Heavy-Light Semileptonic Decays in Staggered Chiral Perturbation Theory

TL;DR

This paper computes form factors for heavy-light meson semileptonic decays using staggered chiral perturbation theory, aiding lattice QCD analyses of B→π and D→K decays with staggered quarks.

Contribution

It extends existing continuum chiral perturbation theory results to the staggered quark case, including non-degenerate sea quarks, and analyzes non-leading chiral effects.

Findings

Derived form factors for heavy-light decays in staggered extsc{schpt}

Generalized continuum results to non-degenerate sea quarks

Identified relations among valence mass dependence coefficients

Abstract

We calculate the form factors for the semileptonic decays of heavy-light pseudoscalar mesons in partially quenched staggered chiral perturbation theory (\schpt), 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 \schpt 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 Becirevic, Prelovsek and Zupan, which we generalize to the staggered (and non-degenerate) case. As a by-product, we obtain the continuum partially quenched results with non-degenerate sea quarks. We analyze the effects of non-leading 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.

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