Non-perturbative running of quark masses in three-flavour QCD

TL;DR

This paper reports high-precision non-perturbative calculations of how quark masses evolve across energy scales in three-flavor QCD, using finite-size scaling and different renormalization schemes.

Contribution

It introduces a novel high-precision computation of quark mass running in three-flavor QCD with scheme matching across scales.

Findings

Precise determination of quark mass running between electroweak and hadronic scales.

Implementation of scheme switching using Schrödinger Functional and Gradient Flow techniques.

Successful matching of different renormalization schemes at an intermediate scale.

Abstract

We present our preliminary results for the computation of the non-perturbative running of renormalized quark masses in $N_f = 3$ QCD, between the electroweak and hadronic scales, using standard finite-size scaling techniques. The computation is carried out to very high precision, using massless $\mathcal{O}(a)$-improved Wilson quarks. Following the strategy adopted by the ALPHA Collaboration for the running coupling, different schemes are used above and below a scale $\mu_0 \sim m_b$, which differ by using either the Schr\"odinger Functional or Gradient Flow renormalized coupling. We discuss our results for the running in both regions, and the procedure to match the two schemes.