Heavy-light semileptonic decays in staggered chiral perturbation theory

Abstract

We calculate the form factors for the semileptonic decays of heavy-light pseudoscalar mesons in partially quenched staggered chiral perturbation theory ($\mathrm{S}\ensuremath{\chi}\mathrm{PT}$), working to leading order in $1/{m}_{Q}$, where ${m}_{Q}$ is the heavy-quark mass. We take the light meson in the final state to be a pseudoscalar corresponding to the exact chiral symmetry of staggered quarks. The treatment assumes the validity of the standard prescription for representing the staggered ``fourth-root trick'' within $\mathrm{S}\ensuremath{\chi}\mathrm{PT}$ by insertions of factors of $1/4$ for each sea-quark loop. Our calculation is based on an existing partially quenched continuum chiral perturbation theory calculation with degenerate sea quarks by Be\ifmmode \acute{c}\else \'{c}\fi{}irevi\ifmmode \acute{c}\else \'{c}\fi{}, Prelovsek, and Zupan, which we generalize to the staggered (and nondegenerate) case. As a byproduct, we obtain the continuum partially quenched results with nondegenerate sea quarks. We analyze the effects of nonleading chiral terms, and find a relation among the coefficients governing the analytic valence mass dependence at this order. Our results are useful in analyzing lattice computations of form factors $B\ensuremath{\rightarrow}\ensuremath{\pi}$ and $D\ensuremath{\rightarrow}K$, when the light quarks are simulated with the staggered action.