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

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 ${\hat{I}}^2=6.2$, 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 $\hat{I}{¾}^{\prime }(1)=-1.7\pm 0.2$ and $\hat{I}{¾}^{\prime }(1)=-1.4+0.2-0.1$ 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.

25 pages, uuencoded compressed postscript file containing 11 figures, LaTeX, Edinburgh Preprint 94/548, Rome Preprint 94/1057 and Southampton Preprint SHEP 94/95-5