The Isgur-Wise Function from the Lattice

Abstract

We calculate the Isgur-Wise function by measuring the elastic scattering amplitude of a $D$ meson in the quenched approximation on a $24^3\times48$ lattice at $\beta=6.2$, using an $O(a)$-improved fermion action. Fitting the resulting chirally-extrapolated Isgur-Wise function to Stech's relativistic-oscillator parametrization, we obtain a slope parameter $\rho^2=1.2+7-3. We then use this result, in conjunction with heavy-quark symmetry, to extract $V_{cb}$\ from the experimentally measured $\bar B\to D^*l\bar\nu\,$\ differential decay width. We find $|V_{cb}|\sqrt{\tau_B/1.48{\mathrm ps}}= 0.038 +2-2 +8-3, where the first set of errors is due to experimental uncertainties, while the second is due to the uncertainty in our lattice determination of $\rho^2$.