Determining the Efficacy of Different Parameterizations of the z-expansion

TL;DR

This paper introduces a methodology to evaluate the accuracy of lattice form factor extrapolations using experimental data, comparing two parameterizations for B decays and finding BCL slightly superior in low q^2 regions.

Contribution

It develops a new methodology for testing lattice extrapolation accuracy directly with experimental data and compares two popular parameterizations in B decay analysis.

Findings

BCL parameterization better predicts low q^2 region than BGL

Methodology can be extended to other B decays

Provides a data-driven approach for form factor validation

Abstract

We develop a methodology to test the accuracy of lattice extrapolations of the form factors in B decays only using experimental data. We test this methodology by comparing the BGL parameterization proposed by Boyd, Grinstein, and Lebed (1996) and the BCL parameterization proposed by Bourrely Caprini and Lellouch (2008) in the context of $B \rightarrow \pi \ell \nu$. Our results suggest that the BCL parameterization is a slightly better predictor of the low $q^2$ region than the BGL parameterization and that this methodology can be extended to other decays such as $B\rightarrow D\ell \nu$.