High-precision scale setting in lattice QCD

TL;DR

This paper introduces a new scale-setting quantity, w_0, in lattice QCD that is easy to compute, precise, and robust across different actions and quark masses, aiding accurate physical predictions.

Contribution

The paper proposes and validates a new scale-setting method, w_0, based on Wilson flow, which simplifies and improves the precision of lattice QCD calculations.

Findings

w_0 can be determined at the per-mil level.

Results for w_0 agree across different fermion actions in the continuum limit.

w_0 is suitable for mass-independent scale setting in lattice QCD.

Abstract

Scale setting is of central importance in lattice QCD. It is required to predict dimensional quantities in physical units. Moreover, it determines the relative lattice spacings of computations performed at different values of the bare coupling, and this is needed for extrapolating results into the continuum. Thus, we calculate a new quantity, $w_0$, for setting the scale in lattice QCD, which is based on the Wilson flow like the scale $t_0$ (M. Luscher, JHEP 1008 (2010) 071). It is cheap and straightforward to implement and compute. In particular, it does not involve the delicate fitting of correlation functions at asymptotic times. It typically can be determined on the few per-mil level. We compute its continuum extrapolated value in 2+1-flavor QCD for physical and non-physical pion and kaon masses, to allow for mass-independent scale setting even away from the physical mass point. We demonstrate its robustness by computing it with two very different actions (one of them with staggered, the other with Wilson fermions) and by showing that the results agree for physical quark masses in the continuum limit.