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AQA A Physics - Particle Physics

PHYA1 (Unit 1) Spec 3.1.1

Particles, Antiparticles and Photons

J.J. Thompson in 1896 identified that cathode rays were fundamental negatively charged particles

rather than ionised molecules and the name ‘electron’, previously proposed by George Johnston

Stoney for the elementary charge, was adopted for this particle. Experiments performed by Ernest

Rutherford in 1917 led him to believe that the hydrogen nucleus was composed of a single particle

which he named the proton. Then he proposed the existence of the neutron in 1920 which was

discovered by James Chadwick in 1932.

Paul Dirac predicted the existence of antimatter (1928). He predicted that each particle has a

corresponding antiparticle. According to his theory: these antiparticles

have exactly the same rest mass as the particle

have exactly the opposite charge to the particle, if that is charged.

annihilate themselves and a corresponding particle if they meet, converting their total mass

in to photons.

Carl Anderson discovered the antiparticle to the electron, called the positron, denoted by , in

1932 whilst photographing cosmic ray trails in a cloud chamber. Particles are either denoted by

symbols with a bar above them or in the case of some charged particles, by the same symbol as for

the particle but with an opposite charge superscript. The preferred symbols for the proton and

antiproton are and respectively but and are sometimes seen.

Photons, being electromagnetic radiation have zero rest mass, but carry energy according to the

Planck formula

. In particle physics we mainly encounter high energy (> 0.1 MeV)

photons: gamma rays ( ), produced by unstable nuclei.

Annihilation

On annihilation, the total mass of the colliding particles is converted into radiation energy in the

form a of a pair of -rays according to Einstein’s mass-energy equivalence relation . PET

(Positron Emission Tomography) scanners rely on electron-positron annihilation: a pair of -rays are

produced travelling in opposite directions (momentum conservation) that are then detected and

their origin computed.

Pair Production

The reverse process to annihilation can occur and for electrons and positrons is called pair

production. Again, momentum (and charge) must be conserved. For conservation of energy, the -

ray must have a minimum energy of 1.022MeV.

Particle physics may be exotic, but particle interactions have to obey two of the most basic

conservation laws of physics: charge and mass-energy. There was no problem with charge, all

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observed particles and interactions involved no charge, single or multiple electron charges or their

positive equivalent and these charge units were conserved in reactions. However, with β— decay, it

was found that some mass-energy was missing. Specifically, when carbon-14 undergoes β— decay to

nitrogen-14, the surplus energy is carried off in the form of kinetic energy of the emitted electron.

The kinetic energy is found to be variable and always less than that calculated. In 1930 Wolfgang

Pauli proposed that another particle, one of low mass and no charge and so hard-to-detect is

emitted at the same time with variable partitioning of the kinetic energy between it and the

electron. He called this particle the neutrino. This particle was discovered experimentally in 1956 by

Frederick Reines and Clyde Cowan Jr.

In 1960, Ray Davis was able to show that the antineutrino (produced in β— decay) is a distinct

particle from the neutrino used in an inverse β- decay.

In 1935, Hidekei Yukawa proposed the existence of exchange particles between nucleons and gave

them the name mesons. Carl Anderson (1936) discovered a ‘heavy electron’ (has electron charge but

106 MeV mass) which he thought to be this particle and called it the μ-meson. It is now known to be

a lepton and was renamed the muon in consequence. Muons decay into electrons and antineutrinos.

Yukawa’s meson was discovered by Cecil Powell (1947) and he called it the π-meson, often

contracted to pion. Pions also decay, but into muons and antineutrinos. Less than one year later

Rochester and Butler discovered another kind of short-lived particle, now called a K meson or kaon.

Kaons decay into pions, muons and antineutrinos and antimuons and neutrinos. There are three

kinds of muon, three kinds of pion and three kinds of kaon. One kind of each particle type carries a

positive charge, a second kind of each type carries a negative charge and the third kind of each type

is neutral.

Experiments performed at Brookhaven in 1962 showed that the neutrinos produced during pion

decays into muons are different from those produced during β decays into electrons, so neutrinos

can be divided into electron-neutrinos and muon-neutrinos as well as their corresponding

antiparticles, and .

Table 1: Some Example Particles and Their Antiparticles

Particle/Symbol/Charge Corresponding Antiparticle/Symbol/Charge

Rest Mass in MeV/c2 / kg

proton/ / +1 antiproton/ / -1 938 / 1.67×10-27

neutron/ / 0 antineutron/ / 0 939 / 1.67×10-27

electron/ / -1 positron/ / +1 0.511 / 9.11×10-31

muon/ μ- / -1 antimuon/μ+/ +1 105.659 / 1.88×10-28

electron neutrino/ / 0 electron antineutrino/ / 0 ~1 eV / 1.8×10-36 (equiv.)

muon neutrino/ / 0 muon antineutrino/ / 0 ~1 eV / 1.8×10-36 (equiv.)

The proton is a stable particle with a half-life in excess of 1032 years. All other baryons are unstable

and decay into protons. A free neutron has a half-life of 10.2 minutes and decays into a proton, an

electron and an electron antineutrino (β— decay) but in stable nuclei it is stabilised as decay would

make the nucleus proton-rich so less stable and this is energetically unfavourable.

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Particle Interactions

There are four ‘forces’ (or interactions) of

nature which, in order of apparent

increasing strength, are: gravitation;

weak interaction; electromagnetic

interaction and the strong interaction. In

classical physics forces are usually

conceived as fields, which spread over

space. In quantum theory, forces are

carried (or mediated) by exchange

particles known as gauge bosons, with

different types of gauge boson for each

force. Richard Feynman developed a

diagrammatic representation for particle

interactions by exchange particles. An example is shown here for the repulsion between two

protons.

Table 2: The Forces of Nature

Force Intensity Carrier (Gauge Bosons) Example

Gravitation ~10-42 Graviton Galaxies, star systems

Weak force ~10-5 Weak Bosons: W+, W-, Z0 β-decay

Electromagnetism ~10-2 Virtual photon Electron shells around atoms

Strong force 1 Gluon Nuclear binding

It is assumed that you already have some familiarity with the properties of gravitation and of the

electromagnetic force.

The strong force (or interaction)

This has the following properties:

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It binds the nucleons found in atomic nuclei together against the electrostatic repulsion of

the protons. This is known as the residual strong force.

It has a range of 3 – 4 femtometres or Fermi (fm).

It is attractive from 3 – 4 fm down to 0.5 fm. If nucleons are closer than this, the force is

repulsive preventing them collapsing into each other.

Although, like gravitons and virtual photons, gluons are massless, the strong force does not

have normal inverse-square law behaviour with distance. It grows stronger as quark

separation increases constraining the quarks to a limited ‘femtouniverse’ of 10-15m.

The residual strong force behaves the same way between two protons, two neutrons or

between one of each.

Within hadrons, the force between quarks and antiquarks is mediated by gluons, but

between the baryons of an atomic nucleus, the residual strong force is mediated by π-

mesons (more usually called pions).

Weak Force

Unlike the exchanges particles of other three forces which are mass less, the exchange particles of

the weak force, W+, W-, Z0 are massive (80GeV/c2 for the W+ and W-, 90GeV/c2 for Z0). Since they can

only exist by virtue of the Heisenberg Uncertainty Principle, this large mass energy means they can

only exist for 10-24 second, giving them a very limited range (10-17- 10-16 m), making the force appear

weak on a scales of the size of a nucleon (10-15 m). If provided with sufficient energy, ~100GeV in a

particle accelerator, the weak force is then found to be relatively as strong as the electromagnetic

force. A major example of a weak interaction is β—decay where a neutron changes into a proton.

Feynman diagrams to illustrate beta-minus and beta-plus decays (figures 3 and 4) are as follows.

Figure 3 Figure 4

Some more examples of Feynman diagrams are those for electron capture and for neutron-neutrino

interaction. These are figures 5 and 6.

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Figure 5 Figure 6

Classification of Particles with Definitions

Hadron – particle and antiparticles that interact through the strong interaction (force). They are

composed of quarks.

Baryon – a hadron composed of three quarks. All baryons are either protons or decay either directly

or indirectly into protons.

Antibaryon – a hadron composed of three antiquarks.

Baryons are assigned a baryon number of +1 and antibaryons a baryon number of -1. Other particle

types are assigned a baryon n umber of zero. Baryon number, like mass-energy and charge, is

conserved in all interactions.

Nucleon – a proton or neutron as contained in an atomic nucleus

Meson – a hadron composed of a quark and an antiquark.

Lepton – one of a number of particles that are not hadrons and do not interact through the strong

force, do interact through the weak force and may (electrons, positrons) interact through the

electromagnetic force. Leptons change into other leptons through the weak interaction and can be

produced or annihilated in particle-antiparticle interactions. Leptons do not break down into non-

leptons and so appear to be elementary particles. Additionally to the conservation of charge and

mass-energy, lepton interactions obey conservation of lepton number. A complication is that there

are two branches of lepton number: an electron branch and a muon branch and these are separately

conserved as well. Baryons and mesons have a lepton number of zero.

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Table 3: Lepton Numbers

Lepton Properties Electron Lepton Number Muon Lepton Number

e-, +1 0

e+, -1 0

μ-, 0 +1

μ+, 0 -1

Examples of interactions showing the conservation laws.

Example 1: Proton-antiproton interaction – charge and baryon number conservation

Reaction: + + Charge: +1 + -1 +1 + -1 Baryon Number: +1 + -1 0 + 0

Example 2: Antimuon decay – charge, electron lepton and muon lepton number conservation

Reaction: μ+ e+ + +

Charge: +1 +1 + 0 + 0 Electron Lepton Number: 0 -1 + 0 + +1 Muon Lepton Number -1 0 + -1 + 0 Strangeness

K-mesons or kaons have some unusual characteristics, a relatively long life and frequent decay into

pion-antipion pairs. So kaons came to be known as strange particles. When other particles (e.g.

lambda particle , 1950 Hopper and Biswas) were found with similar properties, the concept of a

new particle property called strangeness was introduced in 1953 by Murray Gell-Mann and Nishijima

to account for which reactions are observed and which are unobserved. Strangeness is always

conserved in strong interactions but is not conserved in weak interactions.

Table 4: Strangeness of some baryons and mesons (N.B. is for sigma and for lambda particles)

Particle , , , , , ,

Strangeness 0 0 +1 -1 -1 -2 -1

Example 3: Pion-neutron interaction – conservation of baryon number and strangeness

Reaction: + + Baryon Number: 0 + +1 0 + +1 Strangeness: 0 + 0 +1 + -1

Quarks and Antiquarks

The discoveries of many subatomic particles in the mid-twentieth century created a problem in

classification. Various diagrammatic schemes to arrange and organise them were devised, involving

octets and decuplets.

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Figure 7: Baryon Decuplet (the axes are Figure 8: Meson Octet (the axes are charge and

charge and strangeness) strangeness)

In 1964 Murray Gell-Mann and George Zweig independently proposed the existence of quarks as the

fundamental building blocks of hadrons. The model was a development of Gell-Mann’s particle

classification system which he called The Eight-fold Way. In this scheme, the quark arrangements are

elements of special unity group SU(3). This is a mathematical group of unitary matrices and the

octets and other diagrams may be seen as different representations of this group. Note that an

introduction to group theory is beyond the scope of this document.

In 1968 at the Stanford Linear Accelerator Centre, deep inelastic scattering experiments

demonstrated that the proton contains much smaller ‘point-like’ objects so is not an elementary

particle itself. It was some time before these objects, originally called ‘partons’ were identified by

further scattering experiments as quarks. According to current understanding, quarks are

elementary particles. Quarks have mass, charge, colour charge, spin and flavour properties and can

be either particles or antiparticles (given generic symbols and . Considering these attributes in

turn:

Quark masses are considerably less than the nucleons which contain them; the difference being

made up of kinetic energy.

Quarks have fractional amounts of the elementary charge, combining to give either electrically

neutral particles or particles carrying an integer charge.

Colour charge can take one of three values: red, blue or green in a quark and one of antired, antiblue

or antigreen in an antiquark. It is the colour charge which is acted upon by the strong force. The

exchange particles between quarks (gluons) carry a colour-anticolour charge combination,

permitting strong interaction between quarks by exchanges of colour charge.

Flavour is involved with the weak force and for ‘normal’ nucleons (found in the atomic nucleus) can

be either ‘up’ or ‘down’. The colour charge is independent of the flavour of quark, but the electric

charge is linked to the flavour. Antiquarks have the corresponding antiflavour: antiup and antidown.

Unstable higher mass particles contain other flavours of quark. The only one of these required for

AQA ‘A’ Physics is the strange quark which is a heavier version of the down quark. It is this particle

which gives kaons and other particles such sigma and lambda particles their non-zero strangeness.

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Spin is not required for AQA ‘A’ Physics, but for completeness , all elementary particles, that is

quarks, leptons and the bosons are considered to have an intrinsic quantized angular momentum,

called ‘spin’. Although it bears some resemblance to classical spinning objects, there are significant

differences and it is best thought of as another quantum mechanical property. It is defined by a spin

quantum number that takes positive half-integer values. Spin has a magnitude and direction, similar

to a normal vector and is of half integer multiples of the ‘reduced Planck’s constant’, which is

equal to . Particles having half-integer spin, the leptons, quarks, neutrons and protons are

classed as fermions and obey Fermi-Dirac statistics and so obey the Pauli Exclusion Principle,

whereby identical fermions cannot simultaneously occupy the same quantum state. Particles having

integer spin (including zero) are bosons and obey Bose-Einstein statistics, where an unlimited

number of such particles can condense into the same quantum state. This difference between

bosons and fermions is a product of the spin-statistics theorem which concerns how the wave

functions which define a system of identical spin particles behaves when two particles are swapped.

Bosons have symmetric wave functions and fermions antisymmetric wave functions under such

particle pair swaps.

The first three rows of the following table contain the quarks required for AQA ‘A’ Physics, but for

completeness, the other possible quarks are given in the remaining three rows. Note that the

corresponding antiquarks have the same mass but the other properties are all sign reversed. The

symbols are given a bar to denote the antiparticle, just as for composite particles. Note that, due an

accident of history, the strange particle has ended up with a negative value for strangeness.

Table 5: Properties of Quarks

Type name

Type symbol

Mass/ MeV/c2

Charge/ e Baryon number

Strangeness Spin/

up u ~4

0

down d ~5

0

strange s ~150

-1

charm c ~1500

0

bottom b ~4500

0

top t ~180GeV

0

The proton is composed of two up and one down quark ( ) giving a charge of

and a baryon number of

. The neutron is likewise composed of one

up and two down quarks ( ) giving a charge of

and a baryon number of

. The antiproton has quark structure (so charge -1 and baryon number -1) and

the antineutron (so charge 0 and baryon number -1).

The various particle decuplets and octets can now be reinterpreted as different quark combinations.

For example, the baryon and meson octets:

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Figure 9: A Baryon Octet Showing Figure 10: A Meson Octet Showing Quark Combinations Quark Combinations

The weak interaction changes the flavour of quark, so for example, a beta-minus decay can be

thought of as a change of a down quark to an up quark instead of the change of a neutron to a

proton. So, the corresponding Feynman diagram for a beta-minus decay showing the quark flavour

changes is shown here in below.

Figure 11: Beta-minus Decay showing

change of quark flavour

The following topics are not required for A-level but are included as more background.

Standard Model

Developed by a number of particle physicists during the latter part of the half of the twentieth

century, the standard model envisions three generations of particles. Shelden Glashow discovered

how to combine the electromagnetic and weak interactions into the electroweak theory in 1961.

Stephen Weinberg and Abdus Salam incorporated the Higgs mechanism into this theory, giving the

standard model its modern form. The standard model does not include a full theory of gravitation,

does not account for particle masses or coupling constants (strengths of forces interactions) or the

asymmetry between the presence of matter and antimatter in the universe.

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The standard model gives three generations of fermions, both quarks and leptons but one (or in the

case of the weak force, a single set of) gauge bosons for each force interaction. Experimental data on

precision electroweak measurements suggests that there are no further generations of such

particles. The standard model cannot account for why there are exactly three generations of matter.

Figure 12: Standard Model of Elementary Particles

Higgs Force and Particle

In 1964, Peter Higgs proposed, along with Robert

Brout, Francois Englert, Gerald Guralnik, C.R. Hagen and Tom Kibble, the existence of the Higgs field

permeating all space which is able to give rise to the masses of those elementary particles which

have mass. The theory was able to account for both the high mass of the weak bosons and the lack

of mass of photons and gluons. This field is mediated by a particle, known as the Higgs particle which

was predicted to be a massive scalar (spin-zero) boson, although it is not classed as a gauge boson.

In July 2012, at the Large Hadron Collider, two experiments identified a 125GeV/c2 particle,

consistent with the Higgs predictions. After further work, in March 2013, this was tentatively

identified to be the Higgs boson.

Supersymmetry

The theories of supersymmetry (SUSY) arise partly out of the theories of mathematical symmetries

which underpin all of the particle models at a deeper level and partly to stabilize the quantum

theories of behaviour at high energies of the existing standard model particles and the Higgs boson.

In SUSY, each fermion is partnered by a high mass boson (superpartner) with a spin differing from it

by a half-integer and similarly, each boson has a superpartner that is a fermion. The superpartner

bosons are denoted by the name of their fermion partner, but prefixed by ‘s’. Thus, for example the

superpartner of the electron is the ‘selectron’. The fermion superpartners of the bosons are denoted

by the boson name (truncated for euphony, if required) suffixed by ‘ino’. Thus the superpartner of

the gluon is the ‘gluino’. Due to these ‘gauginos’ sharing the same quantum numbers, they can

combine in different ways to form ‘neutralinos’ which are candidates for Dark Matter. So far, no

experimental evidence for supersymmetry exists, all evidence is indirect.

References and Sources for Diagrams

Breithaupt, J. (2008) AQA Physics A AS. Cheltenham: Nelson Thornes

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Close, F. (2004) Particle Physics: A Very Short Introduction. Oxford: Oxford University Press

Energy Without Carbon Radioactive Decay. [Online] Available from: http://www.energy-without-

carbon.org/RadioactiveDecay [Accessed: 11th October 2014]

Pierce, R., 1.1a Particles & Radiation Matter & Radiation Breithaupt pages 4 to 15 April 8 th, 2010.

[Online] Available from: http://slideplayer.us/slide/274428/ [Accessed: 2nd October 2014]

Roberts, W., Department of Physics, Florida State University (2006) The Quark Model [Online]

Available from: http://www.physics.fsu.edu/users/roberts/roberts_quark_model.html [Accessed:

11th October 2014]

The Particle Data Group, Lawrence Berkeley National Laboratory (2014) The Particle Adventure The

Fundamentals of Matter and Force. [Online] Available from: http://www.particleadventure.org

[Accessed: 30th September 2014]

The T2K Collaboration 2013 A Brief History of Neutrinos [Online] Available from: http://t2k-

experiment.org/neutrinos/a-brief-history/ [Accessed: 30th September 2014]

Wikimedia Commons, Beta Negative Decay [Online] Available from:

http://commons.wikimedia.org/wiki/File:Beta_Negative_Decay.svg

Wikipedia, Gauge Boson [Online] Available from: http://en.wikipedia.org/wiki/Gauge_boson

Wikipedia, Generation (particle physics) [Online] Available from:

http://en.wikipedia.org/wiki/Generation_(particle_physics)

Wikipedia, Quark [Online] Available from: http://en.wikipedia.org/wiki/Quark

Wikipedia, Spin [Online] Available from: http://en.wikipedia.org/wiki/Spin

Wikipedia, Spin Statistics Theorem [Online] Available from: http://en.wikipedia.org/wiki/Spin–

statistics_theorem

Wikipedia, Standard Model [Online] Available from: http://en.wikipedia.org/wiki/Standard_Model

Wikipedia, Supersymmetry [Online] Available from: http://en.wikipedia.org/wiki/Supersymmetry