Determining $|V_{ub}|$ from the $\bar{B}\to X_u\ell \bar{\nu }$ dilepton invariant mass spectrum

Abstract

The invariant mass spectrum of the lepton pair in inclusive semileptonic $\bar{B}\to X_u\ell \bar{\nu }$ decay yields a model independent determination of $|V_{ub}|$. Unlike the lepton energy and hadronic invariant mass spectra, nonperturbative effects are only important in the resonance region, and play a parametrically suppressed role when $d\Gamma /d{q}^2$ is integrated over $q^2>(m_B-m_D{)}^2$, which is required to eliminate the $\bar{B}\to X_c\ell \bar{\nu }$ background. We discuss these backgrounds for $q^2$ slightly below $(m_B-m_D{)}^2$, and point out that instead of $q^2>(m_B-m_D{)}^2=11.6Ge{V}^2$, the cut can be lowered to $q^2\gtrsim 10.5Ge{V}^2$. This is important experimentally, particularly when effects of a finite neutrino reconstruction resolution are included.

Comments: 9 pages, 5 figures. Manuscript has considerable overlap with hep-ph/0007054. Invited talk presented by Michael Luke at the 5th International Symposium on Radiative Corrections (RADCOR 2000) Carmel CA, USA, 11-15 September, 2000