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

## TL;DR

This paper uses lattice QCD and quenched QED simulations to precisely determine the up and down quark masses, corrections to Dashen's theorem, and provides strong evidence against the massless up quark solution to the strong CP problem.

## Contribution

It presents the first high-precision lattice calculation of quark masses and Dashen's theorem corrections including systematic and QED quenching errors.

## Key findings

- Quantifies violations to Dashen's theorem with epsilon=0.73(2)(5)(17)
- Determines light quark masses: m_u=2.27(6)(5)(4) MeV, m_d=4.67(6)(5)(4) MeV
- Excludes m_u=0 solution to strong CP problem by over 24 standard deviations

## 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, $m_u=2.27(6)(5)(4) \, MeV$ 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 strong CP problem by more than 24 standard deviations.