Lattice study of semileptonicBdecays:B¯→Dlν¯ decays

We present a study of semileptonic B¯→Dlν¯ decays in quenched lattice QCD through a calculation of the matrix element 〈D‖c¯${\gamma }^{\mathrm{\mu }}$b‖B¯〉 on a ${24}^3$×48 lattice at β=6.2, using an O(a)-improved fermion action. We perform the calculation for several values of the initial and final heavy-quark masses around the charm mass, and three values of the light-(anti)quark mass around the strange mass. Because the charm quark has a bare mass which is almost 1/3 the inverse lattice spacing, we study the ensuing mass-dependent discretization errors, and propose a procedure for subtracting at least some of them nonperturbatively. We extract the form factors ${\mathit{h}}^{+}$ and ${\mathit{h}}^{\mathrm{-}}$. After radiative corrections, we find that ${\mathit{h}}^{+}$ displays no dependence on the heavy-quark mass, enabling us to identify it with an Isgur-Wise function ξ. Interpolating the light-quark mass to that of the strange, we obtain an Isgur-Wise function relevant for B${\mathrm{¯}}_{\mathit{s}}$→${\mathit{D}}_{\mathit{s}}^{\left(\mathrm{*}\right)}$lν¯ decays which has a slope -${\xi }_{\mathit{s}}^{\prime }$=1.$2_{\mathrm{-}2}^{+2\mathrm{}}$ (stat${)}_{\mathrm{-}1}^{+2\mathrm{}}$ (syst) at zero recoil. An extrapolation to a massless light quark enables us to obtain an Isgur-Wise function relevant for B¯→${\mathit{D}}^{\left(\mathrm{*}\right)}$lν¯ decays. This function has a slope -${\xi }_{\mathit{u},}$ ${\mathit{d}}^{\prime }$=0.$9_{\mathrm{-}3}^{+2\mathrm{}}$ (stat${)}_{\mathrm{-}2}^{+4\mathrm{}}$ (syst) at zero recoil. We observe a slight decrease in the magnitude of the central value of the slope as the mass of the light quark is reduced; given the errors, however, the significance of this observation is limited.