Lattice QCD at the physical point: light quark masses

TL;DR

This paper precisely determines the light quark masses (up, down, and strange) using advanced lattice QCD calculations, significantly improving accuracy over previous estimates by controlling all systematic uncertainties.

Contribution

It introduces a comprehensive lattice QCD approach with physical pion masses, large lattice volumes, multiple spacings, and nonperturbative renormalization to accurately compute light quark masses.

Findings

Quark masses determined with below 2% uncertainty

All systematic effects are rigorously controlled

Results improve upon previous estimates by an order of magnitude

Abstract

Ordinary matter is described by six fundamental parameters: three couplings (gravitational, electromagnetic and strong) and three masses: the electron's (m_e) and those of the up (m_u) and down (m_d) quarks. An additional mass enters through quantum fluctuations: the strange quark mass (m_s). The three couplings and m_e are known with an accuracy of better than a few per mil. Despite their importance, $m_u$, $m_d$ (their average m_{ud}) and m_s are relatively poorly known: e.g. the Particle Data Group quotes them with conservative errors close to 25%. Here we determine these quantities with a precision below 2% by performing ab initio lattice quantum chromodynamics (QCD) calculations, in which all systematics are controlled. We use pion and quark masses down to (and even below) their physical values, lattice sizes of up to 6 fm, and five lattice spacings to extrapolate to continuum spacetime. All necessary renormalizations are performed nonperturbatively.