The Isgur-Wise function from the lattice

We calculate the Isgur-Wise function by measuring the elastic scattering amplitude of a D meson in the quenched approximation on a ${24}^3$×48 lattice at β=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 ${\mathrm{\rho }}^2$=1.$2_{\mathrm{-}3}^{+7\mathrm{}}$. We then use this result, in conjunction with heavy-quark symmetry, to extract ${\mathit{V}}_{\mathit{c}\mathit{b}}$ from the measured B¯→${\mathit{D}}^{\mathrm{*}}$lν¯ differential decay width. We find ‖${\mathit{V}}_{\mathit{c}\mathit{b}}$‖ √${\mathrm{\tau }}_{\mathit{B}}$/1.48 ps =0.${038}_{\mathrm{-}2\mathrm{-}3}^{+2+8\mathrm{}}$, where the first error is due to experimental uncertainties, while the second is due to the uncertainty in our lattice determination of ${\mathrm{\rho }}^2$.