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“Elementary Particles” Lecture 6

“Elementary Particles” Lecture 6. Niels Tuning Harry van der Graaf. Thanks. Ik ben schatplichtig aan: Dr. Ivo van Vulpen (UvA) Prof. dr. ir. Bob van Eijk (UT) Prof. dr. Marcel Merk (VU). Homework. Exercises Lecture 5:. Exercises Lecture 5:. Exercises Lecture 5:. Exercises Lecture 5:.

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“Elementary Particles” Lecture 6

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  1. “Elementary Particles”Lecture 6 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 5: Niels Tuning (4)

  5. Exercises Lecture 5: Niels Tuning (5)

  6. Exercises Lecture 5: Niels Tuning (6)

  7. Exercises Lecture 5: Niels Tuning (7)

  8. 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 (8)

  9. Outline for today: • Higgs mechanism • Higgs discovery at ATLAS • CKM-mechanism • CP violations at LHCb Niels Tuning (9)

  10. Summary Lects. 1-5

  11. 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 (11)

  12. 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 (12)

  13. 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 (13)

  14. 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 (14)

  15. 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 (15)

  16. Lecture 5: e+e- scattering and DIS • e+e- scattering:QED at work: R • e+e-→μ+μ- • e+e-→cc • e+e-→qq g • e+e-→Z • e+e-→WW • e+p scattering:QCD at work: F2 • Quarkmodel: do quarks exist?? • Substructure • Bjorken-x, sum rules • Scaling • ‘Parton density functions’ (pdf) and ‘structure functions’ • Scaling violations: more quarks at higher Q2 due to QCD Niels Tuning (16)

  17. Standard Model Todo-list: • No masses for W, Z !? • (LHC/ATLAS) Higgs mechanism, Yukawa couplings • Interactions between the three families !? • (LHC/LHCb) CKM-mechanism, CP violation Niels Tuning (17)

  18. Prof.dr. J. Ellis Half-way there?!

  19. Higgs mechanism

  20. Higgs mechanism • Let’s give the photon a mass! • Introduce a complex scalar field: • with: • and the Lagrangian is invariant under: Niels Tuning (20)

  21. Scalar potential V(φ) If 2 > 0: • φ will acquire a vaccumexpectation value v, • “spontaneously” ! • System not any more “spherical” symmetric SSB vev • Spontaneous Symmetry Breaking Niels Tuning (21)

  22. Complex scalar field φ If 2 > 0: • φ will acquire a vaccum expectation value v • Parameterize φ as: • h: Higgs boson • : Goldstone boson • Both real scalar fields  h Niels Tuning (22)

  23. Higgs mechanism • Let’s give the photon a mass! • Introduce a complex scalar field: • with: • and: • Then: Niels Tuning (23)

  24. Higgs mechanism e2v2 22 Photon A with mass e2v2 Higgs hwith mass 22 Interactions Photon field Aμ Niels Tuning (24)

  25. Higgs mechanism • What about this field ? e2v2 22 Photon A with mass e2v2 Higgs hwith mass 22 Interactions Photon field Aμ Niels Tuning (25)

  26. Higgs mechanism • Unitary gauge: • Goldstone boson has been “eaten” by the photon mass e2v2 22 Photon A with mass e2v2 Higgs hwith mass 22 Interactions Photon field Aμ (26)

  27. Higgs mechanism • Unitary gauge: • Degrees of freedom • Before: massless photon: 2, complex scalar field φ: 2 Total: 4 • After: massive photon: 3, one real scalar field h: 1 Total: 4 • Goldstone boson has been “eaten” by the photon mass e2v2 22 Photon A with mass e2v2 Higgs hwith mass 22 Interactions Photon field Aμ (27)

  28. Higgs mechanism in the Standard Model • Let’s give the W,Z a mass! • Introduce a doublet of complex scalar fields: Niels Tuning (28)

  29. Spontaneous symmetry breaking • Mass terms! • How about the physical fields? Niels Tuning (29)

  30. Rewriting in terms of physical gauge bosons • W1, W2 : • W3, B: • Let’s do a ‘trick’ and ‘rotate’ the W3 and B fields to get the Z and A fields Niels Tuning (30)

  31. Rewriting in terms of physical gauge bosons • W1, W2 : • W3, B: Niels Tuning (31)

  32. Rewriting in terms of physical gauge bosons • W1, W2 : • W3, B: Niels Tuning (32)

  33. Weak mixing angle (or Weinberg angle):W Rewriting in terms of physical gauge bosons • W1, W2 : • W3, B: Niels Tuning (33)

  34. Rewriting in terms of physical gauge bosons • W1, W2 : • W3, B: Niels Tuning (34)

  35. Spontaneous symmetry breaking (Keep the vacuum neutral) • Massterms! • How about the physicalfields? Niels Tuning (35)

  36. Spontaneous symmetry breaking Physical fields: Mass term Mass Niels Tuning (36)

  37. Summary: • Introduce doublet of scalar fields: • With potential: • S.S.B.: • Mass terms for gauge fields: Niels Tuning (37)

  38. Boson masses? • Photon couples to e: • Prediction for ratio of masses: • Veltman parameter: • Higgs mass: Niels Tuning (38)

  39. Fermion masses? • Add ad-hoc (!?) term to Lagrangian: Niels Tuning (39)

  40. Prof.dr. J. Ellis Done

  41. Prof.dr. J. Ellis Let’s tackle the Yukawa couplings

  42. First: Higgs discovery

  43. LHCb ATLAS CMS ALICE

  44. How are discoveries made? New ? Normal muon muon ? muon muon

  45. l+ Higgs  ZZ  4 leptonssmall number of beautiful events Z l- higgs l- Z 120.000 Higgs bosons l- HZZ  l+l-l+l- Only 1 in 1000 Higgs bosons decays to 4 leptons 50% chance that ATLAS detector finds them 60 (Higgs  4 lepton) events peak !? ‘other’ 52 events with Higgs 68 events

  46. Higgs  2 photons photon higgs photon Hγγ decay peak !?

  47. Interpretation of excess Claim discovery if: Probability of observing excess smaller than 1 in 1 milion Throwing 8 times 6 in a row

  48. Discovery in slow-motion jul/11 jul/11 mar/12 mar/12 dec/11 dec/11 Time-line higgs discovery jul/12 aug/12 jul/11 jul/11 mar/12 dec/11 dec/11 jul/12

  49. Discovery of Higgs particle on July 4, 2012

  50. What is mass ?? Anno 1687 Mass is de ‘exchange rate’ between force and acceleration: Does not describe what mass is ... F = m x a Newton

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