QED-Corrections to Weak Decays

Roman Zwicky

doi:10.3390/sym13112036

Abstract

Important aspects of QED-corrections to hadronic decays are reviewed with emphasis on conceptual points such as infrared divergences and structure dependence. These matter are illustrated for the e+e−→hadrons, the leptonic decay π+→ℓ+ν¯ and the semileptonic decay B→πℓ+ν¯. Aspects of structure dependence include the (non)-cancellation of hard-collinear logs (e.g., lnmℓ and lnmπ) of charged final states.

Highlights

Quantum electrodynamics (QED) can be regarded as the oldest and possibly most accurate and successful quantum field theory (QFT) there is
The renormalisation of QED, by the pioneers Dyson, Feynman, Schwinger, Tomonaga and others [1], gave birth to the successful application of quantum field theory to all of particle physics culminating in the Standard Model (SM) in the 1960s [2,3,4] and the Higgs-boson discovery in 2012 [5,6]
The application of QED to particle decays comes with additional subtleties that can be traced back to two idealisations, infinite space and infinitely precise measurement apparatuses, which do not hold in practice leading to infrared- (IR) divergences and IR

Summary

Introduction

Quantum electrodynamics (QED) can be regarded as the oldest and possibly most accurate and successful quantum field theory (QFT) there is. In reporting experimental results in flavour physics the QED-radiation is regarded as a background and is removed by using Monte-Carlo programs such as PHOTOS [12] Such tools are based on versions of scalar QED (point-like approximations). The crossvalidation of these programs seems essential in assuring precision extraction of CKM matrix elements (e.g., |Vu(c)b|) or the testing of lepton flavour universality [13] (e.g., RK = Γ[B → Kμ+μ−/Γ[B → Ke+e−]). (Let us add that one needs to distinguish kaon physics from D- and B-physics in this respect In the former case the situation is better as the logs are not that large, structure-dependent analyses in chiral perturbation theory exist and experiment is more inclusive in the photon such that Monte-Carlo tools are not indispensable in principle.). Aspects of infrared physics such as the Low-theorem, the KLN-theorem, coherent states, infrared singularities of oneloop diagrams and terminology are briefly discussed in Appendices A–F, respectively

Infrared Divergences and Infrared-Sensitivity

Decay Rates and Their Infrared-Effects

Leading Logs with S-P Interaction

Leading Order Result with V-A Interaction as in the Standard Model

Cancellation of Hard-Collinear Logs for Structure Dependent Contribution

Discussions ans Conclusions