The hadronic recoil mass spectrum in semileptonic $B$ decays and extracting $|V_{ub}|$ in a model-insensitive way

I. Bigi; R.D. Dikeman; N. Uraltsev

doi:doi:10.1007/s100529800783

EPJ

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2018 Impact factor 4.843

Particles and Fields

Eur. Phys. J. C 4, 453-461
DOI 10.1007/s100529800783

The hadronic recoil mass spectrum in semileptonic B decays
and extracting |V_ub| in a model-insensitive way

I. Bigi¹ - R.D. Dikeman² - N. Uraltsev^2,3

¹ Department of Physics, University of Notre Dame du Lac, Notre Dame, IN 46556, USA
² Theoretical Physics Institute, University of Minnesota, Minneapolis, MN 55455
³ St.Petersburg Nuclear Physics Institute, Gatchina, St.Petersburg 188350, Russia

Received: 30 July 1997 / Published online: 23 February 1998

Abstract
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.