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Presentation based on “ Introduction to Elementary Particles ” by David Griffiths

WEAK INTERACTION (2). Presentation based on “ Introduction to Elementary Particles ” by David Griffiths. Physics 842, March 2006 Bogdan Popescu. WEAK INTERACTION (2).

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Presentation based on “ Introduction to Elementary Particles ” by David Griffiths

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  1. WEAK INTERACTION (2) Presentation based on “Introduction to Elementary Particles” by David Griffiths Physics 842, March 2006 Bogdan Popescu

  2. WEAK INTERACTION (2) - NEUTRAL WEAK INTERACTION - Elastic Neutrino-Electron Scattering - Electron-Positron Scattering Near the Z0 Pole - ELECTROWEAK UNIFICATION - Chiral Fermion States - Weak Isospin and Hypercharge - Electro-Weak Mixing Physics 842, March 2006 Bogdan Popescu

  3. NEUTRAL WEAK INTERACTIONS Neutral weak interaction mediated by Z0 f stands for any lepton or quark Not allowed : Physics 842, March 2006 Bogdan Popescu

  4. NEUTRAL WEAK INTERACTIONS It doesn’t matter if we use physical states or Cabibbo rotated states. Physics 842, March 2006 Bogdan Popescu

  5. NEUTRAL WEAK INTERACTIONS First process mediated by Z0 (Bubble chamber photograph at CERN, 1973) Physics 842, March 2006 Bogdan Popescu

  6. NEUTRAL WEAK INTERACTIONS In the same series of experiments : neutrino-quark process in the form of inclusive neutrino-nucleon scattering The cross sections were three times smaller than the correspondent charged events : Indication of a new kind of interaction, and not simply a high order process. (which correspond to a far smaller cross section) Physics 842, March 2006 Bogdan Popescu

  7. NEUTRAL WEAK INTERACTIONS The coupling to Z0 : where : (“Weak mixing angle” or “Weinberg angle”) Physics 842, March 2006 Bogdan Popescu

  8. NEUTRAL WEAK INTERACTIONS Neutral vector and axial vector coupling in GWS model : Physics 842, March 2006 Bogdan Popescu

  9. NEUTRAL WEAK INTERACTIONS ( Z0 propagator ) When : the propagator is simply : The masses of the bosons are related by the formula : Physics 842, March 2006 Bogdan Popescu

  10. WEAK INTERACTION (2) - NEUTRAL WEAK INTERACTION - Elastic Neutrino-Electron Scattering - Electron-Positron Scattering Near the Z0 Pole - ELECTROWEAK UNIFICATION - Chiral Fermion States - Weak Isospin and Hypercharge - Electro-Weak Mixing Physics 842, March 2006 Bogdan Popescu

  11. Example : Elastic Neutrino-Electron Scattering Physics 842, March 2006 Bogdan Popescu

  12. Example : Elastic Neutrino-Electron Scattering Now compute in CM frame and let : (mass of the electron) Physics 842, March 2006 Bogdan Popescu

  13. Example : Elastic Neutrino-Electron Scattering ( E is the electron or neutrino energy ) Using : Physics 842, March 2006 Bogdan Popescu

  14. Example : Elastic Neutrino-Electron Scattering The total cross section : Compare to : (computed in the previous lecture) (0.08 , experimental) Physics 842, March 2006 Bogdan Popescu

  15. Example : Elastic Neutrino-Electron Scattering Most neutral processes are “masked” by electromagnetic ones. Physics 842, March 2006 Bogdan Popescu

  16. WEAK INTERACTION (2) - NEUTRAL WEAK INTERACTION - Elastic Neutrino-Electron Scattering - Electron-Positron Scattering Near the Z0 Pole - ELECTROWEAK UNIFICATION - Chiral Fermion States - Weak Isospin and Hypercharge - Electro-Weak Mixing Physics 842, March 2006 Bogdan Popescu

  17. Example : Electron-Positron Scattering Near the Z0 Pole f is any quark or lepton (except electron – we must include one more diagram) We are interested in the regime : The amplitude : where : Physics 842, March 2006 Bogdan Popescu

  18. Example : Electron-Positron Scattering Near the Z0 Pole ( since we are working in the vicinity of 90 GeV ) ignore de mass of quark or lepton Finally : Physics 842, March 2006 Bogdan Popescu

  19. Example : Electron-Positron Scattering Near the Z0 Pole problems at Z0pole Physics 842, March 2006 Bogdan Popescu

  20. Example : Electron-Positron Scattering Near the Z0 Pole Z0 is not a stable particle. Its lifetime has the effect of “smearing out” the mass. Replacement in the propagator : = decay rate The cross section : Because : the above correction is negligible outside Z0 pole. Physics 842, March 2006 Bogdan Popescu

  21. Example : Electron-Positron Scattering Near the Z0 Pole Cross section for the same process, mediated by a photon : ( Qf is the charge of f in units of e ) The ratio : Physics 842, March 2006 Bogdan Popescu

  22. Example : Electron-Positron Scattering Near the Z0 Pole (problem 10.22) Physics 842, March 2006 Bogdan Popescu

  23. Example : Electron-Positron Scattering Near the Z0 Pole Well below the Z0 pole : Right on the Z0 pole : Physics 842, March 2006 Bogdan Popescu

  24. Example : Electron-Positron Scattering Near the Z0 Pole Physics 842, March 2006 Bogdan Popescu

  25. WEAK INTERACTION (2) - NEUTRAL WEAK INTERACTION - Elastic Neutrino-Electron Scattering - Electron-Positron Scattering Near the Z0 Pole - ELECTROWEAK UNIFICATION - Chiral Fermion States - Weak Isospin and Hypercharge - Electro-Weak Mixing Physics 842, March 2006 Bogdan Popescu

  26. CHIRAL FERMION STATES To unify the weak and electromagnetic interaction, let’s move the matrix into the particle spinor. ( L stands for “left-handed” ) (But uLis not, in general, a helicity eigenstate) Physics 842, March 2006 Bogdan Popescu

  27. CHIRAL FERMION STATES If the particle is massless : helicity where : “projection operator” (! Advanced Quantum Mechanics Homework) Using : we can compute the following table : Physics 842, March 2006 Bogdan Popescu

  28. CHIRAL FERMION STATES Physics 842, March 2006 Bogdan Popescu

  29. CHIRAL FERMION STATES (inverse beta decay) The contribution to the amplitude from this vertex : Negatively charged weak current and e stand for the particle spinors. Rewrite as : (coupling between left-handed particles only) Note that : Electromagnetic current : Physics 842, March 2006 Bogdan Popescu

  30. WEAK INTERACTION (2) - NEUTRAL WEAK INTERACTION - Elastic Neutrino-Electron Scattering - Electron-Positron Scattering Near the Z0 Pole - ELECTROWEAK UNIFICATION - Chiral Fermion States - Weak Isospin and Hypercharge - Electro-Weak Mixing Physics 842, March 2006 Bogdan Popescu

  31. WEAK ISOSPIN AND HYPERCHARGE Negatively charged weak current Positively charged weak current Physics 842, March 2006 Bogdan Popescu

  32. WEAK ISOSPIN AND HYPERCHARGE We can express both by introducing the left handed doublet : and the matrices : Physics 842, March 2006 Bogdan Popescu

  33. WEAK ISOSPIN AND HYPERCHARGE We could have a full “weak isospin” symmetry if only there is a third weak current, “neutral weak current”. Weak analog of hypercharge (Y) in the Gell-Mann – Nishijima formula : Weak hypercharge : Physics 842, March 2006 Bogdan Popescu

  34. WEAK ISOSPIN AND HYPERCHARGE Everything could be extended to the other leptons and quarks : Weak isospin currents : Weak hypercharge current : where : Physics 842, March 2006 Bogdan Popescu

  35. WEAK INTERACTION (2) - NEUTRAL WEAK INTERACTION - Elastic Neutrino-Electron Scattering - Electron-Positron Scattering Near the Z0 Pole - ELECTROWEAK UNIFICATION - Chiral Fermion States - Weak Isospin and Hypercharge - Electro-Weak Mixing Physics 842, March 2006 Bogdan Popescu

  36. ELECTRO-WEAK MIXING GWS model asserts that the three weak isospin currents couple to a weak isotriplet of intermediate vector bosons, whereas the weak hypercharge current couples to an isosinglet intermediate vector boson. wave functions representing the particles. Physics 842, March 2006 Bogdan Popescu

  37. ELECTRO-WEAK MIXING “Broken” symmetry in GWS theory : The two neutral states W3 and B “mix”, producing one massless linear combination (the photon), and an orthogonal massive combination (the Z0). The weak and electromagnetic coupling constant are not independent. Physics 842, March 2006 Bogdan Popescu

  38. WEAK INTERACTION END OF PART TWO THANK YOU ! Physics 842, March 2006 Bogdan Popescu

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