A Lattice Calculation of the Isgur-Wise Function

TL;DR

This paper presents a lattice QCD calculation of the Isgur-Wise function for heavy meson transitions, providing numerical results that are compared with models and experimental data, and estimating the slope parameter with different fits.

Contribution

It introduces a lattice calculation of the Isgur-Wise function using the quenched approximation and compares different parametrizations to extract the slope parameter.

Findings

Estimated slope parameter $ ho^2$ around 1.24 to 1.41.

Good agreement with some model predictions and experimental data.

Provides lattice-based numerical results for heavy meson transition form factors.

Abstract

We calculate the Isgur-Wise function ($\xi_0$) by measuring the heavy-heavy meson transition matrix element on the lattice in the quenched approximation. The standard Wilson action is used for both the heavy and the light quarks. Our numerical results are compared with various model calculations and experimental data. In particular, using a linear fit, we find $\rho^2 = 1.24\pm .26 \pm .26 $. (The slope of $\xi_0$ at the zero-recoil point is $-\rho^2$.) Using instead the parametrization of $\xi_0$ suggested by Neubert and Rieckert and fitting the lattice data up to $v\cdot v' \sim 1.2$, we find $\rho^2_{NR}=1.41\pm.19\pm.19$