The Leptonic Decay Constants of $\bar{Q}q$ Mesons and the Lattice Resolution

TL;DR

This study investigates the leptonic decay constants of heavy mesons using lattice QCD with Wilson quarks, highlighting the dependence on lattice spacing and the challenges in accurately predicting $f_B$ in the quenched approximation.

Contribution

It compares different quark field normalization schemes and analyzes their effects on decay constant calculations, providing insights into lattice artifacts and continuum extrapolation.

Findings

Significant lattice spacing dependence of $f_P$ with Kronfeld-Mackenzie normalization.

Weak dependence observed with standard relativistic normalization.

Extrapolation to continuum yields $f_B=0.18(5)$ GeV, indicating large uncertainties.

Abstract

We present a high statistics study of the leptonic decay constant $f_P$ of heavy pseudoscalar mesons using propagating heavy Wilson quarks within the quenched approximation, on lattices covering sizes from about 0.7~fm to 2~fm. Varying $\beta$ between 5.74 and 6.26 we observe a sizeable $a$ dependence of $f_P$ when one uses the quark field normalization that was suggested by Kronfeld and Mackenzie, compared with the weaker dependence observed for the standard relativistic norm. The two schemes come into agreement when one extrapolates to $a \rightarrow 0$. The extrapolations needed to reach the continuum quantity $f_B$ introduce large errors and lead to the value $f_B=0.18(5)$~GeV in the quenched approximation. This suggests that much more effort will be needed to obtain an accurate lattice prediction for $f_B$.