Perturbative corrections to power suppressed effects in $\bar B\to X_u\ell\nu$

TL;DR

This paper calculates the first-order QCD corrections to certain operators in inclusive semileptonic B decays, confirming previous results and constraining shape functions relevant for decay predictions.

Contribution

It provides the $O(\,\alpha_s)$ corrections to Wilson coefficients of dimension five operators in B decays, aligning with reparameterization invariance and previous total width results.

Findings

Confirmed consistency with reparameterization invariance

Aligned with previous total width calculations

Placed constraints on shape functions

Abstract

We compute the $O(\alpha_s)$ corrections to the Wilson coefficients of the dimension five operators in inclusive semileptonic $B$ decays in the limit of a massless final quark. Our calculation agrees with reparameterization invariance and with previous results for the total width and places constraints on the shape functions that enter those decays.