Particle Physics 2

1. Particle Physics 2 Prof. Glenn Patrick Quantum, Atomic and Nuclear Physics, Year 2 University of Portsmouth, 2012 - 2013

2. Last Week - Recap Particle Physics & Cosmology Matter Particles, Generations Spin – Fermions & Bosons Charged Leptons Antimatter Neutral Leptons - Neutrinos Hadrons Strange Particles and Strangeness Symmetries, Conservation Laws Quantum Numbers, Isospin Eightfold Way and Quark Model Charm, Bottom, Top, Quark Counting

3. Today’s Plan 20 November Particle Physics 2 Force Carriers Four Fundamental Interactions Quantum Field Theory Feynman Diagrams Higher Orders/Radiative Corrections Anomalous magnetic moment of muon Charged and Neutral Currents Z and W Vector Bosons Gluons Colour Charge and Quantum Chromodynamics (QCD) Unification of Fundamental Forces, Running Coupling Constants Higgs Boson and Field Copies of Lectures:http://hepwww.rl.ac.uk/gpatrick/portsmouth/courses.htm BOOKS B.R. Martin & G. Shaw, Particle Physics, 3rd Edition, Wiley Donald H. Perkins, Introduction to High Energy Physics, 4th edition, CUP Coughlan et al, The Ideas of Particle Physics, Cambridge

4. I II III Observed in 2000

5. Force Carriers Last week we looked at the Matter Particles (quarks and leptons). This week we look at the four gauge bosons that make up the Force Particles. Now the smallest Particles of Matter may cohere by strongest Attractions, and compose bigger Particles of weaker Virtue. There are therefore Agents in Nature able to make Particles of Bodies stick together by very strong Attractions. And it is the business of experimental Philosophy to find them out. ISAAC NEWTON (1680)

6. The Four Forces of Nature STRONG ELECTRO - MAGNETIC WEAK GRAVITY

7. Forces in Classical Physics Classically, forces are described by charges and fields Field is a physical quantity which has a value for each point in space-time. Can be a scalar or vector field.

8. Quantum Field Theory Forces are transmitted by exchange of force particles between matter particles. 4 forces with different force particles. Quantum Mechanics + Relativity Heisenberg Uncertainty Principle Energy ΔE is “borrowed for a time Δt Maximum distance of exchange particle Photon has zero mass, so infinite range If we associate M with the pion mass, we get the Yukawa potential that we saw when we talked about the “nuclear force” in Nuclear Physics 1.

9. Four Forces of Nature STRONG FORCE Strength: 1, Range: 10-15 m Exchange: Gluon ELECTROMAGNETIC FORCE Strength: 1/137, Range: Infinite Exchange: Photon A FIFTH FORCE? GRAVITY Strength: 6x10-39 m, Range: Infinite, Exchange: ? WEAK FORCE Strength: 10-6 m, Range: 10-18 m Exchange: W±, Z0 Modified gravity? Dark matter, Dark energy, etc.

11. Fundamental Interactions u u e- e- gluon Z0  d d e- e- Strong Weak EM e e e- e- e- W- d n Weak d e u u p d u

12. Feynman Diagrams electron At each ‘vertex’ charge is conserved. Heisenberg Uncertainty Principle allows energy borrowing. Virtual Particle Does not have mass of a physical particle. Known as “off –mass shell” (e.g. not zero for photon)  Richard Feynman Quantum Electrodynamics (QED) positron (anti-electron)

13. Feynman Diagrams Exchange Annihilation • External legs represent amplitudesof initial and final state particles. • Positron is drawn as electron travelling backwards in time. • Internal lines (propagators) represent amplitude of exchanged particle. • Charge, baryon number and lepton number conserved at each vertex. Quark flavour conserved for strong and EM interactions. • Vertices represent coupling strength of interacting particles. • Perturbation theory. Expand and keep the most important terms for calculations.

14. Feynman Diagrams Associate each vertex with the square root of the appropriate coupling constant, i.e. . When the amplitude is squared to yield a cross-section there will be a factor , where n is the number of vertices (known as the “order” of the diagram). For QED: Lowest order Second order Add the amplitudes from all possible diagrams to get the total amplitude, M, for a process  transition probability. Fermi’s Golden Rule

15. Bhabha Scattering e- e- e- e- Z0  e+ e+ e+ e+ e- e- e- e-  Z0 e+ e+ e+ e+ 4 Born Diagrams (Electroweak) + Amplitude = + +

16. Radiative Corrections Vacuum polarisation Higher Order Quantum Loop Diagrams (QED only)

17. Anomalous Magnetic Moment of the Muon + e QED - e B µ µ 0 Z µ µ WEAK W W  µ + e + e + e - e - - e e 3rd order corrections Dirac theory predicts g=2, but this is modified by quantum fluctuations. + STRONG Radiation and re-absorption of virtual photons contributes an anomalous magnetic moment. Lowest order correction ~3.6σ effect New Physics? Hundreds of diagrams!

18. Muon g-2: Testing the Standard Model Experimental measurements of aμ Beyond the Standard Model (BSM) Physics? Uncertainty on aμ and physics reach as the uncertainty has decreased. J.P. Miller et al, Ann. Rev. Nucl. Part. Sci., 62 (Nov. 2012), 237

19. Photon – EM Boson Quantum energy of photon h = Planck’s constant  = frequency 1900Planck Black Body Radiation explained in terms of light quanta  Nobel Prize. 1905Einstein explained the Photoelectric Effectin terms of quanta of energy  Nobel Prize. 1925G.N. Lewisproposed the name Photon for quanta of light. 1925Compton showed quantum (particle) nature of X-rays  Nobel Prize.

20. Charged and Neutral Currents    - W+ Z0 X X N N Neutral Current Charged Current

21. Discovery of Weak Neutral Currents (1973) Bremsstrahlung effects electron  Gargamelle Bubble Chamber

22. Z and W Story Carlo Rubbia (UA1) Simon van der Meer Two Experiments: UA1 and UA2. Rubbia came up with idea and led UA1. Super Proton Synchrotron turned into proton-antiproton collider. Stochastic cooling technique. 1984 UA1 UA2

23. W Boson Discovery – UA1 (1982) “Missing Energy” = neutrino electron

24. Z Boson Discovery – UA1 (1983) electron positron

25. Weak Charged Current and Quarks t b u d c s W W W W- d n d e u u d p u Flavour Changing Charged Currents. Quark flavour never changes except by weak interactions that involve W± bosons. In decay processes, quark always decays to lighter quark to conserve energy. t  b  c  s  u  d + ..  decay finally understood! Weak charged current changes lepton and quark flavours. Possible that flavour changing neutral currents exist beyond (tree level) Standard Model.

26. Gluon Discovery (1979) PETRA e+e- Collider, DESY, Hamburg JADE, TASSO, MARK-J, PLUTO Third jet produced by gluon bremsstrahlung 3-Jet Event quark anti-quark gluon

27. Inside the Proton There are 3 “valence”quarks inside the proton bound together by gluons. Quantum theory allows quarks to change into quark-antiquark pairs for a short time. There is a bubbling “sea” of gluons, quarks and antiquarks. There is however a problem with the basic quark model…..

28. Colour Charge Some particles apparently contain quarks in the same state violates Pauli Exclusion Principle(e.g. ++ = uuu). Proposed that quarks carry an extra quantum number called “colour”. Green Blue Red Quarks Cyan Magenta Yellow Anti-quarks All physical particles are colour neutral or “white”. baryon meson

29. Quark Species u u u d d d c c c charm top t t t b b b bottom quarks antiquarks up down strange s s s

30. 8 Interacting Gluons Expect 9 gluons from all combinations (3 colours x 3 anti-colours): rb,rg, gr,gb,bg,br,rr,gg,bb However, real gluons are a linear combinations of states. This combination is colourless and symmetric. Does not take part in the strong interaction. Hence, we have 8 gluons. These two plus those from , , , , ,

31. Counting Colours In Particle Physics 1, we counted quarks. Can also count colours using R. below top energy threshold

32. Quantum Chromodynamics (QCD) Gluons carry colour+anti-colour charge, e.g. red-anti blue. Colour charge always conserved so quarks can change colour when emitting a gluon. Quantum Chromodynamics (QCD)is the theory of the Strong Interaction in the Standard Model. Since gluons (8) carry colour charge, they can interact with one another! Fragmentation If a quark is pulled from a neighbour, the colour field “stretches”. At some point, it is easier for the field to snap into two new quarks.

33. Confinement Confinement Confinement is a property of the strong force. The strong force works by gluon exchange, but at “large” distance the self-interaction of the gluons breaks the inverse square-law forming “flux tubes”: Quarks and gluons carry “colour “ quantum numbers analogous to electric charge – but only “colourless” objects like baryons (3-quark states) and mesons (quark-antiquark states) escape confinement.

34. Quark Interactions Only one pair of quarks interact, the rest are spectators.

35. Residual Forces How do molecules form if atoms are electrically neutral? How do protons bind to form the nucleus? Protons & neutrons are colour neutral. Residual EM Force Electrons in one atom are attracted to protons in another atom. Residual Strong Interaction between quarks in different protons overcomes EM repulsion.

36. Force Particles Bosons = Spin 1 Force Particle Charge Mass Relative Range (GeV) Strength (m) Strong gluon (g) 0 0 1 10-15 EM photon () 0 0 1/137infinite Weak Z0 boson 091.2 10-5 10-18 W boson 180.4 Bosons = Spin 2 Gravity graviton 0 0 10-39 infinite (not observed yet!)

37. Particles and Forces Summary of how different particles feel the different forces: Charge Strong EM Weak u quark +2/3 Yes Yes Yes d quark -1/3 Yes Yes Yes electron -1 No Yes Yes e 0 No No Yes c quark +2/3 Yes Yes Yes s quark -1/3 Yes Yes Yes muon -1 No Yes Yes  0 No No Yes t quark +2/3 Yes Yes Yes b quark -1/3 Yes Yes Yes tau -1 No Yes Yes  0 No No Yes

38. Unification of the Forces Grand Unification – Unite strong interaction with electroweak interaction. Grand Unified Theories (GUTs) predict that protons are unstable. Final step would then be to add quantum gravity to form a Theory of Everything (TOE). Because gravitons interact with one another field theory is non-re-normalisable. Graviton has not been discovered! ~Planck scale Planck Units Length 1.62 x 10-35 m Time 5.39 x 10-44 s Energy 1.22 x 1019 GeV/c2 Temp 1.42 x 1032 K

39. Electroweak Force or EW symmetry breaking

40. Running Coupling Constants at low energy EM coupling constant = fine structure constant Weak Strong Gravity Coupling constants have an energy dependence due to (higher order) virtual interactions. These change the measured value of the coupling constant and make it depend on the energy scale at which it is measured (logarithmic dependence). The strong and weak couplings decrease with energy whilst the EM coupling increases. It is therefore possible that at some energy scale, all 3 forces become equal.

41. Grand Unification • Grand-Unified Theories (GUT), favoured, (e.g. by non-zero masses) predict the 3 coupling constants (QED, Weak, QCD) to unify at GUT scale of 3x1016GeV. • This unification does not happen in the Standard Model (+GUT), but does in Supersymmetry with a 1 TeV scale. • Starting from the measured values of • αQED(mZ) and sin2W as input, one can predict: • To be compared to the experimental • value (mostly constrained by LEP): • Baryon Number violated in GUTs. Conflict with measurements? Standard Model + GUT LEP, Amaldi et al, 1991 SUSY at 1 TeV + GUT

42. Missing Ingredient: Higgs Sector Generates mass? Graviton not yet found

43. The Mystery of Mass The masses of composite particles like protons and neutrons are mainly given by the motion of the constituents. u However, for fundamental particles, like electrons and quarks it has long been a mystery how they acquire their masses and why they are so different. d u Proton Why do some particles have large masses whilst others have little or no mass? W Electron Mass = 511 eV Photon Mass < 10-18 eV e W boson Mass = 80 x 109 eV Neutrino Mass < 2eV

44. Top Quark Heavier than Silver Atom! Silver (A=108) M(top) = 172 GeV ± 0.9 ± 1.3 GeV

45. Higgs Mechanism Standard Model in basic form leads to massless particles. 1961- 1968: Glashow, Weinberg & Salam developed theory that unifies EM and weak forces into one electroweak force. Predicted weak neutral current. Nobel Prize: 1979 1964: Higgs, Kibble, Brout, Englert et al introduced the Higg’s field. Gives mass to Z and W bosons. Nobel Prize: ?? 1971: Veltman, t Hooft - Solved the problems of infinities through renormalisation. Nobel Prize: 1999 Peter Higgs • Higgs boson is a neutral, scalar (spin=0) particle. • Coupling to particles is proportional to their mass. • No prediction for Higgs mass. • Vacuum should be filled with Higgs field – boson is the quantum of this field in the same way that the photon is the quantum of the EM field.

46. Space is not Empty The classical vacuum just consists of empty space-time and is featureless. In reality, it’s sea of virtual particle-antiparticle pairs from quantum fluctuations. Vacuum is the state of minimum energy for the Universe. WARNING: Quantum field theory gives cosmological constant (or zero point energy) 120 orders of magnitude too high!

47. Higgs Field and Higgs Boson H Higg’s Boson H H H H H H H H H H H H Higg’s Field

48. Mexican Hat Potential State in which the Higgs field is zero is not the lowest energy state. EW - Higgs Field (Scalar) EM - Electric & Magnetic Fields (Vector) Energy lowest when field is zero. Energy lowest when field is not zero. Law is basically symmetric, but equilibrium state is not. Symmetry is said to be spontaneously broken.

49. Electroweak Symmetry Breaking At high enough temperatures, particles were (symmetrically) massless. As the Universe cooled, ring of stable points appeared. W and Z got mass from the field, but the  stayed massless.

50. Higgs Hunting f f e- Z* Z0 H e+ f f Indirect Fit to LEP EW Measurements Direct Searches at LEP Collider Also, limits from Tevatron