title: 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 ϵ=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.
authors: Department of Physics, Wuppertal University, Gaussstr. 20, D-42119 Wuppertal, Germany.|Institute for Theoretical Physics, Eötvös University, Pázmány P. sét. 1/A, H-1117 Budapest, Hungary.|IAS/JSC, Forschungszentrum Jülich, D-52425 Jülich, Germany.
authors: Z
authors: Z
authors: Fodor
authors: Department of Physics, Wuppertal University, Gaussstr. 20, D-42119 Wuppertal, Germany.
authors: C
authors: C
authors: Hoelbling
authors: Department of Physics, Wuppertal University, Gaussstr. 20, D-42119 Wuppertal, Germany.|IAS/JSC, Forschungszentrum Jülich, D-52425 Jülich, Germany.
authors: S
authors: S
authors: Krieg
authors: CNRS, Aix-Marseille U., U. de Toulon, Centre de Physique Théorique, UMR 7332, F-13288 Marseille, France.
authors: L
authors: L
authors: Lellouch
authors: IAS/JSC, Forschungszentrum Jülich, D-52425 Jülich, Germany.
authors: Th
authors: T
authors: Lippert
authors: CNRS, Aix-Marseille U., U. de Toulon, Centre de Physique Théorique, UMR 7332, F-13288 Marseille, France.|School of Physics & Astronomy, University of Southampton, SO17 1BJ Southampton, United Kingdom.|School of Physics & Astronomy, The University of Edinburgh, EH9 3FD Edinburgh, United Kingdom.
authors: A
authors: A
authors: Portelli
authors: Department of Physics, Wuppertal University, Gaussstr. 20, D-42119 Wuppertal, Germany.|CNRS, Aix-Marseille U., U. de Toulon, Centre de Physique Théorique, UMR 7332, F-13288 Marseille, France.
authors: A
authors: A
authors: Sastre
authors: Department of Physics, Wuppertal University, Gaussstr. 20, D-42119 Wuppertal, Germany.|IAS/JSC, Forschungszentrum Jülich, D-52425 Jülich, Germany.
authors: K K
authors: KK
authors: Szabo
authors: Department of Physics, Wuppertal University, Gaussstr. 20, D-42119 Wuppertal, Germany.
authors: L
authors: L
authors: Varnhorst