Electromagnetic splittings of low lying hadrons and light quark masses in 2+1 flavor QCD+QED

Date of Completion

January 2010


Physics, Theory




The u, d and s quark masses are the fundamental parameters in standard model. They are determined from the QCD+QED dynamics. The low energy QCD is a non-perturbatively defined theory and hard to compute analytically. Lattice QCD, on the contrary, plays an important role in the application of QCD to hadron physics. The introduction of lattice QCD and numerical technique is given at the beginning. Results computed in lattice QCD+QED are given for the electromagnetic mass splittings of the low lying hadrons. These are used to determine the renormalized, non-degenerate, light quark masses. It is found that mMSu = 2.37 (10) (24), mMSd = 4.52 (15) (24), and mMSd = 97.7 (2.9) (4.9) MeV at the renormalization scale 2 GeV, where the first error is statistical and the second systematic. 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). Non-compact 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. Finally, detailed analysis of systematic errors in our results and methods for improving them are discussed. ^