Variations to the z-Expansion of the Form Factor Describing the Decay of B Mesons

TL;DR

This paper compares different parameterizations of the form factor in B meson decay, analyzing their stability and extrapolation accuracy using Belle data to inform lattice QCD simulations.

Contribution

It evaluates the stability of various form factor parameterizations by fitting low recoil data and comparing predictions at high recoil, providing insights for lattice QCD.

Findings

Different parameterizations show varying stability in extrapolation.

Fitting low recoil data can predict high recoil behavior.

Results inform the choice of form factor models for decay analysis.

Abstract

We examine the decay rate of the particle decay $B^0 \rightarrow D^- \ell^+ \nu_{\ell}$ using data collected from the Belle Collaboration. We studied three parameterizations of the form factor which describe the differential decay rate, the Caprini, Lellouch, and Neubert (CLN) parametrization, the Boyd, Grinstein, and Lebed (BGL) parametrization, and the Bourrely, Caprini, and Lellouch (BCL) parameterization. The form factor is a function of the hadronic recoil variable $w$, and each parameterization contains unique free parameters which are the focus of this work. We test the extrapolations of the form factor by fitting many different subsets of the low $w$ data and then compare the prediction of the fit to the high $w$ data using a $\chi^2$-metric. By only fitting the low $w$ data we are able to examine the stability of extrapolations which will be informative for lattice simulations.