Lattice gauge theory computation of the static force

TL;DR

This paper introduces a new lattice gauge theory method to directly compute the static quark-antiquark force using Wilson and Polyakov loops with chromoelectric insertions, improving accuracy and efficiency.

Contribution

It presents a novel direct computation approach for the static force in lattice gauge theory, including renormalization and multilevel algorithms, with comparison to traditional methods.

Findings

The new method reduces discretization errors.

Numerical results agree with traditional potential-based calculations.

The approach enhances computational efficiency and accuracy.

Abstract

We explore a novel approach to compute the force between a static quark and a static antiquark with lattice gauge theory directly. The approach is based on expectation values of Wilson loops or Polyakov loops with chromoelectric field insertions. We discuss theoretical and technical aspects in detail, in particular, how to compensate large discretization errors with a multiplicative renormalization factor and the evaluation using a multilevel algorithm. We also compare numerical results for the static force to corresponding results obtained in the traditional way, i.e., by computing first the static potential and then taking the derivative.