Non-perturbative computation of the strong coupling constant on the lattice

TL;DR

This paper reviews the ALPHA collaboration's non-perturbative lattice QCD methods for computing the strong coupling constant and quark masses across energy scales, emphasizing systematic error control and recent results.

Contribution

It presents a comprehensive overview of non-perturbative techniques for calculating fundamental QCD parameters on the lattice, including recent results and future extensions.

Findings

Complete results in two-flavor QCD are presented.

Techniques for multiscale non-perturbative calculations are summarized.

An outlook on three-flavor extension with improved precision is provided.

Abstract

We review the long term project of the ALPHA collaboration to compute in QCD the running coupling constant and quark masses at high energy scales in terms of low energy hadronic quantities. The adapted techniques required to numerically carry out the required multiscale non-perturbative calculation with our special emphasis on the control of systematic errors are summarized. The complete results in the two dynamical flavor approximation are reviewed and an outlook is given on the ongoing three flavor extension of the programme with improved target precision.