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

TL;DR

This paper introduces a novel, model-independent approach to determine the CKM matrix element |V_{ub}| by leveraging the global q^2 dependence of dispersive bounds on B→πlν form factors, integrating lattice QCD, experimental data, and dispersive bounds.

Contribution

It presents a new method that uses the global q^2 dependence of dispersive bounds to improve the determination of |V_{ub}|, overcoming limitations of lattice calculations and limited experimental data.

Findings

The method can utilize the entire kinematic range of data.

It improves the accuracy of |V_{ub}| determination.

Feasibility is demonstrated with lattice QCD, dispersive bounds, and CLEO data.

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.