TTP02-06 Subleading shape functions in $B \to X_u \ell \bar \nu$ and the determination of $|V_{ub}|$

TTP02-06 Subleading shape functions in $B \to X_u \ell \bar \nu$ and the determination of $|V_{ub}|$

TTP02-06 Subleading shape functions in $B \to X_u \ell \bar \nu$ and the determination of $|V_{ub}|$

We calculate the subleading twist contributions to the endpoint of the inclusive lepton energy spectrum in $B \to X_u \ell \bar\nu$. We show that the same two subleading twist functions that appear in the decay $B \to X_s \gamma$ govern the subleading effects in this decay. Using these results we find large ${O}(\lqcd/m_B)$ corrections to the determination of $|V_{ub}|$ from the endpoint of the charged lepton spectrum. Using a simple model for the relevant subleading shape functions, we estimate the uncertainty in $|V_{ub}|$ from $\lqcd/m_b$ corrections to be at the $\sim 15\%$ level for a lower lepton energy cut of 2.2 GeV.

Christian W. Bauer, Michael Luke, Thomas Mannel
Phys. Lett. B543 261-268 2002
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