Eur. Phys. J. C (2018) 78: 387
https://doi.org/10.1140/epjc/s10052-018-5870-5

Regular Article - Theoretical Physics

Non-perturbative quark mass renormalisation and running in QCD

¹ Instituto de Física de Cantabria IFCA-CSIC, Avda. de los Castros s/n, 39005, Santander, Spain
² Theoretical Physics Department, CERN, 1211, Geneva 23, Switzerland
³ Instituto de Física Teórica UAM-CSIC & Dpto. de Física Teórica, Universidad Autónoma de Madrid, Cantoblanco, 28049, Madrid, Spain
⁴ INFN, Sezione di Torino, Via Pietro Giuria 1, 10125, Turin, Italy
⁵ School of Mathematics, Trinity College Dublin, Dublin 2, Ireland
⁶ INFN, Sezione di Tor Vergata c/o Dipartimento di Fisica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133, Rome, Italy

^* e-mail: patrick.fritzsch@cern.ch

Received: 21 February 2018
Accepted: 4 May 2018
Published online: 18 May 2018

Abstract

We determine from first principles the quark mass anomalous dimension in QCD between the electroweak and hadronic scales. This allows for a fully non-perturbative connection of the perturbative and non-perturbative regimes of the Standard Model in the hadronic sector. The computation is carried out to high accuracy, employing massless -improved Wilson quarks and finite-size scaling techniques. We also provide the matching factors required in the renormalisation of light quark masses from lattice computations with -improved Wilson fermions and a tree-level Symanzik improved gauge action. The total uncertainty due to renormalisation and running in the determination of light quark masses in the SM is thus reduced to about .