Can $B->X_c\ell \nu$ help us extract |V_{ub}| ?

Abstract

We study radiative corrections to $\bar{B}\to X_c\ell {\bar{\nu }}_{\ell }$ decays assuming the power counting $m_c\sim \sqrt{{\Lambda }_{Q}CD{m}_b}$ for the charm-quark mass. Concentrating on the shape-function region, we use effective field-theory methods to calculate the hadronic tensor at NLO accuracy. From this we deduce a shape-function independent relation between partially integrated $\bar{B}\to X_c\ell {\bar{\nu }}_{\ell }$ and $\bar{B}\to X_u\ell {\bar{\nu }}_{\ell }$ spectra to leading power in $1/m_b$, including first-order corrections in the strong coupling constant. This may provide an independent cross-check on the determination of the CKM element |V_{ub}|.

Comments: 22 pages, 8 figures, comparison with OPE in Sec.3 and references [26-28] added, section 5 (discussion/plots) reorganized, version to be published in JHEP