Inclusive Semileptonic B and Polarized Lambda_b Decays from QCD

TL;DR

There is a subtlety in the use of the equations of motion at order 1/[ital m][sub [ital b]][sup 2] in the heavy quark expansion which is explained.

Abstract

The differential decay spectrum $dΓ/dE_e dq^2$ for the semileptonic decay of an unpolarized hadron containing a b-quark, and the decay spectrum $dΓ/dE_e dq^2 d\!\cosθ$ for polarized $Λ_b$ decay are computed to second order in the $1/m_b$ expansion. Most of the $1/m_b^2$ corrections have a simple physical interpretation, which is discussed in detail. The implications of the results for the determination of $V_{ub}$ are discussed. The decay spectra for semileptonic decay of hadrons containing a c-quark are also given. There is a subtlety in the use of the equations of motion at order $1/m_b^2$ in the heavy quark expansion which is explained.