HQET at order 1/m: III. Decay constants in the quenched approximation

TL;DR

This paper computes the $B_s$ meson decay constant using lattice HQET with non-perturbative corrections, controlling errors via advanced techniques, and also estimates the decay constant of the first radially excited $B_s$ state.

Contribution

It presents a non-perturbative lattice calculation of $B_s$ decay constants including next-to-leading order HQET corrections and introduces technical improvements for error control.

Findings

Small higher order contributions estimated

Decay constant $f_{B_s}$ extrapolated to continuum limit

Decay constant $f_{B'_s}$ of excited state computed in static limit

Abstract

We report on the computation of the $B_s$ meson decay constant in Heavy Quark Effective Theory on the lattice. The next to leading order corrections in the HQET expansion are included non-perturbatively. We estimate higher order contributions to be very small. The results are extrapolated to the continuum limit, the main systematic error affecting the computation is therefore the quenched approximation used here. The Generalized Eigenvalue Problem and the use of all-to-all propagators are important technical ingredients of our approach that allow to keep statistical and systematic errors under control. We also report on the decay constant $f_{B'_s}$ of the first radially excited state in the $B_s$ sector, computed in the static limit.