# Second order QCD corrections to inclusive semileptonic b \to Xc l \bar \nu_l decays with massless and massive lepton

## TL;DR

This paper computes second order QCD corrections to inclusive semileptonic b to c decays, including cases with massive leptons, enabling precise theoretical predictions for b to c tau nu decays.

## Contribution

It extends previous calculations of O(α_s^2) corrections to include massive leptons, improving the accuracy of theoretical models for b to c semileptonic decays.

## Key findings

- Numerical results for O(α_s^2) corrections to b to c l nu decays.
- Enhanced understanding of QCD effects in b to c tau nu decays.
- Methodological review of computational techniques for higher-order corrections.

## Abstract

We extend previous computations of the second order QCD corrections to semileptonic b \to c inclusive transitions, to the case where the charged lepton in the final state is massive. This allows accurate description of b \to c \tau \bar \nu_\tau decays. We review techniques used in the computation of O(\alpha_s^2) corrections to inclusive semileptonic b \to c transitions and present extensive numerical studies of O(\alpha_s^2) QCD corrections to b \to c l \bar \nu_l decays, for l =e, \tau.