Understand
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.
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