A Model Independent Determination of |V_{ub}|

Abstract

It is shown that measuring the lepton invariant mass spectrum in inclusive semileptonic B -> X_u l 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 dΓ/dq^2 is integrated over q^2 > (m_B-m_D)^2, which is required to eliminate the charm background. Perturbative and nonperturbative corrections are presented to order α_s^2β_0 and Λ_{QCD}^2/m_b^2, and the Λ_{QCD}^3/m_b^3 corrections are used to estimate the uncertainty in our results. The utility of the B -> X_s l^+ l^- decay rate above the ψ(2S) resonance is discussed.

Figures (3)

• Figure 1: The lepton energy and hadronic invariant mass spectra. The dashed curves are the $b$ quark decay results to ${\cal O}(\alpha_s)$, while the solid curves are obtained by smearing with the model distribution function $f(k_+)$ in Eq. (\ref{['sfn']}). The unshaded side of the vertical lines indicate the region free from charm background. The area under each curve has been normalized to one.
• Figure 2: The lepton invariant mass spectrum to ${\cal O}(\alpha_s)$. The meaning of the curves is the same as in Fig. \ref{['twospectra']}.
• Figure 3: (a) The fraction of $\bar{B}\to X_u \ell\bar{\nu}$ events with $q^2 > q_0^2$, $F(q_0^2)$, to order $\epsilon_{\rm BLM}^2$ and $\Lambda_{\rm QCD}^2/m_b^2$ in the upsilon expansion. The shaded region is the uncertainty due to $\Lambda_{\rm QCD}^3 / m_b^3$ terms, as discussed in the text. The dashed line indicates the lower cut $q_0^2 = (m_B-m_D)^2 \simeq 11.6\,{\rm GeV}^2$, which corresponds to $F = 0.178 \pm 0.012$. (b) The estimated uncertainty in $F(q_0^2)$ due to $\Lambda_{\rm QCD}^3 / m_b^3$ terms as a percentage of $F(q_0^2)$.