Up and Down Quark Masses and Corrections to Dashen’s Theorem from Lattice QCD and Quenched QED

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

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

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.

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

Z. Fodor, C. Hoelbling, S. Krieg, Laurent Lellouch, Th. Lippert, et al.. Up and Down Quark Masses and Corrections to Dashen’s Theorem from Lattice QCD and Quenched QED. Physical Review Letters, 2016, 117 (8), pp.082001. ⟨10.1103/PhysRevLett.117.082001⟩. ⟨hal-01309723⟩