C. Kelly

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

Domain wall QCD with physical quark masses

We present results for several light hadronic quantities ( f π , f K , B K , m ud , m s , t 0 ½, w 0 ) obtained from simulations of 2+1 flavor domain wall lattice QCD with large physical volumes and nearly physical pion masses at two lattice spacings. We perform a short, O (3) %, extrapolation in pion mass to the physical values by combining our new data in a simultaneous chiral/continuum “global fit” with a number of other ensembles with heavier pion masses. We use the physical values of m π , m K and m Ω to determine the two quark masses and the scale—all other quantities are outputs from our simulations. We obtain results with subpercent statistical errors and negligible chiral and finite-volume systematics for these light hadronic quantities, including f π = 130.2(9) MeV; f K = 155.5(8) MeV; the average up/down quark mass and strange quark mass in the ‾MS scheme at 3 GeV, 2.997(49) and 81.64(1.17) MeV respectively; and the neutral kaon mixing parameter, B K , in the renormalization group invariant scheme, 0.750(15) and the ‾MS scheme at 3 GeV, 0.530(11).

Lattice determination of the K → ( π π ) I = 2 decay amplitude A 2

We describe the computation of the amplitude A2 for a kaon to decay into two pions with isospin I = 2. The results presented in the letter [1] from an analysis of 63 gluon configurations are updated to 146 configurations giving ReA2 = 1:381(46)stat(258)syst 10 8 GeV and ImA2 = 6:54(46)stat(120) syst10 13 GeV . ReA2 is in good agreement with the experimental result, whereas the value of ImA2 was hitherto unknown. We are also working towards a direct computation of the K! (pp)I=0 amplitude A0 but, within the standard model, our result for ImA2 can be combined with the experimental results for ReA0, ReA2 and e 0 =e to give ImA0=ReA0 = 1:61(28) 10 4 . Our result for ImA2 implies that the electroweak penguin

The pion's electromagnetic form factor at small momentum transfer in full lattice QCD

We compute the electromagnetic form factor of a ``pion with mass m? = 330?MeV at low values of Q2??q2, where q is the momentum transfer. The computations are performed in a lattice simulation using an ensemble of the RBC/UKQCD collaborations gauge configurations with Domain Wall Fermions and the Iwasaki gauge action with an inverse lattice spacing of 1.73(3)?GeV. In order to be able to reach low momentum transfers we use partially twisted boundary conditions using the techniques we have developed and tested earlier. For the pion of mass 330?MeV we find a charge radius given by r?2330?MeV = 0.354(31)?fm2 which, using NLO SU(2) chiral perturbation theory, translates to a value of r?2 = 0.418(31)?fm2 for a physical pion, in agreement with the experimentally determined result. We confirm that there is a significant reduction in computational cost when using propagators computed from a single time-slice stochastic source compared to using those with a point source; for m? = 330?MeV and volume (2.74?fm)3 we find the reduction is approximately a factor of 12.

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 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%.

from 2+1 Flavor Domain Wall QCD

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 ?? 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.

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

We compute the K`3 form factors using partially twisted boundary conditions. The twists are chosen so that the K`3 form factors are calculated directly at zero momentum transfer (q2 = 0),removing the need for a q^2 interpolation. The simulations are performed on an ensemble of the RBC/UKQCD collaboration’s gauge configurations with Domain Wall Fermions and the Iwaski gauge action with an inverse lattice spacing of 1.73(3) GeV. For the value of the K`3 form factor,f Kp+ (q2), determined directly at q2 = 0, we find a value of f Kp+ (0) = 0.9757(38) at this particular quark mass, which agrees well with our earlier result (0.9774(35)) obtained using the standard, indirect method.

Low energy constants of SU(2) partially quenched chiral perturbation theory from Nf=2+1 domain wall QCD

Lattice QCD calculations including the effects of one or more non-degenerate sea quark flavors are conventionally performed using the Rational Hybrid Monte Carlo (RHMC) algorithm, which computes the square root of the determinant of

Determining the Kl3 form factors directly at zero momentum transfer

\mathscr{D}^{\dagger} \mathscr{D}