### Abstract

We present a determination of the corrections to Dashen's theorem and of the individual up and down quark masses from a lattice calculation based on quenched QED and N_{f} = 2+1 QCD simulations with 5 lattice spacings down to 0.054 fm. The simulations feature 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 Dashens's theorem we obtain e =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)MeV and m_{d} = 4:67(6)(5)(4)MeV in the MS scheme at 2GeV 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.

Original language | English |
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Journal | Proceedings of Science |

Volume | Part F128557 |

Publication status | Published - Jan 1 2016 |

Event | 34th Annual International Symposium on Lattice Field Theory, LATTICE 2016 - Southampton, United Kingdom Duration: Jul 24 2016 → Jul 30 2016 |

### ASJC Scopus subject areas

- General

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## Cite this

*Proceedings of Science*,

*Part F128557*.