Geometrical Volume Effects in the Computation of the Slope of the Isgur-Wise Function

TL;DR

This paper investigates the geometrical volume effects in lattice QCD calculations of the Isgur-Wise function's slope, revealing significant finite-volume effects that are purely geometrical and providing corrected estimates for the slope.

Contribution

It introduces a method to evaluate the Isgur-Wise function's slope on the lattice and accounts for geometrical finite-volume effects, improving the accuracy of the results.

Findings

Finite-volume effects are large and purely geometrical.

Approximate expressions correct for these volume effects.

Estimated slope of the Isgur-Wise function is around -1.7 and -1.4 for different mesons.

Abstract

We use a method recently suggested for evaluating the slope of the Isgur-Wise function, at the zero-recoil point, on the lattice. The computations are performed in the quenched approximation to lattice QCD, on a $24^3 \times 48$ lattice at $\beta=6.2$, using an $O(a)$-improved action for the fermions. We have found unexpectedly large finite-volume effects in such a calculation. These volume corrections turned out to be purely geometrical and independent of the dynamics of the system. After the study of these effects on a smaller volume and for different quark masses, we give approximate expressions that account for them. Using these approximations we find $\xi^\prime(1)=-1.7 \pm 0.2$ and $\xi^\prime(1)=-1.4 +0.2-0.1$ for the slope of the Isgur-Wise function, for two mesons composed of a heavy quark slightly heavier and lighter, respectively, than the charm quark, and in both cases, a light antiquark whose mass is about that of the strange quark.