DBW2 Gauge Action Research Articles

On-shellΔI=3/2kaon weak matrix elements with nonzero total momentum

We present our results for the on-shell $\ensuremath{\Delta}I=3/2$ kaon decay matrix elements using domain wall fermions and the DBW2 gauge action at one coarse lattice spacing corresponding to ${a}^{\ensuremath{-}1}=1.31\text{ }\text{ }\mathrm{GeV}$ in the quenched approximation. The on-shell matrix elements are evaluated in two different frames: the center-of-mass frame and nonzero total-momentum frame. We employ the formula proposed by Lellouch and L\"uscher in the center-of-mass frame, and its extension for a nonzero total-momentum frame to extract the infinite volume, on-shell, center-of-mass frame decay amplitudes. We determine the decay amplitude at the physical pion mass and momentum from the chiral extrapolation and an interpolation of the relative momentum using the results calculated in the two frames. We have obtained $\mathrm{Re}{A}_{2}=1.66(23)(\genfrac{}{}{0}{}{+48}{\ensuremath{-}03})(\genfrac{}{}{0}{}{+53}{\ensuremath{-}0})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\text{ }\text{ }\mathrm{GeV}$ and $\mathrm{Im}{A}_{2}=\ensuremath{-}1.181(26)(\genfrac{}{}{0}{}{+141}{\ensuremath{-}014})(\genfrac{}{}{0}{}{+44}{\ensuremath{-}0})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\text{ }\text{ }\mathrm{GeV}$ at the physical point, using the data at the relatively large pion mass, ${m}_{\ensuremath{\pi}}>0.35\text{ }\text{ }\mathrm{GeV}$. The first error is statistic, and the second and third are systematic. The second error is estimated with several fits of the chiral extrapolation including the (quenched) chiral perturbation formula at next to leading order using only lighter pion masses. The third one is estimated with an analysis using the lattice dispersion relation. The result of $\mathrm{Re}{A}_{2}$ is reasonably consistent with experiment.

Nucleon structure with two flavors of dynamical domain-wall fermions

We present a numerical lattice quantum chromodynamics calculation of isovector form factors and the first few moments of the isovector structure functions of the nucleon. The calculation employs two degenerate dynamical flavors of domain-wall fermions, resulting in good control of chiral symmetry breaking. Nonperturbative renormalization of the relevant quark currents is performed where necessary. The DBW2 gauge action is used to further improve the chiral behavior while maintaining a reasonable physical lattice volume. The inverse lattice spacing, a{sup -1}, is approximately 1.7 GeV. Degenerate up and down dynamical quark masses of approximately 1, 3/4 and 1/2 times the strange quark mass are used. The physical volume of the lattice is about (1.9 fm){sup 3}. The ratio of the isovector vector to axial charges, g{sub A}/g{sub V}, tends to a lower value than the experimental value as the quark mass is reduced toward the physical point. Momentum-transfer dependences of the isovector vector, axial, induced-tensor and induced-pseudoscalar form factors are calculated. The Goldberger-Treiman relation holds at low momentum transfer and yields an estimation of the pion-nucleon coupling, g{sub {pi}}{sub NN}=15.5(1.4), where the quoted error is only statistical. We find that the flavor nonsinglet quark momentum fraction {sub u-d} and quark helicity fractionmore » {sub {delta}}{sub u-{delta}}{sub d} overshoot their experimental values after linear chiral extrapolation. We discuss possible systematic errors for this discrepancy. An estimate for transversity, {sub {delta}}{sub u-{delta}}{sub d}=0.93(6) in MS at 2 GeV, is obtained and a twist-3 polarized moment, d{sub 1}, appears small, suggesting that the Wandzura-Wilczek relation holds approximately. We discuss in detail the systematic errors in the calculation, with particular attention paid to finite volume, excited-state contamination, and chiral extrapolations.« less

Localization and chiral symmetry in three flavor domain wall QCD

We present results for the dependence of the residual mass of domain wall fermions (DWF) on the size of the fifth dimension and its relation to the density and localization properties of low-lying eigenvectors of the corresponding hermitian Wilson Dirac operator relevant to simulations of 2+1 flavor domain wall QCD. Using the DBW2 and Iwasaki gauge actions, we generate ensembles of configurations with a $$16^3\times 32$$ space-time volume and an extent of 8 in the fifth dimension for the sea quarks. We demonstrate the existence of a regime where the degree of locality, the size of chiral symmetry breaking and the rate of topology change can be acceptable for inverse lattice spacings $$a^{-1} \ge 1.6$$ GeV.

Numerical simulations with two flavours of twisted-mass Wilson quarks and DBW2 gauge action

Discretisation errors in two-flavour lattice QCD with Wilson-quarks and DBW2 gauge action are investigated by comparing numerical simulation data at two values of the bare gauge coupling. Both non-zero and zero twisted mass values are considered. The results, including also data from simulations using the Wilson plaquette gauge action, are compared to next-to-leading order chiral perturbation theory formulas.

KaonB-parameter from quenched domain-wall QCD

We present numerical results for the kaon B-parameter, B_K, determined in the quenched approximation of lattice QCD. Our simulations are performed using domain-wall fermions and the renormalization group improved, DBW2 gauge action which combine to give quarks with good chiral symmetry at finite lattice spacing. Operators are renormalized non-perturbatively using the RI/MOM scheme. We study scaling by performing the simulation on two different lattices with a^{-1} = 1.982(30) and 2.914(54) GeV. We combine this quenched scaling study with an earlier calculation of B_K using two flavors of dynamical, domain-wall quarks at a single lattice spacing to obtain B_K(MS,NDR,mu=2GeV)=0.563(21)(39)(30), were the first error is statistical, the second systematic (without quenching errors) and the third estimates the error due to quenching.

Calculation of the neutron electric dipole moment with two dynamical flavors of domain wall fermions

We present a study of the neutron electric dipole moment (${\stackrel{\ensuremath{\rightarrow}}{d}}_{N}$) within the framework of lattice QCD with two flavors of dynamical light quarks. The dipole moment is sensitive to the topological structure of the gauge fields, and accuracy can only be achieved by using dynamical, or sea quark, calculations. However, the topological charge evolves slowly in these calculations, leading to a relatively large uncertainty in ${\stackrel{\ensuremath{\rightarrow}}{d}}_{N}$. It is shown, using quenched configurations, that a better sampling of the charge distribution reduces this problem, but because the $CP$ even part of the fermion determinant is absent, both the topological charge distribution and ${\stackrel{\ensuremath{\rightarrow}}{d}}_{N}$ are pathological in the chiral limit. We discuss the statistical and systematic uncertainties arising from the topological charge distribution and unphysical size of the quark mass in our calculations and prospects for eliminating them. Our calculations employ the RBC collaboration two flavor domain wall fermion and DBW2 gauge action lattices with inverse lattice spacing ${a}^{\ensuremath{-}1}\ensuremath{\approx}1.7\text{ }\text{ }\mathrm{GeV}$, physical volume $V\ensuremath{\approx}(2\text{ }\text{ }\mathrm{fm}{)}^{3}$, and light quark mass roughly equal to the strange quark mass (${m}_{\mathrm{sea}}=0.03$ and 0.04). We determine a value of the electric dipole moment that is zero within (statistical) errors, from which we obtain the bound $|{\stackrel{\ensuremath{\rightarrow}}{d}}_{N}|\ensuremath{\lesssim}0.02e\mathrm{\text{\ensuremath{-}}}\ensuremath{\theta}\mathrm{\text{\ensuremath{-}}}\mathrm{fm}$. Satisfactory results for the magnetic and electric form factors of the proton and neutron are also obtained and presented.

Localization properties of lattice fermions with plaquette and improved gauge actions

We determine the location ${\ensuremath{\lambda}}_{c}$ of the mobility edge in the spectrum of the Hermitian Wilson operator in pure-gauge ensembles with plaquette, Iwasaki, and DBW2 gauge actions. The results allow mapping a portion of the (quenched) Aoki phase diagram. We use Green function techniques to study the localized and extended modes. Where ${\ensuremath{\lambda}}_{c}>0$ we characterize the localized modes in terms of an average support length and an average localization length, the latter determined from the asymptotic decay rate of the mode density. We argue that, since the overlap operator is commonly constructed from the Wilson operator, its range is set by the value of ${\ensuremath{\lambda}}_{c}^{\ensuremath{-}1}$ for the Wilson operator. It follows from our numerical results that overlap simulations carried out with a cutoff of 1 GeV, even with improved gauge actions, could be afflicted by unphysical degrees of freedom as light as 250 MeV.

The phase structure of lattice QCD with two flavors of Wilson quarks and renormalization group improved gluons

The effect of changing the lattice action for the gluon field on the recently observed [F. Farchioni, R. Frezzotti, K. Jansen, I. Montvay, G.C. Rossi, E. Scholz, A. Shindler, N. Ukita, C. Urbach, I. Wetzorke, Eur. Phys. J. C 39, 421 (2005); hep-lat/0406039] first order phase transition near zero quark mass is investigated by replacing the Wilson plaquette action by the DBW2 action. The lattice action for quarks is unchanged: it is in both cases the original Wilson action. It turns out that Wilson fermions with the DBW2 gauge action have a phase structure where the minimal pion mass and the jump of the average plaquette are decreased, when compared to Wilson fermions with Wilson plaquette action at similar values of the lattice spacing. Taking the DBW2 gauge action is advantageous also from the point of view of the computational costs of numerical simulations.

Kaon matrix elements in domain-wall QCD with DBW2 gauge action

We present calculations of the decay constants and kaon B-parameter B K as the first stage of RBC Collaboration's quenched numerical simulations using DBW2 gauge action and domain-wall fermions. Some of potential systematic errors and consistency to previous works are discussed.

One-loop determination of mass dependent O( a) improvement coefficients for the heavy-light vector and axial-vector currents with relativistic heavy and domain-wall light quarks

We present the one-loop results of the mass dependent $O(a)$ improvement coefficients for the heavy-light vector and axial-vector currents consisting of the relativistic heavy and the domain-wall light quarks. The calculations are performed with the plaquette, Iwasaki and DBW2 gauge actions. The heavy quark mass and domain-wall height dependence is investigated. We point out that the exact chiral symmetry held by the lattice light quark action leads to an exact relation between the improvement coefficients for the vector and axial-vector currents without regard to the lattice heavy quark action.

A First Look at Nf = 3 Dynamical DWF Simulations

The RBC collaboration has done a preliminary simulation of full QCD with 3 degenerate avors of domain wall fermions and the DBW2 gauge action. About 1,500 trajectories have been accumulated for a 16 3 × 32 lattice with L s = 8 , with a lattice spacing of a −1 = 1.6 - 1.7 GeV . Basic hadronic results from this simulation will be presented, as well as the residual mass.

Static [formula omitted]- Q Potential from [formula omitted] Dynamical Domain-Wall QCD

We calculate the static quark and anti-quark potential both in quenched and two-flavor dynamical quark lattice QCD using DBW2 gauge and domain-wall quark actions. Lattice spacings from Sommer scale are determined. We find (i) mixing of excited states is different in between quenched and dynamical, (ii) lattice spacing a r 0 ∼ a m ρ in dynamical and (iii) coefficient of Coulomb term being α N f = 0 < α N f = 2 at a −1 ∼ 2 GeV .

One-loop renormalisation of quark bilinears for overlap fermions with improved gauge actions

We compute lattice renormalisation constants of local bilinear quark operators for overlap fermions and improved gauge actions. Among the actions we consider are the Symanzik, Lüscher–Weisz, Iwasaki and DBW2 gauge actions. The results are given for a variety of ρ parameters. We show how to apply mean field (tadpole) improvement to overlap fermions. The question, what is a good gauge action, is discussed from the perturbative point of view. Finally, we show analytically that the gauge dependent part of the self-energy and the amputated Green functions are independent of the lattice fermion representation, using either Wilson or overlap fermions.

Domain wall fermions with improved gauge actions

We study the chiral properties of quenched domain wall fermions with several gauge actions. We demonstrate that the residual chiral symmetry breaking, which is present for a finite number of lattice sites in the fifth dimension ${(L}_{s}),$ can be substantially suppressed using improved gauge actions. In particular the Symanzik action, the Iwasaki action, and a renormalization group improved gauge action, called the doubly blocked Wilson (DBW2) action, are studied and compared to the Wilson action. All improved gauge actions studied show a reduction in the additive residual quark mass ${m}_{\mathrm{res}}.$ Remarkably, in the DBW2 case ${m}_{\mathrm{res}}$ is roughly two orders of magnitude smaller than the Wilson gauge action at ${a}^{\ensuremath{-}1}=2\mathrm{GeV}$ and ${L}_{s}=16.$ Significant reduction in ${m}_{\mathrm{res}}$ is also realized at stronger gauge coupling corresponding to ${a}^{\ensuremath{-}1}=1.3\mathrm{GeV}.$ As our numerical investigation indicates, this reduction is achieved by reducing the number of topological lattice dislocations present in the gauge field configurations. We also present detailed results for the quenched light hadron spectrum and the pion decay constant using the DBW2 gauge action.

Calculation of kaon matrix elements in quenched domain-wall QCD with DBW2 gauge action

We give a progress report of our new $a^{-1}\approx 3$ GeV quenched calculation of kaon matrix elements with domain-wall fermion and DBW2 gauge action. Our smaller lattice spacing allows us to address the effect of charmed quark on the lattice. We show preliminary results of $B_K$ renormalized non-perturbatively and $K\to\pi$ matrix elements.

Nonperturbative renormalization for domain wall fermions and the chiral condensate

We study the chiral condensate, $<\bar\psi\psi>$, and various quark bilinear vertex functions for domain wall fermions at different lattice scales, with both the Wilson and DBW2 gauge actions, in both quenched and dynamical fermion simulations. We use the vertex functions to calculate renormalization factors within a non-perturbative scheme.

Dynamical domain wall fermions

We report on an exploratory study of Nf = 2 dynamical domain wall fermions and the DBW2 gauge action at weak coupling. Details of improved simulation algorithms and preliminary results for the hadron spectrum and renormalised light and strange quark masses will be presented.

Systematic effects in Kaon matrix elements calculations

Abstract During the last year, the RBC collaboration has generated an ensemble of lattices using the DBW2 gauge action, the domain wall fermion (DWF) action, 2 dynamical flavors of degenerate quarks, and three different dynamical quark masses with values of approximately 1 2 , 3 4 and 1 times the strange quark mass. With ∼ 4, 000 Hybrid Monte Carlo (HMC) trajectories for each dynamical mass on 163 × 32 lattices with LS = 12, we can begin to examine the matrix elements for the δS = 1 operators relevant to the δI = 1 2 rule and ϵ′/ϵ. Our statistics are too limited to quote physical values at this time; instead we compare the unrenormalized lattice matrix elements on these dynamical lattices with those from our earlier quenched lattices, which have a very similar lattice spacing, physical volume and range of quark masses.

Nucleon axial charge and structure functions with domain wall fermions

We report the current status of RBCK calculations on nucleon structure with both quenched and unquenched lattice QCD. The combination of domain wall fermions and DBW2 gauge action works well for isovector vector and axial charges, and moments of structure functions <x>_q, d_1, and <1>_{\delta q}.

Improving dynamical domain-wall Fermion simulations

We report on studies of the chiral properties of dynamical domain wall fermions combined with the DBW2 gauge action for different gauge couplings and fermion masses. For quenched theories, the DBW2 action gives a residual chiral symmetry breaking much smaller than what was found with more traditional choices for the gauge action. Our goal is to investigate the possibilities which this and further improvements provide for the study of QCD thermodynamics and other simulations at stronger couplings.