Semi-Leptonic b-decay at Intermediate Recoil

TL;DR

This paper calculates second-order QCD corrections to semileptonic b-decay at a specific recoil point, improving accuracy and resolving discrepancies in previous theoretical estimates.

Contribution

It extends previous calculations by providing new corrections at intermediate recoil and clarifies inconsistencies in earlier NNLO QCD results.

Findings

Corrected and extended previous results for b -> c decay

Provided new calculations for the case c << b

Resolved discrepancies in NNLO QCD correction estimates

Abstract

We compute the O(\alpha_s^2) corrections to the differential rate of the semileptonic decay b -> clv at the "intermediate recoil" point, where the c-quark mass and the invariant mass of the leptons are equal. The calculation is based on an expansion around two opposite limits of the quark masses m_{b,c}: m_c ~ m_b and m_c << m_b. The former case was previously studied; we correct and extend that result. The latter case is new. The smooth matching of both expansions provides a check of both. We clarify the discrepancy between the recent determinations of the full NNLO QCD correction to the semileptonic b -> c rate, and its earlier estimate.