On the $O(\alpha_s^2)$ corrections to $b \to X_u e \bar \nu$ inclusive decays

TL;DR

This paper calculates second-order QCD corrections to inclusive semileptonic b-quark decays, improving theoretical precision for extracting the CKM matrix element |V_ub| by including genuine two-loop effects beyond previous approximations.

Contribution

It provides the first complete two-loop QCD corrections to inclusive b to u decays, accounting for experimental cuts and reducing theoretical uncertainties.

Findings

Computed non-BLM corrections to decay moments with cuts

Enhanced precision in |V_ub| extraction

Removed key source of theoretical uncertainty

Abstract

We present $O(\alpha_s^2)$ QCD corrections to the fully-differential decay rate of a $b$-quark into inclusive semileptonic charmless final states. Our calculation provides genuine two-loop QCD corrections, beyond the Brodsky-Lepage-Mackenzie (BLM) approximation, to any infra-red safe partonic observable that can be probed in $b \to X_u e \bar \nu$ decays. Kinematic cuts that closely match those used in experiments can be fully accounted for. To illustrate these points, we compute the non-BLM corrections to moments of the hadronic invariant mass and the hadronic energy with cuts on the lepton energy and the hadronic invariant mass. Our results remove one of the sources of theoretical uncertainty that affect the extraction of the CKM matrix element $|V_{ub}|$ from charmless inclusive B-decays.