R. Zhou

Continuum limit physics from 2+1 flavor domain wall QCD

We present physical results obtained from simulations usin g 2+1 flavors of domain wall quarks and the Iwasaki gauge action at two values of the lattice spac ing a, (a−1= 1.73 (3) GeV and a−1= 2.28 (3) GeV). On the coarser lattice, with 24 3×64×16 points (where the 16 corresponds to Ls, the extent of the 5 th dimension inherent in the domain wall fermion (DWF) formula tion

Continuum Limit of

We determine the neutral kaon mixing matrix element BK 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 nonperturbative renormalization (NPR) method in which the bare matrix elements are renormalized nonperturbatively in the regularization invariant momentum scheme (RI-MOM) and are then converted into the MS? scheme using continuum perturbation theory. In addition to RI-MOM, we introduce and implement four nonexceptional intermediate momentum schemes that suppress infrared nonperturbative uncertainties in the renormalization procedure. We compute the conversion factors relating the matrix elements in this family of regularization invariant symmetric momentum schemes (RI-SMOM) 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 next-to-leading order SU(2) chiral effective theory, and an analytic mass expansion. We obtain BKMS? (3??GeV)=0.529(5)stat(15)?(2)FV(11)NPR. This corresponds to B?KRGI? =0.749(7)stat(21)?(3)FV(15)NPR. Adding all sources of error in quadrature, we obtain B?KRGI? =0.749(27)combined, with an overall combined error of 3.6%.

B_K

We report a direct lattice calculation of the K to ?? decay matrix elements for both the ?I=1/2 and 3/2 amplitudes A0 and A2 on 2+1 flavor, domain wall fermion, 163×32×16 lattices. This is a complete calculation in which all contractions for the required ten, four-quark operators are evaluated, including the disconnected graphs in which no quark line connects the initial kaon and final two-pion states. These lattice operators are nonperturbatively renormalized using the Rome-Southampton method and the quadratic divergences are studied and removed. This is an important but notoriously difficult calculation, requiring high statistics on a large volume. In this paper, we take a major step toward the computation of the physical K??? amplitudes by performing a complete calculation at unphysical kinematics with pions of mass 422 MeV at rest in the kaon rest frame. With this simplification, we are able to resolve Re(A0) from zero for the first time, with a 25% statistical error and can develop and evaluate methods for computing the complete, complex amplitude A0, a calculation central to understanding the ?=1/2 rule and testing the standard model of CP violation in the kaon system.

from 2+1 Flavor Domain Wall QCD

We determine the neutral kaon mixing matrix element BK 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 nonperturbative renormalization (NPR) method in which the bare matrix elements are renormalized nonperturbatively in the regularization invariant momentum scheme (RI-MOM) and are then converted into the MS? scheme using continuum perturbation theory. In addition to RI-MOM, we introduce and implement four nonexceptional intermediate momentum schemes that suppress infrared nonperturbative uncertainties in the renormalization procedure. We compute the conversion factors relating the matrix elements in this family of regularization invariant symmetric momentum schemes (RI-SMOM) 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 next-to-leading order SU(2) chiral effective theory, and an analytic mass expansion. We obtain BKMS? (3??GeV)=0.529(5)stat(15)?(2)FV(11)NPR. This corresponds to B?KRGI? =0.749(7)stat(21)?(3)FV(15)NPR. Adding all sources of error in quadrature, we obtain B?KRGI? =0.749(27)combined, with an overall combined error of 3.6%.

K to ππ decay amplitudes from lattice QCD

The effect of sea quark electromagnetic charge on meson masses is investigated, and first results for full QED+QCD low-energy constants are presented. The electromagnetic charge for sea quarks is incorporated in quenched QED+full QCD lattice simulations by a reweighting method. The reweighting factor, which connects quenched and unquenched QED, is estimated using a stochastic method on 2+1 flavor dynamical domain-wall quark ensembles.

Continuum limit of Bk from 2+1 flavor domain wall QCD

We investigate the electromagnetic mass splittings in the pseudoscalar meson and nucleon systems by combining 2+1 flavor domain wall fermion gauge configurations, generated by the RBC and UKQCD collaborations, and quenched, non-compact, lattice QED configurations. We analyze finite volume effects by using

Full QED + QCD Low-Energy Constants through Reweighting

16^3\times 32

Isospin symmetry breaking effects in the pion and nucleon masses

and

Isospin breaking in 2+1 flavor QCD+QED

24^3\times 64

Continuum limit ofBKfrom2+1flavor domain wall QCD

lattices.