A model independent determination of \(|V_{ub}|\) using the global \(q^2\) dependence of the dispersive bounds on the \(B\to\pi l\nu\) form factors

Abstract

We propose a method to determine the CKM matrix element \(|V_{ub}|\) using the global \(q^2\) dependence of the dispersive bound on the form factors for \(B\to \pi l\nu\) decay. Since the lattice calculation of the \(B\to \pi l\nu\) form factor is limited to the large \(q^2\) regime, only the experimental data in a limited kinematic range can be used in a conventional method. In our new method which exploits the statistical distributions of the dispersive bound proposed by Lellouch, we can utilize the information of the global \(q^2\) dependence for all kinematic range. As a feasibility study we determine \(|V_{ub}|\) by combining the form factors from quenched lattice QCD, the dispersive bounds, and the experimental data by CLEO. We show that the accuracy of \(|V_{ub}|\) can be improved by our method.