B $\to$ $\pi$ form factor with 2 flavours of $O(a)$ improved Wilson quarks

Understand

The determinations of $|V_{\rm ub}|$ from the exclusive branching ratios of $B\to \tau \nu$ and $B \to \pi l \nu$ tend to show a tension at the level of $3\sigma$ \cite{Beringer:1900zz}.

• On the theoretical side they depend on the lattice computation of the hadronic matrix elements $f_{\rm B}$ 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.
• Working towards this goal, we present preliminary lattice results of the ALPHA collaboration for the $B\to \pi$ form factor $f_+(q^2)$ with $N_{\rm f}=2$ flavours of $O(a)$-improved Wilson fermions.