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Elementary Particle Physics David Milstead [email protected] A4:1021 tel: 5537 8663/0768727608 FK7003 1 Format ● 14 lecture sessions ● 2 räkneövningnar ● Homepage http://www.fysik.su.se/~milstead/teaching/2017/fk7003/course.html ● Course book Particle Physics (Martin and Shaw,3rd edition, Wiley) ● ● Supplementary books which may be useful but which are not essential Introduction to Elementary Particles (Griffiths, Wiley) Subatomic Physics (Henley and Garcia, World Scientific) Particles and Nuclei (Povh, Rith, Scholz and Zetsche, Springer) ● Earlier editions can be used – handouts to be provided where appropriate. Quarks and Leptons (Halzen and Martin, Wiley) Assessment 2 x inlämningsuppgifter tenta FK7003 2 Lecture outline Lecture Topic Martin and Shaw (2nd edition) Martin and Shaw (3rd edition) Extra info 1 Antiparticles, Feynman diagrams, em and weak forces 1 1 2 Units, fundamental particles and forces, Charged leptons and neutrino oscillations 2 2 3 Quarks and hadrons, multiplets, resonances 2,5 3 4 Räkneövning 1 5 Symmetries: Noether’s theorem, C, P , T, CP and CPT 4,10 5,10 6 Hadrons: isospin and symmetries 5 6 7 Hadrons: bound states, quarkonia 6 6 8 Quantum chromodynamics: asymptotic freedom, jets, elastic lepton-nucleon scattering 7 7 9 Räkneövning 2 10 Relativistic kinematics: four-vectors, cross section Appendix B Appendix B Handouts 11 Deep-inelastic lepton-nucleon scattering: quark parton model, structure functions, scaling violations, parton density functions 7 7 Handouts 12 Weak interaction: charged and neutral currents, Caibbo theory 8 8 13 Standard Model: renormalisation, Electroweak unification, Higgs 9 9 14 Beyond the Standard Model: hierarchy problems, dark matter, supersymmetry, grand unified theories 11 11 15 Accelerators – synchrotron, cylcotron + LHC 3 4 Handouts 16 Detectors: calorimeter, tracking, LHC detectors, particle interactions in matter 3 4 Handouts FK7003 Handout 3 particle physics research Particle physics is frontier research of fundamental importance. FK7003 4 The aim of this course ● ● Survey the elementary constituents in nature Identification and classification of the fundamental particles Theory of the forces which govern them over short distances Experimental techniques Accelerator Particle detectors FK7003 5 Lecture 1 Basic concepts Particles and antiparticles Klein-Gordon and Dirac equations Feynman diagrams Electromagnetic force Weak force FK7003 6 Going beyond the Schrödinger equation E 2 p 2c 2 m2c 4 Collider experiments typically involve energies of several hundred GeV. Eg a proton (mass 1 GeV) with 50 GeV energy E pc - relativity effects can't be ignored. Quantum field theory necessary. small Classical mechanics Quantum mechanics (Schrödingers equation) fast Relativistic mechanics Quantum field theory (Dirac, KleinGordon equations, QED, weak, QCD) FK7003 7 Implications of introducing special relativity Consider a particle of charge q, mass m with momentum p moving along the x-axis What is its energy ? Special relativity gives us a choice: E p 2 c 2 m 2 c 4 E p 2c 2 m 2c 4 (1.2) E p 2 c 2 m 2 c 4 (1.1) (1.3) Surely the negative energy solution is unphysical and daft. Can't we just ignore it ? No - from quantum mechanics, every observable must have a complete set of eigenstates. The negative energy states are needed to form that complete set. They must mean something.... FK7003 8 Negative energy states Plane wave corresponding to momentum p along x-direction. Positive energy solution: x, t Ne px E t px E t i pc 2 mc 2 2 x E x t (1.5) (moves to the right) p Negative energy solution: x, t Ne x (1.4) E px E t i E 0 (1.6) E E 0 E E t t (1.7) p p t E 0 Negative energy state moving forwards in time is equivalent to a positive energy state moving backwards in time. x t FK7003 9 What does a particle moving backwards in time look like ? What are the implications of moving backwards in time ? Lorentz force on particle (charge - q) in a B-field travelling forwards in time at a certain point in space and time r and t d 2r dr F r , t qv B (1.8) F r , t m 2 q B (1.9) dt dt Force on a particle with charge q moving backwards in time: dt -dt. d 2r dr d 2r dr F r ,t m 2 q B (1.10) easily rearranged to (1.9) F r , t m 2 q B dt dt dt dt The equation of motion of charge q moving backwards in time in a magnetic field is the same as the equation of motion of a particle with charge -q moving forwards in time. FK7003 10 Antiparticles Special relativity permits negative energy solutions and quantum mechanics demands we find a use for them. (1) The wave function of a particle with negative energy moving forwards in time is the same as the wave function of a particle with positive energy moving backwards in time. Ok, the negative energy solutions must be used but we can convert them to positive energy states if we reverse the direction of time when considering their interactions. (2) A particle with charge q moving backwards in time looks like a particle with charge –q moving forwards in time. General argument that a particle with negative energy and charge q behaves like a particle with positive energy and charge -q. We expect, for a given particle, to see the ”same particle” but with opposite charge: antiparticles. Antiparticles can be considered to be particles moving backwards in time - Feynman and Stueckelberg. Hole theory (not covered) provides an alternative, though more old fashioned way of thinking about antiparticles. FK7003 11 Electron and the positron 1897 e- discovered by J.J. Thompson 1932 Anderson measured the track of a cosmic ray particle in a magnetic field. Same mass as an electron but positive charge The positron (e+ ) - anti-particle of the electron Nobel prize 1936 B 1.5T (out of page) F q v B (to left) p r eB Every particle has an antiparticle. Some particles, eg photon, are their own antiparticles. Special rules for writing particles and antiparticles, eg antiproton p, given in next lecture. FK7003 12 How particles interact – exchange forces Electromagnetic force Particles carrying charge interact via the exchange of photons (g) mass=0, spin=1 (boson) - - + photon - - - + - - - + Attraction Repulsion Easy to visualise but beware this is a useful but limited "visual toy model" for the quantum world. A photon is emitted - we don't know its momentum p 0 and we don't know where it is x 2p The "quantum path" between the start and end points is not like a classical path. The reaction can take place as per the diagram. FK7003 13 Electromagnetic processes Two possible interpretations (1) A particle moves forward in time, emits two photons at ( x2 , t2 ) and moves back in time with negative energy to point ( x1 , t1 ) where it scatters off a photon and moves forward in time. There is only one particle moving through space and time. (2) At point ( x1 , t1 ) an antiparticle-particle pair is produced. The antiparticle moves forward to point ( x2 , t2 ) where it annihilates with another particle producing to two photons. FK7003 14 Feynman diagrams One possible diagram for Important mathematical tool for calculating rates of processes - Feynman rules. Qualitative treatment here but more detailed e e e e treatment later in the course. Represent any process by contributing diagrams. Strategy: (1) Build Feynman diagrams for electromagnetic processes (2) Consider energy-momentum conservation/violation (3) Consider how they can be used for simple rate estimates. (4) Show Feynman diagram formalism for other fundamental forces. FK7003 15 (1) Electromagnetic processes Convention - time flows to the right The lines do not represent trajectories of a particle. Arrow for antiparticle goes "backward in time". Lines should not be taken as "trajectories" of particles Interactions occur at a vertex. vertex g e e A basic process. Rule of thumb: a vertex carries a factor em associated with the probability of that interaction taking place. Probability 1 e 2 4 0 c s 1 (1.24) Fine structure constant 137 t FK7003 16 (1) Basic electromagnetic diagrams vertex Consider all electromagnetic processes built up from basic processes: (a ) to (h) The basic processes are never seen since they violate energy conservation (next slide) They can be combined to make observable processes: e e e e s t (e) and ( f ) ( g ) vacuum e e g FK7003 (h) e e g vacuum ((g) and (h) become clear soon) 17 (2) Is energy conservation violated ? e e e e (annihilation) Electron and positron in centre-of-mass frame: E1e E1e , p1e p1e (1.24) virtual particle (g) Eg , pg Annihilate to form photon Eg E1e E1e , pg p1e p1e 0 (1.25) E E1e E1e Eg 0 E1e , p1e 2 e Eg2 pg2c 2 mg2 c 4 p1g 0 , m1g 0 Eg 0!! E E1e E1e 0 (1.26) E1e , p1e , p2 e real particle t Nevertheless, the process happens. Two qualitative ways to interpret this (a) Energy-momentum conservation is violated for the short interaction time E E 2 e , p2 e Uncertainty principle: violation can happen over time t (1.27) E (b) The mass of the photon is not zero (goes off mass-shell) for a short time t E c2 (1.28) as permitted by the uncertainty principle t (1.29) c2 m Internal lines correspond to virtual particles (we can never see them) External lines correspond to real particles which can be observed and always carry the expected mass. Mass change m Important: however we think about our diagrams, we never measure energy and momentum violation. The energy and momenta of the real particles always add up: E1e E1e E2 e E2 e p1e p1e p2 e p2 e (1.30) FK7003 s t 18 (3) Using Feynman diagrams Even with a qualitative treatment it is possible to see how the Feynman diagram picture agrees with observed reactions. Aim: compare rates of e e g g and e e g g g Start e e g g and consider possible contributing diagrams. Use the simplest possible diagrams (leading order) - in this case diagrams with two vertices. Life gets much easier if you don't think about things going back in time. Instead, take your diagram, think of the lines as "rubber" and see how they can be bent in such a way as to change the time order of the vertices. Two possibilities here : (a) e emits a photon and goes on to annihilate with a e leading to a photon. (b) e emits a photon and goes on to annihilate with a e leading to a photon. Usually only one such diagram is shown and the others implied. Diagrams with two vertices : probability of process occuring 2 FK7003 Negative energy solutions –antiparticles. QM insists we use them! 19 (3) Using Feynman diagrams e e g g g Three vertices probability 3 R Rate e e g g g Rate e e g g 3 2 0.7 102 (1.31) Observed R 103 Qualitative Feynman diagram picture gives suppression with (very) rough accuracy. + other contributions Full QED calculation gives correct rates. FK7003 20 Question For the interaction e e g g draw three Feynman diagrams which would be suppressed wrt to those we studied earlier. FK7003 21 (3) Using Feynman diagrams e- 2 e- e- Two electrons are observed to repell each other: e e e e Many different indistinguishable processes, eg one-photon, two-photon exchange, 4 can contribute to the scattering 1 Coupling is weak 1 137 higher order processes contribute less and less to the calculation and can be safely be neglected in any approximate solution. 6 e+ e- ee- e+ e- eee+ …. FK7003 22 Question For the interaction e e g g g draw four possible time ordered Feynman diagrams for the leading order (3 vertices) processes FK7003 23 Understanding forces Go beyond EM force Generic force between particles A and B via exchange of particle X . Initially particle A at rest: p 0, E mAc 2 (1.32) After vertex: Particle A: p p A , E E A p 2c 2 mA2 c 4 1/2 (1.33) Particle X : p p A , E E X p 2c 2 mX2 c 4 1/2 (1.34) Energy difference between initial and final state: E E X E A mAc 2 2 pc ( p ) (1.35) EX , pA M X c 2 ( p 0) (1.36) E 0 (apparent energy conservation violation!) Energy violation can only persist time: t E minimum energy violation corresponds to longest time tmax M X c2 m c , 0 2 A EA , pA (1.37) Max speed v c Range of force R MXc (1.38) Electromagnetic range Rg due to massless photon. FK7003 24 The weak force e- e- e- W- (bdecay) e+ ne (neutrinos – next lecture) Use same formalism as for electromagnetic force Very brief overview: Exchange of 3 spin-1 particles: Z 0 (mass=91.2 GeV/c 2 ) ,W , W (mass=80.4 GeV/c 2 ) range RW , Z MW c 2 1018 m (tiny - proton "radius" 1 0 15m) Define coupling constant analagous to fine structure constant gW2 W 4 c (1.39) e2 4 0 c gW analagous to electric charge ( gW2 1 W 4 c 240 (1.24) "weak charge") 1 (1.41) , the weak force is only weak due to W , Z masses . 137 FK7003 25 The fundamental forces Different exchange particles mediate the forces: electromagnetic strong weak Interaction Relative strength Range Exchange Mass (GeV) Charge Spin Strong 1 Short ( fm) Gluon 0 0 1 Electromagnetic 1/137 Long (1/r2) Photon 0 0 1 Weak 10-9 Short ( 10-3 fm) W+ W-,Z 80.4,80.4, 91.2 +e,-e,0 1 Gravitational 10-38 Long (1/r2) Graviton ? 0 0 2 FK7003 No quantum field theory yet for gravity 26 Summary Antiparticles and spin states are predicted when when relativity and quantum mechanics meet up! Antiparticles correspond to negative energy states moving backwards in time. Feynman diagram formalism developed and used for (very basic) rate estimation Generic approach for all forces Weak force is weak because of the mass of the exchanged particles. FK7003 27