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}|.

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

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• $B\to D\ell {\nu }_{\ell }$ form factors beyond leading power and extraction of $|V_{cb}|$ and $R(D)$
• Role of "Intrinsic Charm" in Semi-Leptonic B-Meson Decays
• NNLO corrections to B --> X_u l nu and the determination of |V_ub|
• Inclusive semileptonic decays of the B meson