Yu. Bardin and G. Passarino~ClarendonPress, Oxford, 1999!. ~A!

219. ‘‘Radiative Corrections in Gauge Theories,’’ H. Anlauf, lectures atAdriatic School on Particle Physics and Physics Informatics, Septem-ber 11–21, 2001, http://heplix.ikp.physik.tu-darmstadt.de/ ;anlauf/ha-lectures.html . ~A!

X. PROPOSED EXTENSIONS

A. Supersymmetry

Unification of the electroweak and strong interactions at ahigh mass scale leads to thehierarchy problem, in which thisscale contributes through loop diagrams to the Higgs bosonmass and requires it to be fine-tuned at each order of pertur-bation theory. A similar problem is present whenever there isa large gap between the electroweak scale andany highermass scale contributing to the Higgs boson mass.Supersym-metrysolves this problem by introducing for each particle ofspin J a superpartnerof spin J61/2 whose contribution tosuch loop diagrams cancels the original one in the limit ofdegenerate masses. Recent reviews of supersymmetry and itslikely experimental signatures include Refs. 40, 62–67,while earlier discussions are given by Refs. 68, 69, and 70.For an article at the popular level see Ref. 119.

B. Dynamical electroweak symmetry breaking

If the Higgs boson is not fundamental but arises as theresult of a new super-strong force which, in analogy withcolor, causes thedynamicalgeneration of one or more scalarparticles, the hierarchy problem can be avoided. Thisscheme, sometimes called ‘‘technicolor,’’ was proposed inthe 1970s.220–222 For recent reviews, see. e.g., Refs. 223–225.

220. ‘‘Implications of Dynamical Symmetry Breaking,’’ S. Weinberg,Phys. Rev. D13, 974–996~1976!.~A!

221. ‘‘Implications of Dynamical Symmetry Breaking: An Addendum,’’ S.Weinberg, Phys. Rev. D19, 1277–1280~1979!.~A!

222. ‘‘Dynamics of Spontaneous Symmetry Breaking in the Weinberg–Salam Theory,’’ L. Susskind, Phys. Rev. D20, 2619–2625~1979!.~A!

223. ‘‘Lectures on Technicolor and Compositeness,’’ R. S. Chivukula, inRef. 47, pp. 731–772.~A!

224. ‘‘Two Lectures on Technicolor,’’ K. Lane, Fermilab reportFERMILAB-PUB-02- 040-T, preprint hep-ph/0202255~unpub-lished!.~A!

225. ‘‘Strong dynamics and electroweak symmetry breaking,’’ C. T. Hilland E. H. Simmons, Fermilab report FERMILAB-PUB-02-045-T,preprint hep-ph/0203079, submitted to Phys. Rep.~A!

C. Fermion mass and mixing patterns

The transitions between the (u,c,t) and (d,s,b) quarksowing to virtualW emission or absorption are described bythe Cabibbo–Kobayashi–Maskawa~CKM! matrix men-tioned in Sec. IX A.~For one parametrization of this matrixsee Ref. 226.!The CKM matrix arises because the matricesthat diagonalize the mass matrices of (u,c,t) and of (d,s,b)are not the same. A theory of quark masses would thus entaila specific form of the CKM matrix. For the correspondingmatrix for leptons, see Refs. 227–229. While a theory ofquark and lepton masses still eludes us, attempts have beenmade to guess some of its general features.230–235

226. ‘‘Parametrization of the Kobayashi-Maskawa Matrix,’’ L. Wolfen-stein, Phys. Rev. Lett.51, 1945–1947~1983!.~I!

227. ‘‘Remarks on the Unified Model of Elementary Particles,’’ Z. Maki,M. Nakagawa, and S. Sakata, Prog. Theor. Phys.28, 870–880~1962!.~A!

228. ‘‘Muon and Electron Number Nonconservation in aV–A GaugeModel,’’ B. W. Lee, S. Pakvasa, R. Shrock, and H. Sugawara, Phys.Rev. Lett.38, 937–939~1977!.~A!

312 312Am. J. Phys., Vol. 71, No. 4, April 2003 Jonathan L. Rosner

229. ‘‘Natural Suppression of Symmetry Violation in Gauge Theories:Muon-Lepton and Electron-Lepton Number Nonconservation,’’ B. W.Lee and R. E. Shrock, Phys. Rev. D16, 1444–1473~1977!.~A!

230. ‘‘Weak Interaction Mixing in the Six-Quark Theory,’’ H. Fritzsch,Phys. Lett. B73, 317–322~1978!.~I!

231. ‘‘Hierarchy of Quark Masses, Cabibbo Angles, and CP Violation,’’ C.D. Froggatt and H. B. Nielsen, Nucl. Phys. B147, 277–298~1979!.~A!

232. ‘‘Unified Theories With U~2! Flavor Symmetry,’’ R. Barbieri, L. J.Hall, S. Raby, and A. Romanino, Nucl. Phys. B493, 3–26~1997!.~A!

233. ‘‘A model for Fermion Mass Hierarchies and Mixings,’’ P. Ramond,in Particles, Strings, and Cosmology„PASCOS 98…, Proceedings ofthe 6th International Symposium on Particles, Strings and Cosmol-ogy, Boston, MA, 22–27 Mar. 1998, edited by P. Nath~World Sci-entific, Singapore, 1999!, pp. 567–577.~A!

234. ‘‘Mass and flavor mixing schemes of quarks and leptons,’’ H. Fritzschand Z.-z. Xing, Prog. Part. Nucl. Phys.45, 1–81 ~2000!.~A!

235. ‘‘GUT model predictions for neutrino oscillation parameters compat-ible with the large mixing angle MSW solution,’’ C. H. Albright andS. Geer, Phys. Rev. D65, 073004~2002!, and Refs. 11 and 15therein.~A!

D. Composite quarks and leptons

Families of quarks and leptons appear to be replicas of oneanother~see Table V!, aside from their differing masses andweak couplings. Attempts have been made to explain thisregularity in terms of a composite structure, much as theperiodic table of the elements reflects their underlyingatomic structure. A set of guidelines for this program waslaid down by ’t Hooft.236 For an example of a recent effort,see Ref. 237.

236. ‘‘Naturalness, chiral symmetry, and spontaneous chiral symmetrybreaking,’’ G. ’t Hooft, inRecent Developments in Gauge Theories~Cargese Summer Institute, Aug. 26–Sept. 8, 1979!, edited by G.’t Hooft et al. ~Plenum, New York, 1980!, pp. 135–157.~A!

237. ‘‘Composite quarks and leptons from dynamical supersymmetrybreaking without messengers,’’ N. Arkani-Hamed, M. A. Luty, and J.Terning, Phys. Rev. D58, 015004~1998!.~A!

E. Grand unification and extended gauge groups

An early point in favor of quark–lepton unification wasthe anomaly cancellation182–184mentioned in Sec. IX E. Theidea that lepton number could be regarded as a fourth‘‘color,’’ leading to an extended gauge group embracing bothelectroweak and strong interactions, was proposed by Patiand Salam.238

The strong and electroweak coupling constants are ex-pected to approach one another at very small distance~largemomentum! scales,239 suggestinggrand unified theoriesbased on symmetry groups such as SU~5!,240 SO~10!,241 andE6.242 ~For an early popular article on this program see Ref.114.! These theories typically predict that the proton willdecay,115–117and some of them entail additional observablegauge bosons besides those of the SU~3!3SU~2!3U~1! stan-dard model.71 Some useful group-theoretic techniques formodel-building are described in Ref. 56.

238. ‘‘Unified Lepton–Hadron Symmetry and a Gauge Theory of the Ba-sic Interactions,’’ J. C. Pati and A. Salam, Phys. Rev. D8, 1240–1251~1973!.~A!; see also ‘‘Is Baryon Number Conserved?’’, J. C. Pati andA. Salam, Phys. Rev. Lett.31, 661–664~1973!; ‘‘Lepton Number asthe Fourth Color,’’ J. C. Pati and A. Salam, Phys. Rev. D10, 275–289~1974! ~A!.

239. ‘‘Hierarchy of Interactions in Unified Gauge Theories,’’ H. Georgi, H.R. Quinn, and S. Weinberg, Phys. Rev. Lett.33, 451–454~1974!.~I!

240. ‘‘Unity of All Elementary Particle Forces,’’ H. Georgi and S. L.Glashow, Phys. Rev. Lett.32, 438–441~1974!.~I!

241. ‘‘The State of the Art—Gauge Theories,’’ H. Georgi, inParticles andFields—1974, Proceedings of the Williamsburg Meeting, Sept. 5–7,1974, edited by C. E. Carlson~AIP Conf. Proc. No. 23! ~AIP, NewYork, 1975!, pp. 575–582.~A!

242. ‘‘A Universal Gauge Theory Model Based on E6 ,’’ F. Gursey, P.Ramond, and P. Sikivie, Phys. Lett.60B, 177–180~1976!.~A!

F. Strong CP problem and axions

In a non-Abelian gauge theory such as SU~3! there canarise nontrivial gauge configurations that prevent terms inthe Lagrangian proportional to Tr (GmnGmn) from being ig-nored as pure divergences. Such terms can lead to strongCPviolation. Their coefficient, a parameter conventionallycalled u, must be of order 10210 or smaller in order not toconflict with limits on the electric dipole moment of theneutron.243 Several proposals have been advanced for whyuis so small.40,244In one of the most interesting,u is promotedto the status of a dynamical variable that can relax to a natu-ral value of zero. As a consequence, there arises a nearlymassless particle known as theaxion, whose properties~andthe search for which!are well-described in Refs. 40, 244.

243. ‘‘New Experimental Limit on the Electric Dipole Moment of theNeutron,’’ P. G. Harriset al., Phys. Rev. Lett.82, 904–907~1999!.~I!

244. ‘‘The Strong CP Problem,’’ M. Dine, in Ref. 47, pp. 349–369.

G. String theory

A truly unified theory of interactions must include gravity.The leading candidate for such a theory isstring theory,which originated in pre-QCD attempts to explain the stronginteractions245–248 by replacing the space–time points ofquantum field theories with extended objects~‘‘strings’’!. In1974 it was realized that string theories necessarily entailed amassless spin-2 particle, for which the graviton was an idealcandidate.249 While it appeared that such theories requiredspace–time to be 26-dimensional~or 10-dimensional in thepresence of supersymmetry!, these extra dimensions wereinterpreted in the 1980s as a source of the internal degrees offreedom characterizing particle quantum numbers~see. e.g.,Refs. 250–252!. A typical scenario whereby string theorymight yield predictions for the quark and lepton spectrum isdescribed in Ref. 253.

Early results on string theory are described in the textbookby Green, Schwarz, and Witten.41,42 Later texts are Refs. 43,44. Descriptions for the non-specialist are given by Green,122

Duff,123 Greene,100 and Weinberg.132

245. Y. Nambu, ‘‘Quark Model and the Factorization of the VenezianoAmplitude,’’ in Symmetries and Quark Models: Proceedings~In-ternational Conference on Symmetries and Quark Models, Detroit,Mich., June 1969!, edited by R. Chand~Gordon and Breach, NewYork, 1970!, pp. 269–277.~A!

246. ‘‘A General Treatment of Factorization in Dual Resonance Models,’’S. Fubini, D. Gordon, and G. Veneziano, Phys. Lett.29B, 670–682~1969!.~A!

247. ‘‘Dual Symmetric Theory of Hadrons. 1,’’ L. Susskind, Nuovo Ci-mentoA69, 457–496~1970!.~A!

248. ‘‘Strings, Monopoles, and Gauge Fields,’’ Y. Nambu, Phys. Rev. D10, 4262– 4268~1974!.~A!

249. ‘‘Dual Models for Nonhadrons,’’ J. Scherk and J. H. Schwarz, Nucl.Phys. B81, 118–144~1974!.~A!

250. ‘‘The Heterotic String,’’ D. J. Gross, J. A. Harvey, E. Martinec, andR. Rohm, Phys. Rev. Lett.54, 502–505~1985!.~A!

313 313Am. J. Phys., Vol. 71, No. 4, April 2003 Jonathan L. Rosner

251. ‘‘Heterotic String Theory. 1. The Free Heterotic String,’’ D. J. Gross,J. A. Harvey, E. Martinec, and R. Rohm, Nucl. Phys. B256, 253–284~1985!.~A!

252. ‘‘Heterotic String Theory. 2. The Interacting Heterotic String,’’ D. J.Gross, J. A. Harvey, E. Martinec, and R. Rohm, Nucl. Phys. B267,75–124~1986!.~A!

253. ‘‘Vacuum Configurations for Superstrings,’’ P. Candelas, G. T.Horowitz, A. Strominger, and E. Witten, Nucl. Phys. B258, 46–74~1985!.~A!

H. Large extra dimensions

Although the usual superstring scenario envisions the sixextra dimensions in such theories as having spatial extent ofthe order of the Planck scale, (GN\/c3)1/2.10233 cm, theo-ries have been proposed in which some of the extra dimen-sions are larger, leading to observable effects at acceleratorsor in precise tests of Newton’s universal inverse square lawof gravitation.254–258Reviews for the non-specialist have ap-peared inScientific American137 andPhysics Today.138

254. ‘‘A Possible New Dimension at a Few TeV,’’ I. Antoniadis, Phys.Lett. B 246, 377–384~1990!.~A!

255. ‘‘Weak Scale Superstrings,’’ J. D. Lykken, Phys. Rev. D54, R3693–R3697~1996!.~A!

256. ‘‘The Hierarchy Problem and New Dimensions at a Millimeter,’’ N.Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, Phys. Lett. B429,263–272~1998!.~A!

257. ‘‘New Dimensions at a Millimeter to a Fermi and Superstrings at aTeV,’’ I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos, and G. R.Dvali, Phys. Lett. B436, 257–263~1998!.~A!

258. ‘‘Phenomenology, Astrophysics and Cosmology of Theories withSub-Millimeter Dimensions and TeV Scale Quantum Gravity,’’ N.Arkani-Hamed, S. Dimopoulos, and and G. R. Dvali, Phys. Rev. D59, 086004~1999!.~A!

XI. HINTS OF NEW PHYSICS

A. Neutrino masses

The ability of neutrinos of one species to undergo oscilla-tions into another is an indication of nonzero and nondegen-erate neutrino masses.57,58Several experiments find evidencefor such oscillations. Reviews have appeared in Refs. 59, 61,131; the second of these also deals with precision elec-troweak tests using neutrinos.

1. Solar neutrinos

Since the earliest attempts to detect neutrinos originatingfrom the Sun in the mid-1960s, the flux has been less thanpredicted in the standard solar model.125 Recent experimentsat the Sudbury Neutrino Observatory~SNO! in Ontario259,260

and the KamLAND Experiment in Japan261 strongly suggestthat this deficit is due to oscillations of the electron neutrinosproduced in the Sun into other species, most likely a combi-nation of muon and tau neutrinos, induced by interactionwith the Sun in a manner~now known as the MSW effect!first proposed by Mikheev and Smirnov262 andWolfenstein.263 For reviews, see Refs. 35, 60.

2. Atmospheric neutrinos

Neutrinos produced by the interactions of cosmic rays inthe atmosphere are expected to be in the rationm :ne52:1~summing over neutrinos and antineutrinos!.264 Instead, a ra-tio more like 1:1 is observed. This phenomenon has beentraced to oscillations that are most likelynm→nt , as a resultof definitive experiments performed by the Super-Kamiokande collaboration in Japan.265,266 The mixing ap-

pears to be close to maximal, in contrast to the small mixingsof quarks described by off-diagonal elements of the CKMmatrix.

3. Indications in an accelerator experiment

An experiment performed at Los Alamos NationalLaboratory267 in the Liquid Scintillator Neutrino Detector~LSND! finds evidence fornm→ ne oscillations. An experi-ment known as MiniBooNE which has begun to operate atFermilab will check this possibility.268

259. ‘‘Measurement of the Charged Current Interactions Produced by8BSolar Neutrinos at the Sudbury Neutrino Observatory,’’ SNO Collab.,Q. R. Ahmadet al., Phys. Rev. Lett.87, 071301~2001!.~I!

260. ‘‘Direct Evidence for Neutrino Flavor Transformation from Neutral-Current Interactions in the Sudbury Neutrino Observatory,’’ SNOCollab., Q. R. Ahmadet al., Phys. Rev. Lett.89, 011301 ~2002!;‘‘Measurement of Day and Night Neutrino Energy Spectra at SNOand Constraints on Neutrino Mixing Parameters,’’ SNO Collab., Q.R. Ahmadet al., Phys. Rev. Lett.89, 011302 ~2002!.~I!

261. ‘‘First Results from KamLAND: Evidence for Reactor Anti-NeutrinoDisappearance,’’ KamLAND Collaboration, K. Eguchiet al., Phys.Rev. Lett.90, 021802~2003!.

262. ‘‘Resonance Enhancement of Oscillations in Matter and SolarNeutrino Spectroscopy,’’ S. P. Mikheev and A. Yu. Smirnov, Yad. Fiz.42 , 1441–1448~1985! @Sov. J. Nucl. Phys.42, 913–917~1985!#.~I!

263. ‘‘Neutrino Oscillations in Matter,’’ L. Wolfenstein, Phys. Rev. D17,2369–2374~1978!.~I!

264. ‘‘Flux of Atmospheric Neutrinos,’’ T. K. Gaisser and M. Honda, Ann.Rev. Nucl. Part. Sci.52, 153–199~2002!.

265. ‘‘Evidence for Oscillation of Atmospheric Neutrinos,’’ Super-Kamiokande Collaboration, Y. Fukudaet al., Phys. Rev. Lett.81,1562–1567~1998!.~I!

266. ‘‘ t Neutrinos Favored Over Sterile Neutrinos in Atmospheric MuonNeutrino Oscillations,’’ Super-Kamiokande Collaboration, S. Fukudaet al., Phys. Rev. Lett.85, 3999–4003~2000!.~I!

267. ‘‘Evidence for Neutrino Oscillations from the Observation ofne Ap-pearance in anm Beam,’’ LSND Collaboration, A. Aguilaret al.,Phys. Rev. D64, 112007~2001!.~I!

268. ‘‘The Status of MiniBooNE,’’ E. A. Hawker, Int. J. Mod. Phys. A16„S1B!, 755–757 ~2001!. ~I! For an up-to-date web page see:http://www-boone.fnal.gov/ .

B. Cosmic microwave background radiation

The 2.7 K radiation left over from the Big Bang contains awealth of information about both the early Universe and par-ticle physics. In particular, the spatial pattern of its fluctua-tions indicates that the Universe is exactly on the borderbetween open and closed, and strongly supports the idea thatthe Universe underwent a period of exponential inflationearly in its history.134,135,269–271For a review of the cosmo-logical parameters, see Ref. 272.

269. ‘‘Big-Bang Cosmology,’’ K. A. Olive and J. A. Peacock, inReview ofParticle Physics, K. Hagiwaraet al., Ref. 73, pp. 152–161.~I!

270. ‘‘Global Cosmological Parameters:H0 , VM , andL, ’’ M. Fukugitaand C. J. Hogan, inReview of Particle Physics, K. Hagiwaraet al.,Ref. 73, pp. 166–172.~I!

271. ‘‘Cosmic Background Radiation,’’ G. F. Smoot and D. Scott, inRe-view of Particle Physics, K. Hagiwaraet al., Ref. 73, pp. 177–181.~I!

272. ‘‘The Cosmic Triangle: Revealing the State of the Universe,’’ N. Bah-call, J. P. Ostriker, S. Perlmutter, and P. J. Steinhardt, Science284,1481-1488~1999!.~I!

C. Baryon asymmetry of the Universe

To explain why the visible Universe seems to contain somany more baryons than antibaryons, Sakharov273 proposed

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shortly after the discovery ofCP violation that three ingre-dients were needed:~1! CP ~and C! violation; ~2! baryonnumber violation, and~3! a period in which the Universe isnot in thermal equilibrium. All of these conditions are ex-pected to be satisfied in a wide range of theories, such asgrand unified theories~Sec. XI E! in which quarks and lep-tons, and the electroweak and strong interactions, are unifiedwith one another.274 However, details of the mechanism arenot clear.112,113In some versions of the theory, for example, itis lepton number that is violated in the early stages of theUniverse, giving rise to a lepton asymmetry that is then con-verted to a mixture of lepton and baryon asymmetry whenthe Universe has evolved further. For a recent review of thissuggestion, see Ref. 275.

273. ‘‘Violation of CP Invariance, C Asymmetry, and Baryon Asymmetryof the Universe,’’ A. D. Sakharov, Pis’ma Zh. E´ ksp. Teor. Fiz.5,32–35~1967! @JETP Lett.5, 24–27 ~1967!#.~I!

274. ‘‘Grand Unified Theories and the Origin of the Baryon Asymmetry,’’E. W. Kolb and M. S. Turner, Ann. Rev. Nucl. Part. Sci.33, 645–696~1983!.~I!

275. ‘‘Neutrino Masses and the Baryon Asymmetry,’’ W. Buchmu¨ller andM. Plumacher, Int. J. Mod. Phys. A15, 5047–5086~2000!.~I!

D. Dark matter

Only a small fraction of the matter in the Universe can beaccounted for by baryons, leaving the remainder to consist ofas-yet-unidentified matter or energy density.121 Candidatesfor this dark matterare discussed in theReview of ParticlePhysics.276 One class of candidates consists of the lightestsupersymmetric particle~LSP!, which may be stable; thesesuggestions are reviewed in Ref. 277.

276. ‘‘Dark Matter,’’ M. Srednicki and N. J. C. Spooner, inReview ofParticle Physics, K. Hagiwaraet al., Ref. 73, pp. 173–176.~I!

277. ‘‘Supersymmetric Dark Matter,’’ G. Jungman, M. Kamionkowski,and K. Griest, Phys. Rep.267, 195–373~1996!.~I!

E. Dark energy

The Universe appears not only to be expanding, but itsexpansion appears to be speeding up. Evidence for this be-havior comes from the study of distant supernovae, whichfurnish ‘‘standard candles’’ for a cosmological distancescale.130,272 One interpretation is that acosmological con-stant L ~first proposed by Einstein shortly after he formu-lated the general theory of relativity! accounts for about 65%of the energy density of the Universe. This contribution issometimes referred to as ‘‘dark energy,’’ to distinguish itfrom the ‘‘dark matter’’ accounting for nearly all of the re-maining energy density aside from a few-percent contribu-tion from baryons.269,270An alternative suggestion is that the‘‘dark energy’’ is due to a new field, dubbed‘‘quintessence.’’136 For recent accounts of ‘‘dark energy’’ seeRefs. 278 and 279.

278. ‘‘The Extravagant Universe,’’ R. P. Kirshner~Princeton UniversityPress, 2002.~E!

279. ‘‘The Cosmological Constant and Dark Energy,’’ P. J. E. Peebles andB. Ratra, preprint astro-ph/0207347, to appear in Rev. Mod. Phys.~I!

XII. EXPERIMENTAL APPROACHES

The rise of the standard model would not have been pos-sible without a variety of experimental facilities, includingaccelerators, detectors, and nonaccelerator experiments.

What follows is a brief description of some currently oper-ating laboratories and experiments. Fuller descriptions maybe found through laboratory web sites, listed in Sec. VII B,and through web sites of specific collaborations. Some refer-ences to recent experiments are given in this section.

A. High energy accelerator facilities

1. Beijing Electron–Positron Collider (China)

This electron–positron collider with center-of-mass en-ergy 2–5 GeV recently reported an improved measurementof R ~see Sec. II C!in this energy range.280 It has madeimportant contributions to the study oft leptons, charmed

particles, andcc bound states.

2. Brookhaven National Laboratory (USA)

The Alternating-Gradient Synchrotron~AGS! is a fixed-target proton accelerator with maximum energy of about 30GeV. The first neutrino beam constructed at an acceleratorwas used at the AGS to show that the muon and electronneutrino are distinct from one another.281 One of its mostspectacular discoveries was theJ/c particle, a bound state ofa charmed quark and a charmed antiquark.185 Recent experi-ments include the detection of the rare processK1→p1nn~Ref. 282!and a precise measurement of the muon anoma-lous magnetic moment.283 It serves as an injector to theRela-tivistic Heavy-Ion Collider~RHIC!, whose maximum energyof about 200 GeV per nucleon permits studies of the quark–gluon plasma and other aspects of hadron physics at highdensities.

3. CERN (Switzerland and France)

CERN’s 28-GeV Proton Synchrotron~PS!began operationin 1959. It served as a source of protons for the IntersectingStorage Rings~ISR!, which began operation in the early1970s and achieved a maximum center-of-mass energy of 62GeV. Its protons were used to produce neutrinos which pro-vided the first evidence for neutral currents in 1973.177,178

The Super-Proton-Synchrotron~SPS!, a 400-GeV fixed-target machine built in the mid-1970s, was converted to aproton-antiproton collider~the ‘‘SppS’’! early in the 1980s,leading to the discovery of theW andZ bosons in 1983.284,285

The Large Electron–Positron~LEP! Collider126 was commi-sioned in 1989, making a series of precise measurements atthe center-of-mass energy of theZ boson ~91.2 GeV! ~anearly measurement of theZ width pointed to three families ofquarks and leptons128! before moving up in energy to nearly210 GeV and ending its program in 2000.286 Its magnetshave been removed, making way for the Large Hadron Col-lider ~LHC!, a proton–proton collider that will have a c.m.energy of 14 TeV.133,287

4. CLEOÕCESR at Cornell (USA)

The Wilson Synchrotron at Cornell, a circular electron ac-celerator built in 1967, was converted in 1979 to anelectron–positron collider, the Cornell Electron Storage Ring~CESR!, with maximum energy 8 GeV per beam.288 It ar-rived on the scene just in time to study theY(1S) bb reso-nance and its excited states, including theY(4S) which de-

cays to a BB meson pair. Studies ofB mesons havedominated the program of the CLEO detector at CESR until

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recently. For the next year or two, CLEO will return to theY(1S,2S,3S) resonances, after which it is planned to opti-mize CESR to run at the lower energies appropriate forcharm production.289 This will permit a return to many inter-esting questions with a vastly improved detector and statis-tical sample.

5. DESY (Germany)

A circular electron accelerator at the Deutsches ElektronenSynchrotron ~DESY! laboratory was converted to anelectron–positron collider~DORIS!whose experimental pro-gram paralleled that of CESR/CLEO for a number of years,yielding important information aboutY spectroscopy andBmesons, for example through work of the ARGUS Collabo-ration. Subsequent machines included the largere1e2 col-lider PETRA~maximum c.m. energy 46 GeV!and the cur-rently operating HERA lepton–proton collider, which hasstudied bothe2p ande1p interactions. HERA has extendedinformation on deep inelastic lepton scattering to new kine-matic regimes and provided important information on thegluon structure of the proton.

6. Fermilab (USA)

The Fermi National Accelerator Laboratory in Batavia, Il-linois, USA, began operation in 1972 as a proton acceleratorwith initial energy 200 GeV, rising to 400 GeV within a year.With the addition of a ring of superconducting magnets in1983 it was converted to an energy of 800 GeV capable ofproviding protons to fixed targets and proton-antiproton col-lisions with a center-of-mass energy of 1.8 TeV.127,290 Itsenergy has recently been upgraded to nearly 1 TeV per beamwith the addition of a new 150-GeV proton ring called theMain Injector. Outstanding discoveries at Fermilab includethose of the bottom quark in 1977,188,189 the top quark in1994,190–195and the tau neutrino in 2000.291

7. Frascati (Italy)

A major pioneer in the study of electron–positron colli-sions has been the Laboratori Nazionali di Frascati~INFN!near Rome, Italy. Starting in the early 1960s with the ADAcollider and continuing through the ADONE storage ring,which begain operation in the late 1960s, the laboratory hasnow begun to operate a machine called DAFNE ~DAFNE!,which seeks to produce kaons and other particles through thereactione1e2→f→••• at a center-of-mass energy of 1.02GeV.

8. KEK (Japan)

In the early 1970s, a 12-GeV proton synchrotron was con-structed in Japan near Tokyo at the National Laboratory forHigh Energy Physics, for which KEK~Ko–Energi–Kenkyujo! is the acronym in Japanese. The next majorproject at KEK, the TRISTANe1e2 collider, attained acenter-of-mass energy in excess of 60 GeV, the highest in theworld for such a machine at its debut in 1986. Among thetopics studied by TRISTAN included weak–electromagneticinterference through the processese1e2→(g* ,Z* )→•••,where the asterisk denotes a virtual photon orZ. The latestproject at KEK is the KEK-B e1e2 collider, a lower-energymachine built in the TRISTAN tunnel, which is designed toproduce pairs ofB mesons with net motion on their center-

of-mass by using unequal electron and positron energies. Inthis way the positions at which theB mesons decay can bespread out longitudinally, permitting easier study of time-dependences that are of particular interest inCP-violatingprocesses. The Belle detector operating at KEK-B200 is pro-ducing significant results onB decays, as mentionedabove203!, as is the BaBar detector operating at PEP-II~seethe description of SLAC, below!.

9. Novosibirsk (Russia)

A series of e1e2 colliders has operated at the BudkerInstitute for High Energy Physics in Novosibirsk for a num-ber of years. Indeed, work at this laboratory helped to pio-neer the study of beam dynamics essential for achieving suchcollisions. These colliders performed important measure-ments at the center-of-mass energies of theY(9.46) andf(1.02) resonances, where the numbers denote the mass inGeV/c2.

10. Protvino (Russia)

The largest accelerator at present in Russia is a 76-GeVproton synchrotron at Serphukhov~Protvino!, which beganoperation in the early 1970s. It was the first to detect risingmeson–baryon cross sections,292 followed soon by the obser-vation of a similar effect in proton–proton collisions at theCERN ISR~see above!.

11. SLAC (USA)

The early program of the 30-GeV 2-mile-long linear elec-tron accelerator at the Stanford Linear Accelerator Center~SLAC! included the discovery of pointlike constituents in-side the proton through deep inelastic scattering.96,152,153Inthe early 1970s the SPEAR electron–positron storage ringwas constructed with maximum center-of-mass energy equalto 7.4 GeV. Late in 1973 this machine confirmed a surprisingenhancement of thee1e2 annihilation cross section startingat a c.m. energy of 4 GeV seen earlier at the CambridgeElectron Accelerator~CEA!, and in 1974 was one of twosources of the discovery of theJ/c particle,186 the otherbeing a fixed-target experiment at Brookhaven NationalLaboratory185 ~see above!. In the mid-1970s constructionwas begun on PEP, an electron–positron collider with c.m.energy of about 30 GeV, which performed studies of theelctroweak theory and was the first to measure theb quarklifetime. The energy of the LINAC was then raised to 50GeV, both electrons and positrons were accelerated, andthese were then bent in arcs to collide with one another atenergies equal to or greater than the mass of theZ boson.This machine, the Stanford Linear Collider~SLC!,124 pio-neered in precision studies of theZ boson through its Mark IIand SLD detectors; its early measurement of theZ width wasa piece of evidence for three families of quarks andleptons.128 The latest SLAC project, the PEP-II asymmetrice1e2 collider, has seen evidence forCP violation in B de-cays in its BaBar detector199,202~see also KEK-Band Belle,above!, and has achieved record luminosity for any collider.By the middle of this decade both BaBar and Belle expect tohave produced and recorded several hundred millionBBpairs.

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12. Thomas Jefferson National Laboratory (USA)

A moderate-energy~5.7-GeV! electron accelerator, thismachine studies interactions with nuclei and the photopro-duction and electroproduction of resonances containing lightquarks (u,d,s), with an eye to seeing those that cannot be

explained purely asqq mesons orqqq baryons. An upgradeto 12 GeV is under discussion.

280. ‘‘Measurements of the Cross Section fore1e2→hadrons at Center-of-Mass Energies from 2 GeV to 5 GeV,’’ BES Collaboration, J. Z.Bai et al., Phys. Rev. Lett.88, 101802~2002!.~I!

281. ‘‘Observation of High-Energy Neutrino Reactions and the Existenceof Two Kinds of Neutrinos,’’ G. Danbyet al., Phys. Rev. Lett.9,36–44~1962!.

282. ‘‘Further Evidence for the DecayK1→p1nn, ’’ BNL E787 Collabo-ration, S. Adleret al., Phys. Rev. Lett.88, 041803~2002!.~I!

283. ‘‘Precise Measurement of the Positive Muon Anomalous MagneticMoment,’’ BNL E821 Collaboration, H. N. Brownet al., Phys. Rev.Lett. 86, 2227–2231~2001!.~I! An updated version of this result hasappeared recently with roughly half the experimental error: ‘‘Mea-surement of the Positive Muon Anomalous Magnetic Moment to 0.7ppm,’’ BNL E821 Collaboration, G. W. Bennettet al., Phys. Rev.Lett. 89, 101804 ~2002!; 89, 129903~E! ~2002!. See http://phyppro1.phy.bnl.gov/g2muon/index.shtml for latestdetails.

284. ‘‘Experimental Observation of the Intermediate Vector BosonsW1,W2, andZ0, C. Rubbia, 1984 Nobel Lecture, available athttp://www.nobel.se/physics/laureates/1984/rubbia-lecture.html . ~I!

285. ‘‘Stochastic Cooling and the Accumulation of Antiprotons,’’ S. VanDer Meer, 1984 Nobel Lecture, available athttp://www.nobel.se/physics/laureates/1984/meer-lecture.html . ~I!

286. ‘‘Review of final LEP Results or a Tribute to LEP,’’ J. Drees, inProceedings of 20th International Symposium on Lepton andPhoton Interactions at High Energies„Lepton Photon 01…, ~Ref.3!, pp. 349–373.~I!

287. ‘‘From LEP to LHC, a Review of Results and a Look to the Future,’’L. Foa, Nucl. Phys. Proc. Suppl.75A, 28–36 ~1999!.~I!

288. ‘‘A Personal History of CESR and CLEO,’’ K. Berkelman, CornellUniversity report CLNS 02/1784~unpublished!. ~I!

289. ‘‘CLEO-c and CESR-c: A New Frontier in Weak and Strong Interac-tions,’’ I. Shipsey, in Proceedings of 9th International Symposium onHeavy Flavor Physics, Pasadena, California, 10–13 Sept. 2001, AIPConf. Proc.618, 427–437~2002!.~I!

290. ‘‘The First Large-Scale Application of Superconductivity: The Fermi-lab Energy Doubler, 1972–1983,’’ L. Hoddeson, Historical Studies inthe Physical and Biological Sciences18, 25–54~1987!.

291. ‘‘Observation of nt Interactions,’’ DONUT Collaboration, K.Kodamaet al., Phys. Lett. B504, 218–224~2001!.~I!

292. ‘‘Total Cross-Sections ofp1, K1 andp on Protons and Deuterons inthe Momentum Range 15-GeV/c to 60-GeV/c, ’’ S. P. Denisovet al.,Phys. Lett.36B, 415–421~1971!.~I!

B. Nonaccelerator experiments

1. Underground or underwater laboratories

The ability to perform experiments in a low-backgroundenvironment is greatly increased by going deep underground,where cosmic ray interactions are less frequent. A number ofmajor laboratories now are operating underground, includingones at the Kamioka mine~Japan!,293 Gran Sasso~Italy!,294

and Soudan~Minnesota, USA!.295 Whereas the focus of sev-eral laboratories initially had been the search for proton de-cay, it has now broadened to include the study of interactionsof neutrinos from atmospheric cosmic rays, the Sun, andeven supernovae, and the search for effects of dark matter.

The next stage of operation of detectors in the laboratoriesmentioned above includes the study of artificially produced

neutrinos. The Fermilab accelerator will send neutrinos tothe MINOS detector296 in Soudan. The proton synchrotron atKEK in the K2K experiment,293 and later a machine knownas the Japan Hadron Facility,297 will direct neutrinos to theSuperKamiokande detector in Kamioka. Finally, a detectorknown as KamLAND,298 also in the Kamioka mine, will besensitive to neutrinos from reactors over a large portion ofJapan, and has already reported its first results.261 Some cur-rent and forthcoming detectors will also be sensitive to natu-rally occurring neutrinos. These include the Sudbury Neu-trino Observatory in Ontario,299 the Borexino experiment300

in Gran Sasso, and the SuperKamiokande detector men-tioned above. At the South Pole a number of phototubes havebeen sunk deep into the ice in the AMANDA experiment,301

which is envisioned in the IceCube experiment302 to expandto an effective volume of a cubic kilometer. The RICEexperiment303 seeks to study the low-frequency tail~at sev-eral hundred MHz!of Cerenkov emission by electrons pro-duced by neutrinos, also in South Polar ice. A number ofneutrino detectors are also deployed or planned deep under-water, e.g., in Lake Baikal304 and the Mediterranean Sea~ANTARES,305 NEMO,306 NESTOR307!.

2. Atomic physics

A large accelerator is not always needed to study funda-mental particle physics beyond the standard model. An ex-ample is the window on non-standard physics provided byatomic parity violation.~See the bibliography in Ref. 72.!Studies of weak-electromagnetic interfence in atoms such asCs, Tl, and Pb are in principle sensitive to new interactionsand extended gauge theories, particlarly if the effects ofatomic physics can be separated from more fundamental ef-fects.

3. Electric and magnetic dipole moments

The electric dipole moment of the neutron is an excellentprobe of physics beyond the standard model, which predictsit to be orders of magnitude smaller than its current upperbound243 of udnu,6310226e cm. For a bibliography of ex-perimental literature on electric dipole moments and atomicparity violation, see Ref. 72.

The magnetic dipole moments of particles also provideimportant constraints on the Standard Model. The anomalousmagnetic moment of the muon, in particular, is sensitive tonew-physics effects such as those that arise in some versionsof supersymmetry.308 The current status of measurements ofthis quantity indicates a possible deviation from standard-model predictions, but at a level which is not yet statisticallycompelling.283

293. See the web pagehttp://www-sk.icrr.u-tokyo.ac.jp/ .294. See the web pagehttp://www.lngs.infn.it/ .295. See the web pagehttp://www.hep.umn.edu/soudan/ .296. See the web pagehttp://www-numi.fnal.gov/ .297. See the web pagehttp://jkj.tokai.jaeri.go.jp/ .298. See the web pagehttp://www.awa.tohoku.ac.jp/html/

KamLAND/.299. See the web pagehttp://www.sno.phy.queensu.ca/ .300. See the web page http://pupgg.princeton.edu/

;borexino/.301. See the web pagehttp://amanda.berkeley.edu/amanda/ .302. See the web pagehttp://icecube.wisc.edu/ .303. See the web pagehttp://kuhep4.phsx.ukans.edu/

;iceman/.

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304. See the web pagehttp://www-zeuthen.desy.de/baikal/or http://thalia.ifh.de/baikal/ .

305. See the web pagehttp://antares.in2p3.fr/ .306. See the web pagehttp://nemoweb.lns.infn.it/ .307. See the web pagehttp://www.nestor.org.gr/ .308. ‘‘The Muon Anomalous Magnetic Moment: A Harbinger for ‘New

Physics’,’’ A. Czarnecki and W. J. Marciano, Phys. Rev. D64,013104~2001!.~A!

C. Plans for future facilities

The particle physics community is developing a number ofoptions to probe further beyond the standard model. Theseinclude a large lineare1e2 collider, intense sources of neu-trinos ~‘‘neutrino factories’’!, a muon collider, and a VeryLarge Hadron Collider~VLHC! with energy significantlygreater than the LHC. Descriptions of all of these optionsmay be found in the Proceedings of the 2001 SnowmassWorkshop.309

309. Proceedings of the APS/DPF/DPB Summer Study on the Future ofParticle Physics ~Snowmass 2001!, Snowmass, Colorado, 30June–21 July 2001, eConf C010630~2001!.

XIII. SUMMARY

The standard model of electroweak and strong interactionshas been in place for nearly thirty years, but precise tests

have entered a phase that permits glimpses of physics be-yond this impressive structure, most likely associated withthe yet-to-be discovered Higgs boson and certainly associ-ated with new scales for neutrino masses. Studies of CP vio-lation in decays of neutral kaons orB mesons are attainingimpressive accuracy as well, and could yield cracks in thestandard model at any time. It is time to ask what lies behindthe pattern of fermion masses and mixings. This is aninputto the standard model, characterized by many free param-eters all of which await explanation.

Many avenues exist for exploration beyond the standardmodel, both theoretical and experimental. A lively dialoguebetween the two approaches must be maintained, with ad-equate support for each, if we are to take the next step in thisexciting adventure.

ACKNOWLEDGMENTS

I wish to thank T. Andre´, T. Appelquist, R. Cahn, Z. Luo,C. Quigg, G. Passarino, R. Shrock, R. Stuewer, O. L.Weaver, and B. Winstein for constructive comments on thepaper, and the Theory Group at Fermilab for hospitality. Thiswork was supported in part by the United States Departmentof Energy through Grant No. DE FG02 90ER40560.

318 318Am. J. Phys., Vol. 71, No. 4, April 2003 Jonathan L. Rosner

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