The European Physical Journal C

ISSN: 1434-6044 (printed version)
ISSN: 1434-6052 (electronic version)

Table of Contents

Abstract Volume 4 Issue 3 (1998) pp 453-461
DOI 10.1007/s100529800783

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

I. Bigi (1), R.D. Dikeman (2), 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.

Reported at 3rd BaBar Physics Workshop, Orsay 16-19 June 1997

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Online publication: July 6, 1998
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