paper

Electromagnetic mass splittings of the low lying hadrons and quark masses from 2+1 flavor lattice QCD+QED

arXiv:1006.1311 · doi:10.1103/PhysRevD.82.094508

Abstract

Results are presented for the electromagnetic mass splittings of the low lying hadrons. These are used to determine the non-degenerate light quark masses. It is found that m_u=2.24(10)(34), m_d=4.65(15)(32), and MeV (MSbar scheme, 2 GeV scale). The first error is statistical and the second systematic. We find the lowest order electromagnetic splitting (m_pi+-m_pi0)_QED=3.38(23) MeV, the splittings including next-to-leading order, (m_pi+-m_pi0)_QED=4.50(23) MeV, (m_K+-m_K0)_QED=1.87(10) MeV, and the m_u != m_d contribution to the kaon mass difference, (m_K+-m_K0)_(m_u-m_d)=-5.840(96) MeV. All errors are statistical only, and the next-to-leading order pion splitting is only approximate; it does not contain all next-to-leading order contributions. We also computed the proton-neutron mass difference, including for the first time, QED interactions in a realistic 2+1 flavor calculation. We find MeV, (m_p-m_n)_(m_u-m_d)=-2.51(14) MeV, and the total m_p-m_n=-2.13(16)(70) MeV, where the first error is statistical, and the second, part of the systematic error. We use domain wall fermions and the Iwasaki gauge action (gauge coupling beta=2.13). We use two lattice sizes, 16^3 and 24^3, to address finite volume effects. Non-compact QED is treated in the quenched approximation. We present new results for the electromagnetic low energy constants in SU(3) and SU(2) partially-quenched chiral perturbation theory to the next-to-leading order, obtained from fits to our data. Detailed analysis of systematic errors in our results and methods for improving them are discussed. Finally, new analytic results for SU(2)_L x SU(2)_R-plus-kaon chiral perturbation theory, including the one-loop logs proportional to alpha_em*m, are given.

Significant additions: finite volume analysis of kaon mass (Sec. II and the Appendix) which is used to obtain new central values, extended discussion of the breaking of Dashen's theorem (VII), additional phenomenological results (VII), and a new section (VIII) on isospin breaking effects on the kaon decay constant. No conclusions or results from the first version changed significantly

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