Differential decay rate of [Formula Presented] semileptonic decay with lattice nonrelativistic QCD

Abstract

We present a lattice QCD calculation of (Formula presented) semileptonic decay form factors in the small pion recoil momentum region. The calculation is performed on a quenched (Formula presented) lattice at (Formula presented) with the nonrelativistic QCD action including the full (Formula presented) terms. The form factors (Formula presented) and (Formula presented) defined in the heavy quark effective theory for which the heavy quark scaling is manifest are adopted, and we find that the (Formula presented) correction to the scaling is small for the B meson. The dependence of the form factors on the light quark mass and on the recoil energy is found to be mild, and we use a global fit of the form factors at various quark masses and recoil energies to obtain model independent results for the physical differential decay rate. We find that the (Formula presented) pole contribution dominates the form factor (Formula presented) for small pion recoil energy, and obtain the differential decay rate integrated over the kinematic region (Formula presented) to be (Formula presented) where the first error is statistical, the second is that from perturbative calculation, and the third is the systematic error from the finite lattice spacing and the chiral extrapolation. We also discuss the systematic errors in the soft pion limit for (Formula presented) in the present simulation. © 2001 The American Physical Society.