symmetries - wichita state university€¦ · 28/10/2015 · of the novel angels and demons. ½...

Marj Corcoran Wichita Oct 28, 2015 1

Symmetries

and the matter dominance of the universe


Symmetries are very pleasing to us, both in science and in art. Symmetries also play an important role in physics.


Outline

Symmetries of nature and conservation laws

Standard model in a nutshell

Matter and antimatter

Discrete symmetries and their non-conservation

Relation of discrete symmetries and the matter/antimatter asymmetry

Current state of knowledge and future prospects


Symmetries and conservation laws

Emmy Noether was a German mathematician, described by Einstein and Hilbert as the most important woman in the history of mathematics.

After she received her PhD in mathematics, she taught for seven years without pay at Erlangen, where her father was a professor.

There is a deep relationship between symmetries and conservation laws, discovered in 1915 by mathematician Emmy Noether.


Emmy Noether

In 1915 she was invited by Hilbert to join the mathematics faculty at the University of Goettingen, not without controversy. Other faculty did not want to accept a woman lecturer.

Hilbert was indignant, "I do not see that the sex of the candidate is an argument against her. After all, we are a university, not a bath house."

At first Noether lectured under Hilbert's name, but eventually she had her own position.

In 1915, she proved a theorem which physicists call “Noether's theorem”, which has had a tremendous impact on theoretical physics.


Emmy Noether

Among mathematicians, she is known for her revolutionary contributions to abstract algebra. She was known as exceptionally creative and innovative, and very abstract in her thinking.

In 1933 she was dismissed from her position at Goettingen because she was Jewish. Einstein helped her get a position at Bryn Mawr. She was there less than two years when she died at the age of 53 a few days after an operation to remove an ovarian cyst.


Noether's Theorem

Noether's theorem states that, if a physical system has a continuous symmetry, there is a corresponding conserved quantity. (Remember your Lagrangian mechanics!)

Symmetry under translations in space→ conservation of linear momentum

You know about conservation of linear momentum if you play billiards. Conservation of momentum also controls what happens in a collision of two cars.


Noether's theorem

Noether's theorem also tells us that

Symmetry under rotations → conservation of angular momentum

If you have ever played with a gyroscope, you know about conservation of angular momentum. If you ride a bike, you rely on conservation of angular momentum to keep you upright.


Noether's Theorem

Symmetry under translations in time → conservation of mechanical energy, that is the sum of kinetic and potential energies.

Roller coasters work on the principle of conservation of mechanical energy.

Thought experiment—what if the acceleration of gravity changed with time?


Conservation of electric charge

Does Noether's theorem work the other way? Does a conserved quantity imply an underlying symmetry? Noether did not prove that, but physicists make that connection.

Example: Conservation of electric charge.

We can make particles with electric charge, such as electrons, but we always make equal amounts of positive and negative charge.

Under the right conditions, a photon can materialize into an electron positron pair.

But electric charge is conserved. As far as we know electric charge has been absolutely conserved since the beginning of the universe.

The charge of the proton and electron cancel to at least one part in 1040 !


Can we turn Noether's theorem around?

Is there an underlying symmetry that gives rise to the conservation of electric charge?

Yes, in QFT gauge invariance leads to the conservation of electric charge.

The more restrictive form called local gauge invariance also requires the existence of the photon, the quantum of light. So in the case of electric charge, there is an underlying symmetry associated with the conservation law.

In fact local gauge invariance underlies all of the quantum field theories that lead to the Standard Model.


Standard Model in a nutshell

There are six quarks and six letpons, each with its own antiparticle.

The W, Z, photon, and gluons are the force carriers.

Baryons such as the proton are made of three quarks.

Mesons are made of quark-antiquark pairs. For example K+=(us) , where “bar” means antiparticle.


Standard model in a nutshell

Masses of the quarks and charged leptons increase as we go up in the generations. For neutrinos we don't know yet.

Heavy things decay to lighter things.


Matter and antimatter

All particles have their antiparticles, as predicted by the Dirac equation in 1927.


Antimatter

All fundamental particles (electrons, quarks that make up protons...) have their antiparticles. When matter and antimatter meet, they annihilate in a burst of energy.

Dan Brown used antimatter as a central part of the plot of the novel Angels and Demons.

½ gram of antimatter was hidden in the Vatican, and the battery maintaining the magnetic bottle holding it was due to run out in a day!


Creating antimatter

We create antimatter at particle accelerators all the time, but always, matter and antimatter in equal amounts!

p

p

beam

target

We create proton-antiproton pairs by smashing an energetic beam into a target and making all sorts of stuff. The antiprotons are easy to separate out.


Creating antimatter

Fermilab antiproton accumulator—decommissioned in 2011.

Could we make ½ gram of antimatter? Yes, in 32 million years.

How do you store antiprotons? In a very good vacuum, suspended in a magnetic field, circulating in a ring.


Creating antimatter

The conservation of the number of matter particles (we call it baryon number B) is very similar to conservation of electric charge. B= +1 for a proton and B= -1 for an antiproton.

p

p

beam

target

So is there an underlying symmetry that accounts for the conservation of baryon number?

It turns out NO, and it also turns out that we know that this experimental conservation law cannot be absolute.


The missing antimatter

If matter and antimatter had been produced in equal amounts in the early universe, it would have all annihilated again.

The early universe somehow produced more matter than antimatter, by one part in 1011 .

And that tiny excess of matter is us and the stars, the galaxies....everything we see.

We don't understand how that happened,but we know that this asymmetry is related to thebreaking of fundamental symmetries.


Discrete symmetries

Translational and rotational symmetries are “continuous” symmetries, meaning the changes can take on any value.

The is another class of symmetry operations called discrete symmetries, best illustrated by an example.

The parity operation (P) is the inversion of the coordinate system, equivalent to reflection in a mirror followed by a rotation.

Are the laws of physics invariant under the parity operation?

For Newton's laws, the answer is yes!

XX


Weak nuclear interactions are different in a mirror!

“ Existing experiments do indicate parity conservation in strong and electromagnetic interactions to a high degree of accuracy, but for the weak interactions parity conservation is so far an extrapolated hypotheses unsupported by experimental evidence.”

Physical Review Letters, 104, page 254 (1956).

T. D. Lee C.N. Yang


Violation of parity confirmed by C.S. Wu

Within a year, Madam Wu at Columbia had experimentally shown that the weak interaction is not invariant under mirror reflection It was a very hard experiment in 1956.

Nuclear beta decay


Parity violation established

Nobel prize 1957 for Lee and Yang, but never a Nobel prize for Wu.


Charge conjugation symmetry

We define another discrete symmetry called “charge conjugation” (C) , which means changing all matter to antimatter and vice versa. In 1957 it was discovered that the weak interaction does not respect this symmetry—it treats matter and antimatter differently. This was first observed in neutrinos, the very light, neutral partners of the electron.

antineutrino neutrino

Neutrnios and antineutrinos are intrinsically different.

momentum

spin


Goldhaber experiment

In 1957 Goldhaber showed that neutrinos always have negative helicity.


C, P and CP

ν P

CNegative helicity ν--OK

1957: C P but CP still OKX X

Positive helicity ν X

Negative helicity anti-ν XPositive helicity anti-ν OKP

C


The fall of CP

For about 7 years after the discovery of C and P violation, physicists thought that the combined operation of CP was a good symmetry. That belief was shattered in 1964 by the discovery of CP violation in the neutral kaon system.

K0

Neutral K mesons mix through the box diagram

The essence of Cronin and Fitch's discovery is that the rates for K0→K0 and K0→K0 are not equal.

K0


KL and K

S

It is a lucky accident of the K and π masses that allowed the discovery of CP violation in 1964. ( π+ = ud ) CP eigenstates:K

1= K0 + K0 → π π (CP even final state)

K2= K0 – K0 → π π π (CP odd final state)

Because of the small phase space for K → πππ, the K2 lifetime was expected to be

~ 500x the K1 lifetime. Predicted by Gell-Mann and Pais, observed by Lederman.


KL and K

S

Invert the equations:K0= K

1 + K

2→K

2

K0 = K1 - K

2→ K

2

Kaons are made in a strong interaction as either K0 or K0 .But no matter what the initial state, if they travel some distance in the lab, the short-lived component dies out, leaving only K

2, which should always decay

to π π π.

Or does it?


Discovery of CP violation

In 1964, Christianson, Cronin, Fitch, and Turlay did a 2-week experiment, snuck in between other, more important experients. One of the goals (what they considered the most far-fetched) was to search for K

L→ π π

which would not happen if CP were conserved in the decay.

To their surprise, they found that K

L→ π π at a rate of 2 x 10-3—small but not

minuscule.


KL and K

S

The upshot of the Cronin-Fitch experiment is that the KL is not a

pure CP odd state, but is a mixture

KL= K

2 + ε K

1

ππ (indirect 1964)

ππ (direct—KTeV 2000)


CP violation in B mesons

For over 30 years, CP violation was seen only in the neutral Kaon system. However, it was known that CP violation should also occur in the neutral B mesons.

Just replace the s quark with a b quark—neutral B mesons also mix. Two accelerators (the B factories) were built to search for CP violation in the B mesons.

b

b


CP violation in the SM

We understand CP violation in the SM as arising from quark mixing. In the Standard Model, the weak eigenstates are rotated from the strong/mass eigenstates.

weak statesmass states

3x3 unitarymatrix

The CKM matrix is characterized by three angles and one complex phase. The complex phase leads to CP violation. CKM=Cabibbo-Kobayashi-Maskawa.


CKM matrix

The 2008 Nobel prize was awarded to the KM of CKM (along with Nambu)although the original idea of mixing goes back to Cabibbo in the 1960s.

Nicola Cabibbo 1935-2010


Unitarity triangle

Since the CKM matrix is unitary (conservation of probability), the unitarity condition between rows or columns can be represented by a closed triangle in the complex plane.


Unitary triangle experimental situation

Allowed region CP violation is now well-established in the B-mesons.

After years of hard work, all experimental data agrees...so there is no problem, right?


CP violation and the matter-antimatter asymmetry of the universe

In 1968 Russian physicist Andrei Sakharov showed that violation of C and CP is a necessary condition to generate the matter-antimatter asymmetry of the universe.

The only problem is that the amount of CP violation arising from the CKM matrix is too small by 10 orders of magnitude! So where is the missing CP violation?Its a longstanding puzzle.

The other conditions are a departure from thermal quilbrium and a mechanism for baryon number non-conservation.


Where is the missing CP violation?

Given this level of experimental constraints on the CKM matrix, in my opinion this is not the place to look for new physics.


Where's the missing CP violation?

Neutrinos are a leading candidate. Neutrino mixing is described by the PMNS matrix

which is a 3x3 unitary matrix with three real mixing angles and one complex phase, with the complex phase giving rise to CP violation.

So far we know that two of the mixing angles are large, the third is small but not miniscule and the complex phase is unknown.

flavor states mass states3x3 unitarymatrix

PMNS= Pontecorvo-Maki–Nakagawa–Sakata


Where's the missing CP violation?

Supersymmetry, a model in which every fermion has a boson partner and vice-versa. It could solve the dark matter problem (the lightest neutral supersymmetric particle could be the dark matter), it solves the hierarchy problem (controls the Higgs mass due to cancellations), and it could be the source of the missing CP violation.

The only problem is hundreds of searches have come up empty.

“Supersymmetry isn't dead, but it's certainly humbled”

Joann Hewitt


Other possibilities

A fourth generation would give rise to many more complex phases that could account for the missing CP violation

u c t ?

d s b ?

There are hundreds “Beyond the Standard Model” (BSM) physics scenarios, so far none have been confirmed experimentally.


What next?

The exploration of the neutrino sector will be a major focus of the next decade and beyond. Measuring the CP-violating phase of the PMNS matrix will take a huge effort such as DUNE.

In the nearer term, the LHC experiments will continue to search for supersymmetry and a fourth generation.

Muon experiments such as (g-2) and Mu2e at Fermilab will search for beyond-the-standard-model physics in a very general way.


One experimental anomaly

D0 Experiment at Fermilab


Like-sign dimuon charge asymmetry measurement from D0

The quantity being measured is simple, and could arise from B mixing.

If the rate of B→B is the same as B→B, this quantity will be zero. The SM expectation is nearly zero.


D0 like-sign dimuon charge asymmetry

We see a 3.6 standard deviation discrepancy with the Standard Model expectation.

This result can't be confirmed by either CDF or the LHC.

Maybe the super B-factory in Japan will be able to confirm or refute this result.

bins of impactparameter


Summary

Symmetries play an important role in all of physics, especially in particle physics.

The discrete symmetries of C, P and CP play an especially important role in understanding the matter-antimatter asymmetry of the universe.

The violation of CP in the quark sector is too small to account for our universe, so there must be some other source of CP violation.

Candidates are: neutrino mixing, supersymmetry, a fourth generation, or many BSM models.


Summary

This is a long-standing puzzle which sits on the interface of particle physics, astrophysics, and cosmology.

Maybe we have to leave it to the young people to find the answer.


Thank you!


D0 dimuon charge asymmetry.


Reversal of magnet polarities

The detector can give a fake asymmetry. Reversal of the magnet polarities is crucial for canceling these instrumental asymmetries.


CP violation in b-quarks

For over 30 years, the only place where CP violation had been observed was in the neutral Kaon system. That changed in the early 2000s, as the B-factories came online. CP violation should be observable in neutral B mesons, and indeed it was.

The 2016 Panofsky prize celeb rates the discovery of CP violation in the B-mesons.

Jonathan Dorfin and David Hitlin.

symmetries - wichita state university€¦ · 28/10/2015 · of the novel angels and demons. ½...

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