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

Tom Blum and Ran Zhou*

Takumi Doi

Masashi Hayakawa

Taku Izubuchi

Shunpei Uno

Norikazu Yamada

  • Physics Department, University of Connecticut, Storrs, Connecticut 06269-3046, USA and RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973, USA

  • Graduate School of Pure and Applied Science, University of Tsukuba, Tennodai 1-1-1, Tsukuba, Ibaraki 305-8571, Japan and RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan

  • Department of Physics, Nagoya University, Nagoya 464-8602, Japan and Theoretical Physics Laboratory, Nishina Center, RIKEN, Wako, 351-0198, Japan

  • Brookhaven National Laboratory, Upton, New York 11973, USA and RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973, USA

  • Department of Physics, Nagoya University, Nagoya 464-8602, Japan and RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973, USA

  • KEK Theory Center, Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan and School of High Energy Accelerator Science, The Graduate University for Advanced Studies (Sokendai), Tsukuba 305-0801, Japan

  • *Present Address: Department of Physics, Indiana University, Bloomington, IN 47405, USA
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Phys. Rev. D 82, 094508 – Published 24 November, 2010

DOI: https://doi.org/10.1103/PhysRevD.82.094508

Abstract

Results computed in lattice QCD+QED are presented for the electromagnetic mass splittings of the low-lying hadrons. These are used to determine the renormalized, nondegenerate, light quark masses. It is found that muMS¯=2.24(10)(34), mdMS¯=4.65(15)(32), and msMS¯=97.6(2.9)(5.5)  MeV at the renormalization scale 2 GeV, where the first error is statistical and the second systematic. We find the lowest-order electromagnetic splitting (mπ+−mπ0)QED=3.38(23)  MeV, the splittings including next-to-leading order, (mπ+−mπ0)QED=4.50(23)  MeV, (mK+−mK0)QED=1.87(10)  MeV, and the mu≠md contribution to the kaon mass difference, (mK+−mK0)(mu−md)=−5.840(96)  MeV. All errors are statistical only, and the next-to-leading-order pion splitting is only approximate in that 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 (mp−mn)QED=0.383(68)  MeV, (mp−mn)(mu−md)=−2.51(14)  MeV (statistical errors only), and the total mp−mn=−2.13(16)(70)  MeV, where the first error is statistical, and the second, part of the systematic error. The calculations are carried out on QCD ensembles generated by the RBC and UKQCD collaborations, using domain wall fermions and the Iwasaki gauge action (gauge coupling β=2.13 and lattice cutoff a−1≈1.78  GeV). We use two lattice sizes, 163 and 243 ((1.8  fm)3 and (2.7  fm)3), to address finite-volume effects. Noncompact QED is treated in the quenched approximation. The valence pseudoscalar meson masses in our study cover a range of about 250 to 700 MeV, though we use only those up to about 400 MeV to quote final results. 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×SU(2)R-plus-kaon chiral perturbation theory, including the one-loop logs proportional to αemm, are given.

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Phys. Rev. D 82, 094508– Published 24 November, 2010
  • Received 2 September 2010

© 2010 The American Physical Society

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