Second Order Corrections to the Muon Lifetime and the Semileptonic B Decay

TL;DR

This paper calculates second order quantum corrections to muon decay and bottom quark decay, confirming previous results with an independent method using advanced mathematical techniques.

Contribution

It introduces a novel computational approach employing conformal mapping and Padé approximation to evaluate complex four-loop diagrams in decay processes.

Findings

Confirmed existing two-loop QED corrections to muon decay.

Validated order α_s^2 corrections to bottom quark semileptonic decay.

Demonstrated effectiveness of conformal mapping and Padé approximation in high-order calculations.

Abstract

In this article two-loop QED corrections to the muon decay and corrections of order $\alpha_s^2$ to the semileptonic decay of the bottom quark are considered. We compute the imaginary part of the four-loop diagrams contributing to the corresponding fermion propagator in the limit of small external momentum. The on-shell condition is obtained with the help of a conformal mapping and Pad\'e approximation. Via this method we confirm the existing results by an independent calculation.