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

Understand

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.