34. Herbstschule für Hochenergiephysik 2002
Renormierungsgruppe: Laufende Kopplungen und Massen
Leitung der Übungsgruppe:
André Hoang, MPI München
Voraussetzungen
- Bedeutung von Feynman-Diagrammen
- Behandlung von Störungstheorie auf Loop-Niveau
- dimensionale Regularisierung, MSbar-Subtraktion
Ziele
- Vermittlung von Techniken zur Aufstellung von
Renormierungsgruppengleichungen (RGE's)
- Erkenntnis von Sinn und Nutzen RG-verbesserter Störungstheorie
Programm
- One-Loop Renormalization of Phi^4
- Relation between on-shell und MSbar subtraction scheme for mass parameters
- Two-Loop Renormalization of Phi^4 (optional, for cracks)
- proper treatment of subdivergences
- Solution of RGE's
- Callen-Symanzik-Equation
- role of wave-function renormalization
- Application: Effective Potential of Phi^4
- Fixed order perturbation theory and need to sum up logs
- solution of Callen-Symanzik-Equation
- Solution of RGE for coupling in Phi^4 and introduction
of Lambda_Phi^4 (in analogy to Lambda_QCD)
- RGE for alpha_s in background field gauge at one-loop
- Composite Operator without mixing: Phi^2 in Phi^4 theory
- RG for the composite operator
- QCD-Renormalization of the weak current and the semileptonic
weak Hamiltonian
- conserved current (symmetry) and renormalization
- Fermi theory for semileptonic decays, integrating out Mw
- final Project:
QCD-Renormalization of the weak non-leptonic Hamiltonian
- Problem of large logs, in fixed order perturbation theory
- Fermi-theory and OPE
- Fierz tricks
- RG for operators mixing case
- RGE's for the coefficients
- Fixed order vs. summed results
Lecture Notes
Note that the download of the lecture notes will only be
possible for the duration of the course.
-
List of participants (will be provided later...)
-
1st lecture:
One-loop renormalization of Phi^4 theor; renormalization group equations (RGE's)
-
2nd lecture:
Two-loop renormalization of Phi^4 theory, RGE's
-
3rd lecture:
More on solutions of RGE's; RG-improved perturbation theory
-
4th lecture:
Callen-Symanzik equation, project: RG-improved effective potential
-
5th lecture:
Background field method in QCD (BGFM)
-
6th lecture:
Computation of the QCD beta function using the BGFM
-
7th lecture:
Project: lightest MSSM Higgs mass in rg-improved pert. th.;
renormalization of composite field operators;
one-loop renormalization of the weak current in QCD
-
8th lecture:
One-loop renormalization of the weak Hamiltonian; operator mixing