We present physical results for a variety of light hadronic quantities obtained via a combined analysis of three 2+1 flavour domain wall fermion ensemble sets. For two of our ensemble sets we used the Iwasaki gauge action with β = 2.13 (a −1 = 1.75(4) GeV) and β = 2.25 (a −1 = 2.31(4) We also obtain values for the SU(2) chiral perturbation theory effective couplings,l 3 = 2.91(23) stat (7) sys andl 4 = 3.99(16) stat (9) sys .GeV3

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2We determine the neutral kaon mixing matrix element B K in the continuum limit with 2+1 flavors of domain wall fermions, using the Iwasaki gauge action at two different lattice spacings. These lattice fermions have near exact chiral symmetry and therefore avoid artificial lattice operator mixing.We introduce a significant improvement to the conventional NPR method in which the bare matrix elements are renormalized non-perturbatively in the RI-MOM scheme and are then converted into the MS scheme using continuum perturbation theory. In addition to RI-MOM, we introduce and implement four non-exceptional intermediate momentum schemes that suppress infrared non-perturbative uncertainties in the renormalization procedure. We compute the conversion factors relating the matrix elements in this family of RI-SMOM schemes and MS at one-loop order.Comparison of the results obtained using these different intermediate schemes allows for a more reliable estimate of the unknown higher-order contributions and hence for a correspondingly more robust estimate of the systematic error. We also apply a recently proposed approach in which twisted boundary conditions are used to control the Symanzik expansion for off-shell vertex functions leading to a better control of the renormalization in the continuum limit.We control chiral extrapolation errors by considering both the NLO SU(2) chiral effective theory, and an analytic mass expansion. We obtain B MS K (3 GeV) = 0.529(5) stat (15) χ (2) FV (11) NPR . This corresponds toB RGI K = 0.749(7) stat (21) χ (3) FV (15) NPR . Adding all sources of error in quadrature we obtainB RGI K = 0.749(27) combined , with an overall combined error of 3.6%.3

We have performed fits of the pseudoscalar masses and decay constants, from a variety of RBC-UKQCD domain wall fermion ensembles, to SU (2) partially quenched chiral perturbation theory at next-to leading order (NLO) and next-to-next-to leading order (NNLO). We report values for 9 NLO and 8 linearly independent combinations of NNLO partially quenched low energy constants, which we compare to other lattice and phenomenological determinations. We discuss the size of successive terms in the chiral expansion and use our large set of low energy constants to make predictions for mass splittings due to QCD isospin breaking effects and the S-wave ππ scattering lengths. We conclude that, for the range of pseudoscalar masses explored in this work, 115 MeV mPS 430 MeV, the NNLO SU (2) expansion is quite robust and can fit lattice data with percent-scale accuracy.

Michael; RBC Collaboration; UKQCD Collaboration Kl3 semileptonic form factor from (2+1)-flavor lattice QCD