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Concepts of the Standard Model : r enormalisation

Concepts of the Standard Model : r enormalisation. FK8022, Lecture 2. Core text: Quarks and leptons : an introductory course in modern physics , Halzen and Martin Further reading : Basics of QCD perturbation theory , D.E. Soper ( hep-ph /9702203). Lecture outline.

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Concepts of the Standard Model : r enormalisation

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  1. Conceptsof the Standard Model: renormalisation FK8022, Lecture 2 Core text: Quarks and leptons: an introductorycourse in modern physics, Halzen and Martin Furtherreading: Basics of QCD perturbation theory, D.E. Soper (hep-ph/9702203)

  2. Lectureoutline • Infinitiesarising from loops • Regularisation • Reparameterisationof charge • Renormalisation • finite charge, amplitude • Renormalisationscale • Runningofcouplings

  3. A simple QED process m m p2 p4 q e e p1 p3

  4. Adding a higher order process m m m m + e e e e e e

  5. Renormalised charge

  6. Bare and renormalised charges

  7. Defining the coupling at a scale

  8. Renormalisationscale [ ] - - (A) (B) (C) + higher orders

  9. Higher orders }

  10. Scaledependenceofamplitude ar(Q2) emscattering Singlephotonexchange Order ofcalculation

  11. Runningcoupling

  12. Consistency check

  13. Renormalisation Divergence in amplitude from higher order loop Make finite by redefiningcoupling/charge and removeinfinity Coupling/charge depends on an arbitrarykinematicscalemrfor a given interaction Finiteexpression for runningofcoupling/charge withmr For a complete expansion the amplitude is independent ofmr

  14. Renormalisationworks: electromagneticcouplingrunning Tinyshift (momentum transfer)2 /GeV2 Interaction distance

  15. Physical interpretation of the runningcoupling e- e- e- e- e+,e- + e+,e- e+,e- e- e- e- Coupling Distancescale

  16. Renormalisationofotherquantities • Different loop diagrams cause otherphysicalquantitiesto be renormalised. • Egmass • Massesalsorun: m

  17. Whatabout the strong force ? q q q q q q q q q,q + otherhigher order diagrams q,q q,q q q q q q q q q

  18. Asymptotic freedom as Momentum transfer /GeV Interaction distance

  19. Renormalisationscalesetting

  20. Renormalisationscalesetting

  21. Scale variation

  22. Summary and discussion (1)

  23. Summary and discussion (2)

  24. Summary and discussion (3)

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