Vector correlator and scale determination in lattice QCD

TL;DR

This paper introduces a method to determine lattice spacing in QCD by matching lattice vector correlators with experimental data, addressing finite-size effects for accuracy.

Contribution

It implements a novel approach to set the lattice scale using vector correlator matching, incorporating finite-size effect considerations.

Findings

Successful matching of lattice and experimental correlators at a reference scale

Analysis of finite-size effects on correlator accuracy

Potential for improved precision in lattice QCD scale setting

Abstract

We implement a proposal made in [arXiv:1107.4388] to determine the lattice spacing by matching the lattice vector correlator at a reference distance scale with the same correlator obtained by a dispersion relation based on the $R$-ratio determined experimentally. We work with the isovector current, requiring a separation of the isovector hadronic final states on the phenomenological side. We also discuss the finite-size effect on the correlator, which must be controlled in order for the method to be applicable.