2 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, non-degenerate, light quark masses. It is found that m M S u = 2.24 (10) (34), m M S d = 4.65 (15) (32), and m M S s = 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 π + − m π 0 ) QED = 3.38 (23) MeV, the splittings including next-to-leading order, (m π + − m π 0 ) QED = 4.50 (23) MeV, (m K + − m K 0 ) QED = 1.87(10) MeV, and the m u = m d contribution to the kaon mass difference, (m K + − m K 0 ) (mu−m 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 p − m n ) QED = 0.383 (68) MeV, (m p − m n ) (mu−m d ) = −2.51(14) MeV (statistical errors only), 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. 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, 16 3 and 24 3 ( (1.8 fm) 3 and (2.7 fm) 3 ), to address finite volume effects. Non-compact QED is treated in the quenched approximation.The valence pseudo-scalar 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 α em m, are given. 3

The walking technicolor theory attempts to realize electroweak symmetry breaking as the spontaneous chiral symmetry breakdown caused by the gauge dynamics with slowly varying gauge coupling constant and large mass anomalous dimension. Many-flavor QCD theories are candidates owning these features. We focus on the SU(3) gauge theory with ten flavors of massless fermions in the fundamental representation, and compute the gauge coupling constant in the Schrödinger functional scheme. Numerical simulation is performed with OðaÞ-unimproved lattice action, and the continuum limit is taken in linear in lattice spacing. We observe evidence that this theory possesses an infrared fixed point.

The electroweak gauge symmetry is allowed to be spontaneously broken by the strongly interacting vector-like gauge dynamics. When the gauge coupling of a theory runs slowly in a wide range of energy scale, the theory is a candidate for walking technicolor. This may open up the possibility that the origin of all masses may be traced back to the gauge theory. We use the Schrödinger functional method to see whether the gauge coupling of 10-flavor QCD "walks" or not. Preliminary result is reported.