Investigation of the Perturbative Expansion of Moments of Heavy Quark Correlators for $N_f=0$

TL;DR

This study investigates the perturbative expansion of moments of heavy quark correlators in quenched QCD, highlighting challenges in controlling higher-order corrections and discretization effects despite advanced lattice techniques.

Contribution

The paper presents a lattice QCD analysis of heavy quark correlators to assess the perturbative series truncation and discretization effects in the quenched approximation.

Findings

Higher order corrections or continuum limit are not fully under control.

Small lattice spacings and heavy quark masses do not eliminate systematic uncertainties.

Preliminary results suggest need for improved perturbative or continuum approaches.

Abstract

The QCD-coupling is a necessary input in the computation of many observables, and the parametric error on input parameters can be a dominant source of uncertainty. The coupling can be extracted by comparing high order perturbative computations and lattice evaluated moments of mesonic two-point functions with heavy quarks, which provide a high energy scale for perturbation theory. The truncation of the perturbative series is an important systematic uncertainty. We report on our attempt to study this issue by measuring pseudo-scalar two-point functions in volumes of $L=2\, \text{fm}$ with twisted-mass Wilson fermions in the quenched approximation. We use full twist, the non-perturbative clover term and lattice spacings down to $a=0.015\,\text{fm}$ to tame the sizable discretization effects. Our preliminary results indicate that either higher order perturbative corrections or the continuum limit are not under sufficient control despite our small lattice spacings and quark masses extending beyond $2\,m_{\text{charm}}$.