Lattice Study of Semi-Leptonic B Decays: I. B→ Dℓν Decays

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We present a study of semi-leptonic B Dℓν decays in quenched lattice QCD through a calculation of the matrix element D| cγμb| B on a 24³× 48 lattice at β=6.2, using an 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. We extract the form factors h+ and h-. After radiative corrections, we find that h+ displays no dependence on the heavy-quark mass, enabling us to identify it with an Isgur-Wise function. Thus, we obtain Isgur-Wise functions relevant for Bₛ→ Dₛ⁽*⁾ℓν and B→ D⁽*⁾ℓν decays. We then use these functions, in conjunction with heavy-quark effective theory, to extract Vcb with no free parameters from the B→ D*ℓν decay rate measured by the ALEPH, ARGUS and CLEO collaborations. We also use our Isgur-Wise functions and heavy-quark effective theory to calculate branching ratios for Bₛ→ Dₛ⁽*⁾ℓν and B→ D⁽*⁾ℓν decays.