AQA A Physics - Particle Physics

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1 PHYA1 (Unit 1) Spec Particles, Antiparticles and Photons AQA A Physics - Particle Physics 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 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 Bill Bavington Page 1 V1.1

2 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/c 2 / kg proton/ / +1 antiproton/ / / neutron/ / 0 antineutron/ / / electron/ / -1 positron/ / / muon/ μ - / -1 antimuon/μ + / / electron neutrino/ / 0 electron antineutrino/ / 0 ~1 ev / (equiv.) muon neutrino/ / 0 muon antineutrino/ / 0 ~1 ev / (equiv.) The proton is a stable particle with a half-life in excess of 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. Bill Bavington Page 2 V1.1

3 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 -, Z 0 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: Bill Bavington Page 3 V1.1

4 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 m. 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 -, Z 0 are massive (80GeV/c 2 for the W + and W -, 90GeV/c 2 for Z 0 ). Since they can only exist by virtue of the Heisenberg Uncertainty Principle, this large mass energy means they can only exist for second, giving them a very limited range ( 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. Bill Bavington Page 4 V1.1

5 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 nonleptons 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. Bill Bavington Page 5 V1.1

6 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: Baryon Number: Example 2: Antimuon decay charge, electron lepton and muon lepton number conservation Reaction: μ + e Charge: Electron Lepton Number: Muon Lepton Number 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 Example 3: Pion-neutron interaction conservation of baryon number and strangeness Reaction: + + Baryon Number: Strangeness: 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. Bill Bavington Page 6 V1.1

7 Figure 7: Baryon Decuplet (the axes are charge and strangeness) Figure 8: Meson Octet (the axes are charge and 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. Bill Bavington Page 7 V1.1

8 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 Type Mass/ Charge/ e Baryon Strangeness name symbol MeV/c 2 number up u ~4 0 Spin/ down d ~5 0 strange s ~150-1 charm c ~ bottom b ~ top t ~180GeV 0 The proton is composed of two up and one down quark ( and a baryon number of ) giving a charge 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: Bill Bavington Page 8 V1.1

9 Figure 9: A Baryon Octet Showing Quark Combinations Figure 10: A Meson Octet Showing 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 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. Bill Bavington Page 9 V1.1

10 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/c 2 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 Bill Bavington Page 10 V1.1

11 Close, F. (2004) Particle Physics: A Very Short Introduction. Oxford: Oxford University Press Energy Without Carbon Radioactive Decay. [Online] Available from: [Accessed: 11th October 2014] Pierce, R., 1.1a Particles & Radiation Matter & Radiation Breithaupt pages 4 to 15 April 8 th, [Online] Available from: [Accessed: 2nd October 2014] Roberts, W., Department of Physics, Florida State University (2006) The Quark Model [Online] Available from: [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: [Accessed: 30th September 2014] The T2K Collaboration 2013 A Brief History of Neutrinos [Online] Available from: [Accessed: 30th September 2014] Wikimedia Commons, Beta Negative Decay [Online] Available from: Wikipedia, Gauge Boson [Online] Available from: Wikipedia, Generation (particle physics) [Online] Available from: Wikipedia, Quark [Online] Available from: Wikipedia, Spin [Online] Available from: Wikipedia, Spin Statistics Theorem [Online] Available from: statistics_theorem Wikipedia, Standard Model [Online] Available from: Wikipedia, Supersymmetry [Online] Available from: Bill Bavington Page 11 V1.1