Staggered chiral perturbation theory for heavy-light mesons

Abstract

We incorporate heavy-light mesons into staggered chiral perturbation theory (SPT), working to leading order in 1=m Q , where m Q is the heavy-quark mass. At first nontrivial order in the chiral expansion, staggered taste violations affect the chiral logarithms for heavy-light quantities only through the lightmeson propagators in loops. There are also new analytic contributions coming from additional terms in the Lagrangian involving heavy-light and light mesons. Using this heavy-light SPT, we perform the oneloop calculation of the B (or D) meson leptonic decay constant in the partially quenched and full QCD cases. In our treatment, we assume the validity both of the ''fourth root trick'' to reduce four staggered tastes to one, and of the SPT prescription to represent this trick by insertions of factors of 1=4 for each sea-quark loop.

NeutralB-meson mixing from three-flavor lattice quantum chromodynamics: Determination of theSU(3)-breaking ratioξ<

“…[67] and [104]. The MILC lattices are large enough in the time direction that it can be treated as infinite to a very good approximation, so we are interested in corrections due to finite spatial volume only.…”

“…To obtain information about the quark-mass dependence of the relevant matrix elements, which allows us to extrapolate our results to the physical masses, we perform our calculation at six sea × six valence quark masses, thus including numerous partially quenched data points. In addition, the leading-order taste violations, which arise at O(a 2 α s ), are included in the theory and then removed when the extrapolation is performed using rooted heavy-meson staggered chiral perturbation theory (rHMSχPT) [63,64,67]. The χPT expression for O q 1 , as well as for the matrix elements of all the other operators in the ∆B = 2 effective Hamiltonian was first described in Ref.…”

“…[85] for partially quenched Wilson-type quarks in the framework of continuum heavy-meson χPT (HMχPT). With staggered fermions, we also must include the effects of taste-violating interactions, using rHMSχPT [67].…”

“…IV, we give the details of the procedure for the correlator fits. Section V is devoted to the chiralcontinuum extrapolation, which is performed within the framework of rooted staggered chiral perturbation theory [63][64][65][66][67]. We describe and discuss the choice of the functional form used in the extrapolation, the different fitting methods tested, and the choice of parameters and parametrization.…”

Update on pi and K Physics

“…This is important because these parameters also appear in staggered chiral forms for other physical quantities, e.g., heavy-light decay constants and form factors [5]. Fixing the parameters from the lightlight system reduces the systematic errors in heavy-light computations [6].…”