The hadronic recoil mass spectrum in semileptonic

We present an extended discussion of the previously noted possibility to extract \(|V_{ub}|\) from an analysis of the hadronic recoil mass spectrum in \(B\rightarrow X_u\,\ell \nu\) decays. Invariant mass spectra containing perturbative as well as nonperturbative corrections are given; their shape is manifestly sensitive to the three basic quantities \(\mu _\pi ^2\), \(m_b\) and \(\alpha_s\), whereas the total integrated rate is much less so. Only a small fraction of \(b\rightarrow u\) transitions generates a recoil mass \(M_X\) of at least \(M_D\). Moreover we find that the fraction of events with \(M_X \leq 1.5\,\mbox{GeV}\) (to reject leakage from \(b \rightarrow c\) due to measurement errors) exhibits fairly little dependence on \(\mu_\pi^2\), \(m_b\) and \(\alpha_s\); \(|V_{ub}|\) can then be extracted in a largely model-insensitive way. This conclusion is based on the applicability of the OPE to actual semileptonic \(B\) decays. A direct cross-check of this assumption and a determination of the required basic parameters of the heavy quark expansion will be possible in the future with more experimental data.