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

Journal Article · Mon Nov 01 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.82.094508· OSTI ID:21503816

Blum, Tom; Ran, Zhou; Doi, Takumi; Hayakawa, Masashi; Izubuchi, Taku; Uno, Shunpei; Yamada, Norikazu ^[1]

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1. Physics Department, University of Connecticut, Storrs, Connecticut 06269-3046 (United States) and RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973 (United States)

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 m{sub u}{sup MS}=2.24(10)(34), m{sub d}{sup MS}=4.65(15)(32), and m{sub s}{sup MS}=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 (m{sub {pi}{sup +}}-m{sub {pi}{sup 0}}){sub QED}=3.38(23) MeV, the splittings including next-to-leading order, (m{sub {pi}{sup +}}-m{sub {pi}{sup 0}}){sub QED}=4.50(23) MeV, (m{sub K{sup +}}-m{sub K{sup 0}}){sub QED}=1.87(10) MeV, and the m{sub u}{ne}m{sub d} contribution to the kaon mass difference, (m{sub K{sup +}}-m{sub K{sup 0}}){sub (m{sub u}-m{sub d})}=-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 (m{sub p}-m{sub n}){sub QED}=0.383(68) MeV, (m{sub p}-m{sub n}){sub (m{sub u}-m{sub d})}=-2.51(14) MeV (statistical errors only), and the total m{sub p}-m{sub n}=-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 {beta}=2.13 and lattice cutoff a{sup -1}{approx_equal}1.78 GeV). We use two lattice sizes, 16{sup 3} and 24{sup 3} ((1.8 fm){sup 3} and (2.7 fm){sup 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){sub L}xSU(2){sub R}-plus-kaon chiral perturbation theory, including the one-loop logs proportional to {alpha}{sub em}m, are given.

• OSTI ID: 21503816
• Journal Information: Physical Review. D, Particles Fields, Vol. 82, Issue 9; Other Information: DOI: 10.1103/PhysRevD.82.094508; (c) 2010 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CHIRALITY
COMPUTERIZED SIMULATION
D QUARKS
FLAVOR MODEL
GEV RANGE 01-10
KAONS
LATTICE FIELD THEORY
MASS
MASS DIFFERENCE
MEV RANGE
NEUTRONS
PERTURBATION THEORY
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PROTONS
QUANTUM CHROMODYNAMICS
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SU-2 GROUPS
SU-3 GROUPS
U QUARKS
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COMPOSITE MODELS
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ELEMENTARY PARTICLES
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FERMIONS
FIELD THEORIES
GEV RANGE
HADRONS
LIE GROUPS
MATHEMATICAL MODELS
MESONS
NUCLEONS
PARTICLE MODELS
PARTICLE PROPERTIES
PSEUDOSCALAR MESONS
QUANTUM FIELD THEORY
QUARK MODEL
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