Third order corrections to the semi-leptonic \boldmath{$b\to c$} and the muon decays

TL;DR

This paper calculates third-order quantum corrections to semi-leptonic b-quark decays and muon decay, showing scheme-dependent effects and providing results crucial for precise determination of fundamental constants.

Contribution

It presents the first computation of order  corrections for b-quark decays and muon decay, improving theoretical precision in these processes.

Findings

Large three-loop corrections in on-shell scheme

Perturbation theory remains reliable in the kinetic scheme

Results aid in reducing uncertainty of the Fermi constant G_F

Abstract

We compute corrections of order $\alpha_s^3$ to the decay $b \to c \ell \bar\nu$ taking into account massive charm quarks. In the on-shell scheme large three-loop corrections are found. However, in the kinetic scheme the three-loop corrections are below 1\% and thus perturbation theory is well under control. We furthermore provide results for the order $\alpha_s^3$ corrections to $b \to u \ell \bar\nu$ and the third-order QED corrections to the muon decay which will be important input for reducing the uncertainty of the Fermi coupling constant $G_F$.