Charm mass effects in the static energy computed in 2+1+1 flavor lattice QCD

TL;DR

This study analyzes the static energy in (2+1+1)-flavor lattice QCD, focusing on charm mass effects, and compares results with perturbative predictions, providing insights into how charm quarks influence the static potential.

Contribution

It provides the first detailed analysis of charm mass effects on the static energy in (2+1+1)-flavor lattice QCD and compares lattice results with perturbative calculations.

Findings

Results for r0/r1 and r0√σ agree with (2+1)-flavor results.

The ratio r1/r2 differs significantly from (2+1)-flavor results due to charm effects.

Lattice results align well with two-loop perturbative expressions including charm mass effects.

Abstract

We report our analysis for the static energy in (2+1+1)-flavor QCD over a wide range of lattice spacings and several quark masses. We obtain results for the static energy out to distances of nearly 1 fm, allowing us to perform a simultaneous determination of the lattice scales $r_2$, $r_1$ and $r_0$ as well as the string tension, $\sigma$. While our results for ${r_0}/{r_1}$ and $r_0$ $\sqrt{\sigma}$ agree with published (2+1)-flavor results, our result for ${r_1}/{r_2}$ differs significantly from the value obtained in the (2+1)-flavor case, likely due to the effect of the charm quark. We study in detail the effect of the charm quark on the static energy by comparing our results on the finest lattices with the previously published (2+1)-flavor QCD results at similar lattice spacing. The lattice results agree well with the two-loop perturbative expression of the static energy incorporating finite charm mass effects.