Pion couplings to the scalar $$B$$ B meson

Benoît Blossier,Nicolas Garron,Antoine Gérardin

doi:10.1140/epjc/s10052-015-3321-0

Abstract

We present two-flavor lattice QCD estimates of the hadronic couplings $g_{B^*_0 B \pi}$ and $g_{B_1^* B_0^* \pi}$ that parametrise the non leptonic decays $B^*_0 \to B \pi$ and $B^*_1 \to B_0^* \pi$. We use CLS two-flavour gauge ensembles. Our framework is the Heavy Quark Effective Theory (HQET) in the static limit and solving a Generalized Eigenvalue Problem (GEVP) reveals crucial to disentangle the $B^*_0$($B^*_1$) state from the $B \pi$($B^*\pi$) state. This work brings us some experience on how to treat the possible contribution from multihadronic states to correlation functions calculated on the lattice, especially when $S$-wave states are involved.

Highlights

Heavy Meson Chiral Perturbation Theory (HMχ PT) [1,2]is commonly used to extrapolate lattice data in the heavylight sector to the physical point
We present two-flavor lattice QCD estimates of the the hadronic couplings g non-leptonic decays
It gives a further check that the extraction of the scalar B meson decay constant on those ensembles, which we report in a forthcoming paper, is under control at ∼10 % of precision we hope

Summary

Introduction

Is commonly used to extrapolate lattice data in the heavylight sector to the physical point. The coupling g is similar to g, but for a hadronic transition between positive parity states. Those transitions are energetically not allowed for the B system but are useful for chiral extrapolations in Lattice QCD. Two-point correlation functions of a scalar B meson and a Bπ multihadronic state:. One can show that, in the static limit of HQET [19], MsGEVP(t, t0) −−t−−1→ g + O t e− N+1,nt , t0 =t −1 where mn = Em − En is the energy difference between the mth and nth excited states of the GEVP and N × N is the size of the matrix of correlators defining the GEVP

Lattice setup

Results

Discussion and conclusion