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We study radiative corrections to $\bar{B} \to X_c \ell \bar{\nu}_\ell$decays assuming the power counting $m_c \sim \sqrt{\Lambda_QCD m_b}$ for thecharm-quark mass. Concentrating on the shape-function region, we use effectivefield-theory methods to calculate the hadronic tensor at NLO accuracy. Fromthis we deduce a shape-function independent relation between partiallyintegrated $\bar{B} \to X_c\ell\bar{\nu}_\ell$ and $\bar{B} \to X_u \ell\bar{\nu}_\ell$ spectra to leading power in $1/m_b$, including first-ordercorrections in the strong coupling constant. This may provide an independentcross-check on the determination of the CKM element |V_{ub}|.Comment: 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 JHE

Can bar B→Xcellbar nuellhelp us extract |Vub|?

Can bar B→X_cellbar nu_ellhelp us extract |V_ub|?