O(α_s^2) corrections to semileptonic decay b \to c l \bar ν_l

TL;DR

The paper delivers a fully differential NNLO QCD calculation for the inclusive decay b → X_c l ν_l, enabling arbitrary kinematic cuts and differential moments crucial for precision fits of |V_cb| and heavy-quark parameters. It advances methodology by using a numerical multiloop approach, addressing real-virtual contributions with a linearized Feynman-parameter technique and employing the Larin scheme for γ5, along with thorough cross-checks. The results show that non-BLM NNLO corrections are about 2% and often opposite in sign to BLM corrections, leading to NNLO effects smaller than naive BLM estimates and providing refined normalization impacts on |V_cb|. These findings support improved precision in global fits, while highlighting remaining needs for certain perturbative inputs and potential extensions to b → u and heavy-lepton cases.

Abstract

We compute the next-to-next-to-leading order (NNLO) QCD corrections to b \to c l \bar ν_l decay rate at a fully differential level. Arbitrary cuts on kinematic variables of the decay products can be imposed. Our computation can be used to study the NNLO QCD corrections to the total decay rate as well as to the lepton energy, hadronic invariant mass and hadronic energy moments and to incorporate those corrections into global fits of inclusive semileptonic B-decays.