The Static Approximation of Heavy-Light Quark-Systems - A Systematic Lattice Study

TL;DR

This study systematically investigates finite lattice spacing and volume effects on the decay constant of heavy pseudoscalar mesons in the static approximation, providing insights into volume dependence, wave function effects, and related mass differences.

Contribution

It offers a comprehensive lattice analysis of finite size and discretization effects on heavy-light meson properties in the static limit, including decay constants and mass differences.

Findings

Volume dependence negligible beyond 1.5 fm

No smearing dependence on results

Estimated string breaking distance in static potential

Abstract

We present a study of {\it finite} $a$ and {\it volume} effects of the leptonic decay constant $f$ of heavy pseudoscalar mesons in the static approximation. This study is performed on a number of lattices at $\beta=$ 5.74,~6.0 and 6.26 covering sizes from about 0.7~$fm$ to 2~$fm$. We confirm that beyond 1.5~$fm$ the volume dependence is negligible. By carefully analysing results obtained using different trial wave functions for the heavy meson we find no dependence on the smearing. We also give results for the mass difference of the scalar - pseudoscalar and the $\Lambda _{b}$ - pseudoscalar. Using the mass of the pseudoscalar meson we estimate the distance of string breaking in the static quark potential.