Scaling Study of the Leptonic Decay Constants of Heavy-Light Mesons: A Consumers Report on Improvement Factors

TL;DR

This study examines how leptonic decay constants of heavy-light mesons vary with lattice spacing in high-statistics lattice QCD calculations, revealing weak dependence with standard normalization and stronger variation with alternative normalization.

Contribution

It provides a detailed analysis of the lattice spacing dependence of decay constants using different normalization schemes, highlighting the impact of normalization choices on results.

Findings

Weak $a$ dependence with standard normalization

Stronger $a$ dependence with Kronfeld-Mackenzie normalization

Dependence increases with meson mass from 1.1 GeV to 2.3 GeV

Abstract

A high statistics calculation, performed at $\beta =5.74,\;6.00$ and $6.26$, enables us to study the variation of the leptonic decay constants $f_P$ of heavy pseudoscalar mesons with the lattice spacing $a$. We observe only a weak $a$ dependence when the standard $\sqrt{2\kappa}$ normalization is used for the quark fields, whereas application of the Kronfeld-Mackenzie normalization induces a stronger variation with $a$. Increasing the meson mass from $1.1GeV$ to $2.3GeV$ this situation becomes even more pronounced.