Lattice QCD at the physical point: light quark masses

Abstract Ordinary matter is described by six fundamental parameters: three couplings (gravitational, electromagnetic and strong) and three masses: the electronʼs ( 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 u d ) and m s are far less accurately known. Here we determine them 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.