Alladi Ramakrishnan Hall

Extrapolation and unitarity bounds for the $B \to π$ form factor and its implication to $|V_{ub}|$

Senti Imsong

IMSc

We address the problem of extrapolating the vector form factor $f_{B\pi}^+$, which is relevant to $B\to \pi\ell
u_\ell$
decays, from the region of small to the region of large momentum transfer. As input, we use the QCD light-cone sum rule at small momentum transfer. We carry out a comprehensive Bayesian uncertainty analysis and obtain correlated uncertainties for the normalization and shape parameters of the form factor. The $z$-series parametrization for $f_{B\pi}^+$ is employed to extrapolate our results to large momentum transfer, and to compare with the lattice QCD results. To test the validity of our extrapolation we use the upper and lower bounds from the unitarity and positivity of the two-point correlator of heavy-light quark currents. We finally combine our results with the latest experimental measurements of $B\to \pi \ell
u_\ell$ by the BaBar and Belle collaborations, and obtain $|V_{ub}|= (3.32^{+0.26}_{-0.22}) \cdot 10^{-3}$ from a Bayesian analysis.