Volume 256 -
34th annual International Symposium on Lattice Field Theory (LATTICE2016) -
Standard Model Parameters and Renormalization

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

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Pre-published on:
2017 February 14

Published on:
2017 March 24

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 $\epsilon=0.73(2)(5)(17)$, 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, $m_u=2.27(6)(5)(4) \, \mbox{MeV}$ and $m_d=4.67(6)(5)(4) \, \mbox{MeV}$ in the $\overline{\mbox{MS}}$ scheme at $2 \, \mbox{GeV}$ 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.

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