# Physical results from 2+1 flavor domain wall QCD and SU(2) chiral perturbation theory

Alton, C., Antonio, D.J., Aoki, Y., Blum, T., Boyle, P.A., Christ, N.H., Cohen, S.D., Clark, M.A., Dawson, C., Donnellan, J.M., Flynn, J.M., Hart, A., Izubuchi, T., Juttner, A., Jung, C., Kennedy, A.D., Kenway, R.D., Li, M., Li, S., Lin, M.F., Mawhinney, R.D., Maynard, C.M., Ohta, S., Pendleton, B.J., Sachrajda, C.T., Sasaki, S., Scholz, E.E., Soni, A., Tweedie, R.J., Wennekers, J., Yamazaki, T., Zanotti, J.M. and for the RBC-UKQCD Collaborations, RBC-UKQCD Collaborations (2008) Physical results from 2+1 flavor domain wall QCD and SU(2) chiral perturbation theory. Pre-print, 1-133. (arXiv:0804.0473v1). (Submitted).

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Original Publication URL: http://arxiv.org/abs/0804.0473

## Description/Abstract

We have simulated QCD using 2+1 flavors of domain wall quarks on a (2.74 {\rm fm})^3 volume with an inverse lattice scale of a^{-1} = 1.729(28) GeV. The up and down (light) quarks are degenerate in our calculations and we have used four values for the ratio of light quark masses to the strange (heavy) quark mass in our simulations: 0.217, 0.350, 0.617 and 0.884. We have measured pseudoscalar meson masses and decay constants, the kaon bag parameter B_K and vector meson couplings. We have used SU(2) chiral perturbation theory, which assumes only the up and down quark masses are small, and SU(3) chiral perturbation theory to extrapolate to the physical values for the light quark masses. While next-to-leading order formulae from both approaches fit our data for light quarks, we find the higher order corrections for SU(3) very large, making such fits unreliable. We also find that SU(3) does not fit our data when the quark masses are near the physical strange quark mass. Thus, we rely on SU(2) chiral perturbation theory for accurate results. We use the masses of the \Omega baryon, and the \pi and K mesons to set the lattice scale and determine the quark masses. We then find f_\pi = 124.1(3.6)_{\rm stat}(6.9)_{\rm syst} {\rm MeV}, f_K = 149.6(3.6)_{\rm stat}(6.3)_{\rm syst} {\rm MeV} and f_K/f_\pi = 1.205(0.018)_{\rm stat}(0.062)_{\rm syst}. Using non-perturbative renormalization to relate lattice regularized quark masses to RI-MOM masses, and perturbation theory to relate these to \bar{\rm MS} we find m_{ud}^{\bar{\rm MS}}(2 {\rm GeV}) = 3.72(0.16)_{\rm stat}(0.33)_{\rm ren}(0.18)_{\rm syst} {\rm MeV} and m_{s}^{\bar{\rm MS}}(2 {\rm GeV}) = 107.3(4.4)_{\rm stat}(9.7)_{\rm ren}(4.9)_{\rm syst} {\rm MeV}.

Item Type: Article http://arxiv.org/abs/0804.0473 Q Science > QC Physics University Structure - Pre August 2011 > School of Physics and Astronomy > Southampton High Energy Physics 64187 05 Jan 2009 27 Mar 2014 18:45 http://eprints.soton.ac.uk/id/eprint/64187