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

Abstract

The 2012 PDG reports a tension at the level of $3\ddot{I}ƒ$ between two exclusive determinations of $|V_{ub}|$. They are obtained by combining the experimental branching ratios of $B\to \ddot{I}„\hat{I}½$ and $B\to \ddot{I}€l\hat{I}½$ (respectively) with a theoretical computation of the hadronic matrix elements $\fB$ and the $B\to \ddot{I}€$ 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 $B_s\to \hat{I}{¼}^{+}\hat{I}{¼}^{-}$.}