A Quenched Exploration of Heavy Quark Moments and their Perturbative Expansion

TL;DR

This paper investigates the uncertainties in extracting the QCD coupling from heavy quark moments by analyzing lattice QCD data and perturbative series truncation effects, highlighting significant challenges in continuum and asymptotic extrapolations.

Contribution

It provides an updated lattice study of heavy quark two-point functions in quenched QCD with high precision, focusing on the impact of perturbative truncation and extrapolation difficulties.

Findings

Continuum extrapolations are very challenging.

Extrapolation of the $\Lambda$-parameter to the perturbative region is difficult.

Large discretization effects are mitigated with fine lattice spacings.

Abstract

The parametric error on the QCD-coupling can be a dominant source of uncertainty in several important observables. One way to extract the coupling is to compare high order perturbative computations with lattice evaluated moments of heavy quark two-point functions. The truncation of the perturbative series is a sizable systematic uncertainty that needs to be under control. In this contribution we give an update on our study arXiv:hep-lat/2203.07936v1 on this issue. We measure pseudo-scalar two-point functions in volumes of $L=2$ fm with twisted-mass Wilson fermions in the quenched approximation. We use full twist, the non-perturbative clover term and lattice spacings down to $a=0.010$ fm to tame the large discretization effects. Our results show that both the continuum extrapolations and the extrapolation of the $\Lambda$-parameter to the asymptotic perturbative region are very challenging.