Improved Factorization for Threshold Resummation in Heavy Quark to Heavy Quark Decays

TL;DR

This paper develops a new factorization scheme for threshold resummation in heavy quark decays, enabling accurate predictions of the hadron invariant mass distribution across all kinematic regions, with application to b -> X_s + gamma.

Contribution

It introduces an improved factorization scheme for threshold resummation that works uniformly across different kinematic regimes in heavy quark decays.

Findings

Successfully applied to b -> X_s + gamma decay at NLL accuracy

Allows consistent evaluation of hadron mass distribution in all kinematic regions

Incorporates a dependence on the threshold variable that can be minimized

Abstract

We consider the resummation of soft-gluon effects in heavy quark to heavy quark decays, namely the processes Q1 -> Q2 + (non QCD partons), where Q1 and Q2 are two different heavy quarks. We construct a new factorization scheme for threshold resummed spectra, which allows us to consistently evaluate the distribution of the final hadron invariant mass mX in all the kinematic regions, i.e. when mX is smaller, of the same order, or larger than the mass of the final quark Q2. A dependence of the Improved Coefficient Function on the threshold variable is introduced, which can however be relegated to a small interval of this variable by means of the so-called Partition of Unity. We explicitly apply our improved scheme to the b -> X_s + gamma decay at next-to-leading logarithmic accuracy.