V from the hadronic invariant mass spectrum in semileptonic B decay

Abstract

The hadronic invariant mass spectrum for the inclusive charmless semileptonic decay $B\to X_u e \bar\nu_e$ is studied. Particular attention is paid to the region $s_H<m_D^2$, which may be useful for extracting the value of $|V_{ub}|$. The sensitivity of the spectrum to the parameter $\bar\Lambda \equiv m_B - m_b$ is explored. Perturbative QCD corrections to $d\Gamma/ds_H$ of order $\alpha_s^2\beta_0$ are calculated. For $s_H \sim \bar\Lambda m_b$ nonperturbative QCD effects are important and the shape of the invariant mass spectrum is controlled by the B meson matrix element of an infinite sum of local operators. The utility of the hadronic mass spectrum for extracting $|V_{ub}|$ is explored.