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

We study radiative corrections to $\bar{B}\to X_c\mathrm{\ell }{\bar{\nu }}_{\mathrm{\ell }}$ decays assuming the power counting $m_c\sim \sqrt{{\mathrm{\Lambda }}_{Q}CD{m}_b}$ 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 $\bar{B}\to X_c\mathrm{\ell }{\bar{\nu }}_{\mathrm{\ell }}$ and $\bar{B} \to X_u \ell \bar{\nu}\ell$spectratoleadingpowerin$1/m_b$, 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}|.