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

TL;DR

This study uses lattice QCD and quenched QED to precisely determine the up and down quark masses, corrections to Dashen's theorem, and provides insights that exclude the zero up-quark solution to the strong CP problem.

Contribution

The paper presents the first precise lattice QCD calculation of quark masses and Dashen's theorem corrections using quenched QED with multiple lattice spacings and sizes.

Findings

Quantifies violations to Dashen's theorem with epsilon=0.73(2)(5)(17).

Determines 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

In a previous letter (arXiv:1306.2287) we determined the isospin mass splittings of the baryon octet from a lattice calculation based on quenched QED and $N_f{=}2{+}1$ QCD simulations with 5 lattice spacings down to $0.054~\mathrm{fm}$, lattice sizes up to $6~\mathrm{fm}$ and average up-down quark masses all the way down to their physical value. Using the same data we determine here the corrections to Dashen's theorem and the individual up and down quark masses. 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, $m_u=2.27(6)(5)(4)~\mathrm{MeV}$ and $m_d=4.67(6)(5)(4)~\mathrm{MeV}$ in the $\bar{\mathrm{MS}}$ scheme at $2~\mathrm{GeV}$ 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.