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

L. Varnhorst (1) , S. Durr (1, 2) , Z. Fodor (2, 1, 3) , C. Hoelbling (1) , S. Krieg (2, 1) , Laurent Lellouch (4, 5) , A. Portelli (6, 7, 4, 5) , A. Sastre (1, 4, 5) , K. K. Szabo (1, 2)

1 Theoretische Teilchenphysik
2 JSC - Jülich Supercomputing Centre
3 Departement for Theoretical Physics
4 CPT - Centre de Physique Théorique - UMR 7332
5 CPT - E1 Physique des particules
6 School of Physics and Astronomy [Southampton]
7 SUPA School of Physics and Astronomy [Edinburgh]

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.

Domaines: Physique des Hautes Energies - Phénoménologie [hep-ph]; Physique des Hautes Energies - Réseau [hep-lat]

L. Varnhorst, S. Durr, Z. Fodor, C. Hoelbling, S. Krieg, et al.. Up and down quark masses and corrections to Dashen's theorem from lattice QCD and quenched QED. 34th annual International Symposium on Lattice Field Theory, Jul 2017, Southampton, United Kingdom. ⟨hal-01478010⟩