Renormalization Scheme Dependence in b->u Semileptonic Decays

TL;DR

This paper examines how the choice of renormalization scheme affects the calculation of the b->u semileptonic decay rate, highlighting scheme dependence and the cancellation of certain ambiguities.

Contribution

It demonstrates the scheme dependence in the decay rate calculation and shows how different schemes influence the inclusion of logarithmic contributions.

Findings

Renormalization scheme dependence affects decay rate calculations.

Ambiguities in the strong coupling and b quark mass cancel out.

Different schemes include varying levels of logarithmic contributions.

Abstract

After reviewing how the renormalization group equation can be used to sum logarithmic corrections to the decay rate for the semi-leptonic process b->u when using minimal subtraction, we consider renormalization scheme dependence for this calculation when employing this renor- malization scheme. In this calculation, an ambiguity resides in the running strong coupling and in the running b quark mass. The ambiguity usually associated with the renormalization mass scale mu is shown to cancel. It is demonstrated how in one renormalization scheme, there are only leading-log contributions to this decay rate. Another choice of renormalization scheme results in the decay rate being expressed in terms of the two-loop contribution to the beta-function associated with the strong coupling and the one-loop contribution to the anomalous mass dimension as well as a set of renormalization scheme invariant parameters.