$|V_{ub}|$ from exclusive semileptonic $B\to \pi$ decays revisited

We update the extraction of $|V_{ub}|$ from exclusive semileptonic $B\to \pi$ decays, combining experimental partial branching fraction information with theoretical form-factor calculations, using the recently revised HPQCD results for the form factors $f_{+}$ and $f_0$. We use Omnès representations to provide the required parametrizations of the form factors. The extracted value is $|V_{ub}|=(3.47\pm 0.29\pm 0.03)\times {10}^{-3}$, in striking agreement with $|V_{ub}|$ extracted using all other inputs in CKM fits and showing some disagreement with $|V_{ub}|$ extracted from inclusive semileptonic $B\to \pi$ decays.

Figure 1

Results obtained from the fit to experimental partial branching fraction data and theoretical form-factor calculations. The top left plot shows the two form factors with their error bands, the lattice and LCSR input points (dots: green LCSR, red HPQCD, blue FNAL-MILC), and “experimental” points (black triangles, upward pointing for tagged and downward pointing for untagged data) constructed by plotting at the center of each bin the constant form factor that would reproduce the partial branching fraction in that bin. The top right plot shows the differential decay rate together with the experimental inputs. The bottom plots provide more details of the inputs and fits by showing on the left $\log [(m_{B^{*}}^2-q^2)f_{+}(q^2)/m_{B^{*}}^2]$ as a function of $q^2$, and on the right $P\varphi f_{+}$ as a function of $-z$. The dashed magenta curve in the bottom right plot is a cubic polynomial fit in $z$ to the Omnès curve.