Up and Down Quark Masses and Corrections to Dashen's Theorem from Lattice QCD and Quenched QED

Abstract

In a previous Letter [Borsanyi et al., Phys. Rev. Lett. 111, 252001 (2013)] we determined the isospin mass splittings of the baryon octet from a lattice calculation based on N-f = 2 + 1 QCD simulations to which QED effects have been added in a partially quenched setup. Using the same data we determine here the corrections to Dashen's theorem and the individual up and down quark masses. Our ensembles include 5 lattice spacings down to 0.054 fm, lattice sizes up to 6 fm, and average up-down quark masses all the way down to their physical value. For the parameter which quantifies violations to Dashen's theorem, we obtain epsilon = 0.73(2)(5)(17), where the first error is statistical, the second is systematic, and the third is an estimate of the QED quenching error. For the light quark masses we obtain, m(u) = 2.27(6)(5)(4) and m(d) = 4.67(6)(5)(4) MeV in the modified minimal subtraction scheme at 2 GeV and the isospin breaking ratios m(u)/m(d) = 0.485(11)(8)(14), R = 38.2(1.1)(0.8)(1.4), and Q = 23.4(0.4)(0.3)(0.4). Our results exclude the m(u) = 0 solution to the strong CP problem by more than 24 standard deviations.