1 / 27

Understanding Renormalisation in Particle Physics: Theory and Applications

Delve into core concepts of the Standard Model, from renormalisation to running couplings, to shed light on modern physics. This introductory course explores quarks, leptons, QCD perturbation theory, and more. Learn how renormalisationscales and charge reparameterisation play vital roles in defining couplings at different scales. Discover the intricacies of electromagnetic coupling running, finite charges, running distances, and physical interpretations in interaction processes. Gain insights into renormalisation of masses and the strong force, asymptotic freedom, and setting renormalisation scales for comprehensive understanding.

adanna
Télécharger la présentation

Understanding Renormalisation in Particle Physics: Theory and Applications

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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)

More Related