Weak Hamiltonian, CP Violation and Rare Decays

TL;DR

This paper provides a comprehensive overview of effective Hamiltonians for meson weak decays, detailing calculations of Wilson coefficients, operator mixing, and phenomenological implications for CP violation and rare decays.

Contribution

It offers detailed calculations of anomalous dimensions, discusses renormalization issues including gamma-5, and applies these to phenomenological analyses of CP violation and rare decay processes.

Findings

Explicit 6x6 one-loop anomalous dimension matrix calculated

Discussion on gamma-5 treatment and evanescent operators

Analysis of CP violation and rare decay processes in B and K mesons

Abstract

These lectures describe in detail the effective Hamiltonians for weak decays of mesons constructed by means of the operator product expansion and the renormalization group method. We calculate Wilson coeffcients of local operators, discuss mixing of operators under renormalization, the anomalous dimensions of operators and anomalous dimension matrices. We elaborate on the renormalzation scheme and renormalization scale dependences and their cancellations in physical amplitudes. In particular we discuss the issue of gamma-5 in D-dimensions and the role of evanescent operators in the calculation of two-loop anomalous dimensions. We present an explicit calculation of the 6 times 6 one-loop anomalous dimension matrix involving current-current and QCD-penguin operators and we give some hints how to properly calculate two-loop anomalous dimensions of these operators. In the phenonomenological part of these lectures we discuss in detail: CKM matrix, the unitarity triangle and its determination, two-body non-leptonic B-decays and the generalized factorization, the ratio epsilonprime/epsilon, B to X_s gamma, K^+ to pi^+ nu barnu, K_L to pi^0 nu barnu, B to X_s nu barnu, B_s to mu bar mu and some aspects of CP violation in B-decays.