We calculate the form factors for the semileptonic decays of heavy-light pseudoscalar mesons in partially quenched staggered chiral perturbation theory ($\mathrm{S}\chi \mathrm{PT}$), 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 $\mathrm{S}\chi \mathrm{PT}$ 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 Bećirević, 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 $B\to \pi$ and $D\to K$, when the light quarks are simulated with the staggered action.

• Received 13 April 2007

DOI:https://doi.org/10.1103/PhysRevD.76.014002