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 $24^3\times 48$ 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 ${\rho }^2=1.2+7-3.Wethenusethisresult,inconjunctionwithheavy-quarksymmetry,toextract$V_{cb}$fromtheexperimentallymeasured$\bar B\to D^*l\bar\nu\,$differentialdecaywidth.Wefind$|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 ${\rho }^2$.

Comments: 11 postscript pages + 3 postscript figures, all in one uuencoded, compressed, tar file. This is the published version (Phys. Rev. Lett. 72, pp. 462-465 (1994)). The lattice data were partially re-analyzed and our final results for the slope and Vcb differ from those of our first submission. The text was also trimmed slightly to fit page requirements