“Elementary Particles” Lecture 5

# “Elementary Particles” Lecture 5

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## “Elementary Particles” Lecture 5

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1. “Elementary Particles”Lecture 5 Niels Tuning Harry van der Graaf Niels Tuning (1)

2. Thanks • Ik ben schatplichtig aan: • Dr. Ivo van Vulpen (UvA) • Prof. dr. ir. Bob van Eijk (UT) • Prof. dr. Marcel Merk (VU) Niels Tuning (2)

3. Homework

4. Exercises Lecture 4: Adjointspinor: + Niels Tuning (4)

5. Exercises Lecture 4: Niels Tuning (5)

6. Exercises Lecture 4: Niels Tuning (6)

7. Exercises Lecture 4: Niels Tuning (7)

8. Exercises Lecture 4: Niels Tuning (8)

9. Exercises Lecture 4: Niels Tuning (9)

10. Exercises Lecture 4: Niels Tuning (10)

11. Exercises Lecture 4: Niels Tuning (11)

12. Plan 11 Feb • Intro: Relativity and accelerators • Basis • Atom model, strong and weak force • Scattering theory • Hadrons • Isospin, strangeness • Quark model, GIM • Standard Model • QED • Parity, neutrinos, weak inteaction • QCD • e+e- and DIS • Higgs and CKM 1900-1940 18 Feb 1945-1965 4 Mar 1965-1975 18 Mar 1975-2000 22 Apr 2000-2013 13 May Niels Tuning (12)

13. Summary Lects. 1-4

14. Lecture 1: Accelerators & Relativity • Theory of relativity • Lorentz transformations (“boost”) • Calculate energy in collissions • 4-vector calculus • High energies needed to make (new) particles Niels Tuning (14)

15. Lecture 2: Quantum Mechanics & Scattering • Schrödinger equation • Time-dependence of wave function • Klein-Gordon equation • Relativistic equation of motion of scalar particles • Dirac equation • Relativistically correct, and linear • Equation of motion for spin-1/2 particles • Described by 4-component spinors • Prediction of anti-matter Niels Tuning (15)

16. Lecture 2: Quantum Mechanics & Scattering • Scattering Theory • (Relative) probability for certain process to happen • Cross section • Fermi’s Golden Rule • Decay: “decay width” Γ • Scattering: “cross section” σ Scattering amplitude in Quantum Field Theory Classic a → b + c a + b → c + d Niels Tuning (16)

17. Lecture 3: Quarkmodel & Isospin • “Partice Zoo” not elegant • Hadrons consist of quarks • Observed symmetries • Same mass of hadrons: isospin • Slow decay of K, Λ: strangeness • Fermi-Dirac statistics Δ++, Ω: color • Combining/decaying particles with (iso)spin • Clebsch-Gordan coefficients Niels Tuning (17)

18. Lecture 4: Gauge symmetry and Interactions • Arbitrary “gauge” • Physics invariant • Introduce “gauge” fields in derivative • Interactions! • QED • Weak interactions • QCD 1 photon 3 weak bosons 8 gluons Niels Tuning (18)

19. Outline for today: • Reminder: Gauge invariance, and the Lagrangian • Electro-magnetic interactions: QED Electric charge • Weak interactions: “QFT” Weak isospin/Flavour • Strong interactions: QCD Colour • e+e- scattering • e+e- →μ+μ- • e+e- →ccDiscovery of charm and colour (quantity “R”) • e+e- →qq g Discovery of the gluon • e+e- →Z 3 neutrino’s • e+e- →WW • Deep Inelastic Scattering (DIS) (lepton-proton scattering) • Quarkmodel: do quarks exist?? • Sub-structure • Bjorken-x, sum rules • Scaling (violations) • ‘Parton density functions’ (pdf) and ‘structure functions’ Niels Tuning (19)

20. QED & QCD

21. Lagrangian  Equation of motion • spin-0 particles (Klein-Gordon) • spin-1/2 fermions (Dirac) • Photons Klein-Gordon equation Dirac equation Maxwell equations Niels Tuning (21)

22. Gauge Invariance We started globally: • Assumesymmetryψ→ψ’=ψeiα(x) • Keep Eqsvalid • Covariantderivative • Arbitrarygauge • Keep Eqsvalid • Thisimplies: ψ→ψ’=ψeiα Then we went local: Niels Tuning (22)

23. Quantum Electro Dynamics - QED m qγμ Interaction with coupling q Fermion ψwith mass m Photon field Aμ Niels Tuning (23)

24. Symmetries • Charge U(1) (QED) • IsospinSU(2) (Weak) • ColorSU(3) (QCD) (Why 8…? Group theory: 3x3=8+1 … ) Niels Tuning (24)

25. More gauge transformations • We had: U(1) (QED) • Then: SU(2) (Weak) • How about: SU(3) (QCD) a=1,8: 8 gluons Another covariant derivative: with 8 Aμfields: which transform as: Gluonic field tensor: Niels Tuning (25)

26. QCD Lagrangian qγμ m Interaction with coupling q 8 Gluon fields Aμ Self-interaction Fermion ψwith mass m ! Niels Tuning (26)

27. Lecture 4: QED and QCD QED QCD • Local SU(3) gauge transformation • Introduce 8 Aμa gauge fields • Non-“Abelian” theory, • Self-interacting gluons • Gluons have (color) charge • Different “running” • Local U(1) gauge transformation • Introduce 1 Aμ gauge field • “Abelian” theory, • No self-interacting photon • Photons do not have (electric) charge • Different “running” Niels Tuning (27)

28. Standard Model now (almost) complete! Niels Tuning (28)

29. “Running” Coupling Constant (QED) • Consider e+e- →e+e-scattering: • More possibilities! • “Higher order” diagrams • Each coupling has strength 1/137 • Perturbation series α~q2 q q Niels Tuning (29)

30. “Running” Coupling Constant (QED) • Consider e+e- →e+e-scattering: • More possibilities! • “Higher order” diagrams • Each coupling has strength 1/137 • Perturbation series • Effectively: α~q2 q q Niels Tuning (30)

31. “Running” Coupling Constant (QED) • Coupling depends on the scale! • α(0)=1/137 • α(M2Z)=1/128 • Effectively: Niels Tuning (31)

32. “Running” Coupling Constant • Do you need all fermions in the loop?? • Yes: Niels Tuning (32)

33. “Running” Coupling Constant • Running in QCD • Also gluon loops • It turns out, the gluon has opposite effect! Niels Tuning (33)

34. “Running” Coupling Constant • Running in QCD • NB: if αs>1 perturbation theory breaks down… Niels Tuning (34)

35. Asymptotic Freedom • Running in QCD • High energy: coupling small Asymptotic freedom Niels Tuning (35)

36. “Confinement” • Running in QCD • Low energy: coupling big Confinement barrier Niels Tuning (36)

37. Standard Model Todo-list: • e+e- scattering • QED at work (LEP): R, neutrinos • e+p scattering • QCD at work (HERA): DIS, structure functions, scaling • No masses for W, Z • (LHC/ATLAS) Higgs mechanism, Yukawa couplings • Consequences of three families • (LHC/LHCb) CKM-mechanism, CP violation Today 21 May Niels Tuning (37)

38. e+e- Scattering

39. Shopping list • e+e-→μ+μ- • e+e-→cc • Confirmation of “color” • Discovery of charm • e+e-→qq g • Discovery of the gluon • e+e-→tt • Hunt for the top • e+e-→Z • 3 neutrino’s • e+e-→WW Niels Tuning (39)

40. e+e-colliders Niels Tuning (40)

41. Examples of e+e- processes

42. Scattering • Rutherford scattering (scattering off static point charge) • Mott scattering (now with high energy, taking into account recoil of target and magnetic moment: spin ½) • spin-½ spin-½ scattering (average over incoming spin, sum over outgoing spin) Niels Tuning (43)

43. e+e-→μ+μ- • Point cross section • At √s=10 GeV: σ(e+e-→μ+μ-) ~ 0.9 nb Niels Tuning (44)

44. e+e-→hadrons • Point cross section • At √s=10 GeV: • σ(e+e-→q+q-) ~ 3.6 nb

45. e+e-→hadrons • Compare cross section of σ(e+e-→q+q-) to σ(e+e-→μ+μ-) • Photon couples to fermion charge! • Color of quarks? • Inspect Ratio R: e- f γ - f e+

46. Prediction R: me+e- < 2mc muons quarks Without color: R = 2/3 With 3 colors: R = 2

47. Prediction R: me+e- > 2mc muons quarks Without color: R = 10/9 With 3 colors: R = 30/9

48. 1(3) colors prediction 1.1(3.3) 0.7(2) me+e- (GeV) data with color(udsc) With color (uds) 1 No color (udsc) No color (uds) 0

49. e+e-→hadrons • So, quarks have color! • How about spin? e- f γ - f e+