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We present a determination of the corrections to Dashen's theorem and of theindividual up and down quark masses from a lattice calculation based onquenched QED and $N_f=2+1$ QCD simulations with 5 lattice spacings down to0.054 fm. The simulations feature lattice sizes up to 6 fm and average up-downquark masses all the way down to their physical value. For the parameter whichquantifies violations to Dashens's theorem we obtain $\epsilon=0.73(2)(5)(17)$,where the first error is statistical, the second is systematic, and the thirdis an estimate of the QED quenching error. For the light quark masses weobtain, $m_u=2.27(6)(5)(4) \, MeV$ and $m_d=4.67(6)(5)(4) \, MeV$ in the$\overline{MS}$ 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 strongCP problem by more than 24 standard deviations.

Up and down quark masses and corrections to Dashen's theorem from lattice QCD and quenched QED