$B\pi$ excited-state contamination in lattice calculations of B-meson correlation functions

Abstract

Multi-particle states with additional pions are expected to result in a difficult-to-control excited-state contamination in lattice simulations. We show that heavy meson chiral perturbation theory can be employed to estimate the contamination due to two-particle $B\pi$ states in various $B$-meson observables like the $B$-meson decay constant and the $B{B}^{\ast }\pi$ coupling. We work in the static limit and to next-to-leading order in the chiral expansion, i.e. including $\mathrm{O}(\mathrm{p})$. The $B\pi$ states are found to typically overestimate the observables at the few percent level. We determine two of the LECs from $B\to \pi$ form factor computations of the KEK group and discuss ways to determine the others. In particular two LECs which are associated with smeared interpolating fields seem to be easily accessible and thus open up a way to systematically study the effect of smearing on excited state effects.

Comments: 37 pages, 14 figures