$|V_{ub}|$ determination in lattice QCD

Abstract

The 2012 PDG reports a tension at the level of $3\sigma$ between two exclusive determinations of $|V_{ub}|$. They are obtained by combining the experimental branching ratios of $B\to \tau \nu$ and $B\to \pi l\nu$ (respectively) with a theoretical computation of the hadronic matrix elements $\fB$ and the $B\to \pi$ form factor $f_{+}(q^2)$. To understand the tension, improved precision and a careful analysis of the systematics involved are necessary. We report the results of the ALPHA collaboration for $\fB$ from the lattice with 2 flavors of $O(a)$ improved Wilson fermions. We employ HQET, including $1/m_b$ corrections, with pion masses ranging down to $\approx$ 190 MeV. Renormalization and matching were performed non-perturbatively, and three lattice spacings reaching $a^{-1}\approx 4.1$ GeV are used in the continuum extrapolation. We also present progress towards a computation of $f_{+}(q^2)$, to directly compare two independent exclusive determinations of $|V_{ub}|$ with each other and with inclusive determinations. Additionally, we report on preliminary results for $\fBq{s}$, needed for the analysis of $B_s\to {\mu }^{+}{\mu }^{-}$.}

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Cited by in corpus (5)

• Progress on semi-leptonic $B_{(s)}$ decays
• A one-loop study of matching conditions for static-light flavor currents
• Matching of heavy-light flavour currents between HQET at order 1/m and QCD: I. Strategy and tree-level study
• Quark Flavor Physics Review
• Non-perturbative Heavy Quark Effective Theory: An application to semi-leptonic B-decays