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

F. Bahr, F. Bernardoni, B. Blossier, J. Bulava, M. Della Morte, P. Fritzsch, N. Garron, A. Gérardin, J. Heitger, G. von Hippel, A. Ramos, H. Simma, R. Sommer

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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 $B_s \to \mu^+\mu^-$.}
TidsskriftPoS ICHEP
StatusUdgivet - 27. nov. 2012


  • hep-lat