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We present a lattice QCD calculation of the ΔI=1/2, K→ππ decay amplitude A0 and ϵ′, the measure of direct CP violation in K→ππ decay, improving our 2015 calculation [1] of these quantities. Both calculations were performed with physical kinematics on a 323×64 lattice with an inverse lattice spacing of a-1=1.3784(68) GeV. However, the current calculation includes nearly 4 times the statistics and numerous technical improvements allowing us to more reliably isolate the ππ ground state and more accurately relate the lattice operators to those defined in the standard model. We find Re(A0)=2.99(0.32)(0.59)×10-7 GeV and Im(A0)=-6.98(0.62)(1.44)×10-11 GeV, where the errors are statistical and systematic, respectively. The former agrees well with the experimental result Re(A0)=3.3201(18)×10-7 GeV. These results for A0 can be combined with our earlier lattice calculation of A2 [2] to obtain Re(ϵ′/ϵ)=21.7(2.6)(6.2)(5.0)×10-4, where the third error represents omitted isospin breaking effects, and Re(A0)/Re(A2)=19.9(2.3)(4.4). The first agrees well with the experimental result of Re(ϵ′/ϵ)=16.6(2.3)×10-4. A comparison of the second with the observed ratio Re(A0)/Re(A2)=22.45(6), demonstrates the standard model origin of this “ΔI=1/2 rule” enhancement.

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.

We present new results for the amplitude $A_2$ for a kaon to decay into two pions with isospin $I=2$: Re$A_2 = 1.50(4)_\mathrm{stat}(14)_\mathrm{syst}\times 10^{-8}$ GeV; Im$A_2 = -6.99(20)_\mathrm{stat}(84)_\mathrm{syst}\times 10^{-13}$ GeV. These results were obtained from two ensembles generated at physical quark masses (in the isospin limit) with inverse lattice spacings $a^{-1}=1.728(4)$ GeV and $2.358(7)$ GeV. We are therefore able to perform a continuum extrapolation and hence largely to remove the dominant systematic uncertainty from our earlier results, that due to lattice artefacts. The only previous lattice computation of $K\to\pi\pi$ decays at physical kinematics was performed using an ensemble at a single, rather coarse, value of the lattice spacing ($a^{-1}\simeq 1.37(1)$ GeV). We confirm the observation that there is a significant cancellation between the two dominant contributions to Re$A_2$ which we suggest is an important ingredient in understanding the $\Delta I=1/2$ rule, Re$A_0$/Re$A_2\simeq 22.5$, where the subscript denotes the total isospin of the two-pion final state. Our result for $A_2$ implies that the electroweak penguin contribution to $\epsilon^\prime/\epsilon$ is Re($\epsilon^\prime/\epsilon)_\textrm{EWP}=-(6.6\pm 1.0)\times 10^{-4}$.

We study the autocorrelations of observables constructed from the topological charge density, such as the topological charge on a time slice or in a subvolume, using a series of hybrid Monte Carlo simulations of pure SU(3) gauge theory with both periodic and open boundary conditions. We show that the autocorrelation functions of these observables obey a simple diffusion equation and we measure the diffusion coefficient, finding that it scales like the square of the lattice spacing. We use this result and measurements of the rate of tunneling between topological charge sectors to calculate the scaling behavior of the autocorrelation times of these observables on periodic and open lattices. There is a characteristic lattice spacing at which open boundary conditions become worthwhile for reducing autocorrelations and we show how this lattice spacing is related to the diffusion coefficient, the tunneling rate, and the lattice Euclidean time extent., Comment: 36 pages, 14 figures

We report on a study of the finite-temperature QCD transition region for temperatures between 139 and 196 MeV, with a pion mass of 200 MeV and two space-time volumes: $2{4}^{3}\ifmmode\times\else\texttimes\fi{}8$ and $3{2}^{3}\ifmmode\times\else\texttimes\fi{}8$, where the larger volume varies in linear size between 5.6 fm (at $T=139\text{ }\text{ }\mathrm{MeV}$) and 4.0 fm (at $T=195\text{ }\text{ }\mathrm{MeV}$). These results are compared with the results of an earlier calculation using the same action and quark masses but a smaller, $1{6}^{3}\ifmmode\times\else\texttimes\fi{}8$ volume. The chiral domain wall fermion formulation with a combined Iwasaki and dislocation suppressing determinant ratio gauge action are used. This lattice action accurately reproduces the $SU(2{)}_{L}\ifmmode\times\else\texttimes\fi{}SU(2{)}_{R}$ and $U(1{)}_{A}$ symmetries of the continuum. Results are reported for the chiral condensates, connected and disconnected susceptibilities and the Dirac eigenvalue spectrum. We find a pseudocritical temperature, ${T}_{c}$, of approximately 165 MeV consistent with previous results and strong finite-volume dependence below ${T}_{c}$. Clear evidence is seen for $U(1{)}_{A}$ symmetry breaking above ${T}_{c}$ which is quantitatively explained by the measured density of near-zero modes in accordance with the dilute instanton gas approximation.

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 beta=2.13 (a^-1=1.75(4) GeV) and beta=2.25 (a^-1=2.31(4) GeV) and lattice sizes of 24^3 x 64 and 32^3 x 64 respectively, with unitary pion masses in the range 293(5)-417(10) MeV. The extent L_s for the 5^th dimension of the domain wall fermion formulation is L_s=16 in these ensembles. In this analysis we include a third ensemble set that makes use of the novel Iwasaki+DSDR (Dislocation Suppressing Determinant Ratio) gauge action at beta = 1.75 (a^-1=1.37(1) GeV) with a lattice size of 32^3 x 64 and L_s=32 to reach down to partially-quenched pion masses as low as 143(1) MeV and a unitary pion mass of 171(1) MeV, while retaining good chiral symmetry and topological tunneling. We demonstrate a significant improvement in our control over the chiral extrapolation, resulting in much improved continuum predictions for the above quantities. The main results of this analysis include the pion and kaon decay constants, f_\pi=127(3)_{stat}(3)_{sys} MeV and f_K = 152(3)_{stat}(2)_{sys} MeV respectively (f_K/f_\pi = 1.199(12)_{stat}(14)_{sys}); the average up/down quark mass and the strange-quark mass in the MSbar-scheme at 3 GeV, m_{ud}(MSbar, 3 GeV) = 3.05(8)_{stat}(6)_{sys} MeV and m_s(MSbar, 3 GeV) = 83.5(1.7)_{stat}(1.1)_{sys}; the neutral kaon mixing parameter in the MSbar-scheme at 3 GeV, B_K(MSbar,3 GeV) = 0.535(8)_{stat}(13)_{sys}, and in the RGI scheme, \hat B_K = 0.758(11)_{stat}(19)_{sys}; and the Sommer scales r_1 = 0.323(8)_{stat}(4)_{sys} fm and r_0 = 0.480(10)_{stat}(4)_{sys} (r_1/r_0 = 0.673(11)_{stat}(3)_{sys}). We also obtain values for the SU(2) ChPT effective couplings, \bar{l_3} = 2.91(23)_{stat}(7)_{sys}$ and \bar{l_4} = 3.99(16)_{stat}(9)_{sys}., Comment: 95 pages, 23 figures. Added missing author to metadata

We present results on both the restoration of the spontaneously broken chiral symmetry and the effective restoration of the anomalously broken $U(1{)}_{A}$ symmetry in finite temperature QCD at zero chemical potential using lattice QCD. We employ domain wall fermions on lattices with fixed temporal extent ${N}_{\ensuremath{\tau}}=8$ and spatial extent ${N}_{\ensuremath{\sigma}}=16$ in a temperature range of $T=139--195\text{ }\text{ }\mathrm{MeV}$, corresponding to lattice spacings of $a\ensuremath{\approx}0.12--0.18\text{ }\text{ }\mathrm{fm}$. In these calculations, we include two degenerate light quarks and a strange quark at fixed pion mass ${m}_{\ensuremath{\pi}}=200\text{ }\text{ }\mathrm{MeV}$. The strange quark mass is set near its physical value. We also present results from a second set of finite temperature gauge configurations at the same volume and temporal extent with slightly heavier pion mass. To study chiral symmetry restoration, we calculate the chiral condensate, the disconnected chiral susceptibility, and susceptibilities in several meson channels of different quantum numbers. To study $U(1{)}_{A}$ restoration, we calculate spatial correlators in the scalar and pseudoscalar channels, as well as the corresponding susceptibilities. Furthermore, we also show results for the eigenvalue spectrum of the Dirac operator as a function of temperature, which can be connected to both $U(1{)}_{A}$ and chiral symmetry restoration via Banks-Casher relations.

We describe the computation of the amplitude ${A}_{2}$ for a kaon to decay into two pions with isospin $I=2$. The results presented in [T. Blum et al., Phys. Rev. Lett. 108, 141601 (2012)] from an analysis of 63 gluon configurations are updated to 146 configurations giving $\mathrm{Re}{A}_{2}=1.381(46{)}_{\mathrm{stat}}(258{)}_{\mathrm{syst}}{10}^{\ensuremath{-}8}\text{ }\text{ }\mathrm{GeV}$ and $\mathrm{Im}{A}_{2}=\ensuremath{-}6.54(46{)}_{\mathrm{stat}}(120{)}_{\mathrm{syst}}{10}^{\ensuremath{-}13}\text{ }\text{ }\mathrm{GeV}$. $\mathrm{Re}{A}_{2}$ is in good agreement with the experimental result, whereas the value of $\mathrm{Im}{A}_{2}$ was hitherto unknown. We are also working toward a direct computation of the $K\ensuremath{\rightarrow}(\ensuremath{\pi}\ensuremath{\pi}{)}_{I=0}$ amplitude ${A}_{0}$ but, within the Standard Model, our result for $\mathrm{Im}{A}_{2}$ can be combined with the experimental results for $\mathrm{Re}{A}_{0}$, $\mathrm{Re}{A}_{2}$ and ${\ensuremath{\epsilon}}^{\ensuremath{'}}/\ensuremath{\epsilon}$ to give $\mathrm{Im}{A}_{0}/\mathrm{Re}{A}_{0}=\ensuremath{-}1.61(28)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$. Our result for $\mathrm{Im}{A}_{2}$ implies that the electroweak penguin (EWP) contribution to ${\ensuremath{\epsilon}}^{\ensuremath{'}}/\ensuremath{\epsilon}$ is $\mathrm{Re}({\ensuremath{\epsilon}}^{\ensuremath{'}}/\ensuremath{\epsilon}{)}_{\mathrm{EWP}}=\ensuremath{-}(6.25\ifmmode\pm\else\textpm\fi{}{0.44}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{1.19}_{\mathrm{syst}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$.

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.

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%.

We present physical results obtained from simulations using 2+1 flavors of domain wall quarks and the Iwasaki gauge action at two values of the lattice spacing $a$, ($a^{-1}$=\,1.73\,(3)\,GeV and $a^{-1}$=\,2.28\,(3)\,GeV). On the coarser lattice, with $24^3\times 64\times 16$ points, the analysis of ref.[1] is extended to approximately twice the number of configurations. The ensembles on the finer $32^3\times 64\times 16$ lattice are new. We explain how we use lattice data obtained at several values of the lattice spacing and for a range of quark masses in combined continuum-chiral fits in order to obtain results in the continuum limit and at physical quark masses. We implement this procedure at two lattice spacings, with unitary pion masses in the approximate range 290--420\,MeV (225--420\,MeV for partially quenched pions). We use the masses of the $\pi$ and $K$ mesons and the $\Omega$ baryon to determine the physical quark masses and the values of the lattice spacing. While our data are consistent with the predictions of NLO SU(2) chiral perturbation theory, they are also consistent with a simple analytic ansatz leading to an inherent uncertainty in how best to perform the chiral extrapolation that we are reluctant to reduce with model-dependent assumptions about higher order corrections. Our main results include $f_\pi=124(2)_{\rm stat}(5)_{\rm syst}$\,MeV, $f_K/f_\pi=1.204(7)(25)$ where $f_K$ is the kaon decay constant, $m_s^{\bar{\textrm{MS}}}(2\,\textrm{GeV})=(96.2\pm 2.7)$\,MeV and $m_{ud}^{\bar{\textrm{MS}}}(2\,\textrm{GeV})=(3.59\pm 0.21)$\,MeV\, ($m_s/m_{ud}=26.8\pm 1.4$) where $m_s$ and $m_{ud}$ are the mass of the strange-quark and the average of the up and down quark masses respectively, $[\Sigma^{\msbar}(2 {\rm GeV})]^{1/3} = 256(6)\; {\rm MeV}$, where $\Sigma$ is the chiral condensate, the Sommer scale $r_0=0.487(9)$\,fm and $r_1=0.333(9)$\,fm., Comment: 129 pages, 59 figures, Published version containing an extended discussion of reweighting and including a new appendix (Appendix C)

We study the region of the QCD phase transition using $2+1$ flavors of domain wall fermions and a ${16}^{3}\ifmmode\times\else\texttimes\fi{}8$ lattice volume with a fifth dimension of ${L}_{s}=32$. The disconnected light quark chiral susceptibility, quark number susceptibility, and the Polyakov loop suggest a chiral and deconfining crossover transition lying between 155 and 185 MeV for our choice of quark mass and lattice spacing. In this region the lattice scale deduced from the Sommer parameter ${r}_{0}$ is ${a}^{\ensuremath{-}1}\ensuremath{\approx}1.3\text{ }\text{ }\mathrm{GeV}$, the pion mass is $\ensuremath{\approx}300\text{ }\text{ }\mathrm{MeV}$, and the kaon mass is approximately physical. The peak in the chiral susceptibility implies a pseudocritical temperature ${T}_{c}=171(10)(17)\text{ }\text{ }\mathrm{MeV}$ where the first error is associated with determining the peak location and the second with our unphysical light quark mass and nonzero lattice spacing. The effects of residual chiral symmetry breaking on the chiral condensate and disconnected chiral susceptibility are studied using several values of the valence ${L}_{s}$.

QCD with eight flavors is studied on ${16}^{3}\ifmmode\times\else\texttimes\fi{}{N}_{t}$ lattices with ${N}_{t}=4,6, \mathrm{and} 8$, a dynamical quark mass $ma=0.015$, and lattice coupling $\ensuremath{\beta}=\frac{6}{{g}^{2}}$ between 4.5 and 5.0. For ${N}_{t}=16$, hadron masses and screening lengths are computed for a variety of valence quark masses. The previously observed, strong, first-order transition for ${N}_{t}=4,6, \mathrm{and} 8$ is seen, for ${N}_{t}=16$, to become a $\ensuremath{\beta}$-independent, zero-temperature transition characterized by a factor of \ensuremath{\cong} 3 change in lattice scale. This strong, first-order transition restores chiral symmetry, at least for ${N}_{t}=4,6, \mathrm{and} 8$, producing a chirally symmetric, weak-coupling phase. However, as ${N}_{t}$ increases to 16, the chiral-symmetry properties of the weak-coupling side of the zero-temperature transition are unclear and offer a hint of a normal, finite-temperature, chiral-symmetry-breaking transition in the weak-coupling phase.

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.

Pure SU(2) lattice gauge theory in three dimensions is studied by Monte Carlo simulation with a determination of the potential between fundamental- and adjoint-representation sources as a major goal. A ${32}^{3}$ lattice is used and Wilson loops up to 16 by 16 are measured using a modification to the standard multihit variance reduction which improves the statistics by at least a factor of 3 at $\ensuremath{\beta}=6.0$. The integrated autocorrelation times measured for the loops show a peak for loops of size $\ensuremath{\beta}$ by $\ensuremath{\beta}$. The fundamental- and adjoint-representation potentials are seen to have the same functional form to very high accuracy and their numerical values are in the ratio of their Casimir operators. The string tension is extracted and scaling is seen to within a few percent over a range of couplings which correspond to a factor of 2 change in the glueball mass. Correlated errors have been taken into account in the extraction of the potentials from the Wilson-loop values.

We present results for light meson masses and pseudoscalar decay constants from the first of a series of lattice calculations with 2+1 dynamical flavors of domain wall fermions and the Iwasaki gauge action. The work reported here was done at a fixed lattice spacing of about 0.12 fm on a 16^3\times32 lattice, which amounts to a spatial volume of (2 fm)^3 in physical units. The number of sites in the fifth dimension is 16, which gives m_{res} = 0.00308(4) in these simulations. Three values of input light sea quark masses, m_l^{sea} \approx 0.85 m_s, 0.59 m_s and 0.33 m_s were used to allow for extrapolations to the physical light quark limit, whilst the heavier sea quark mass was fixed to approximately the physical strange quark mass m_s. The exact rational hybrid Monte Carlo algorithm was used to evaluate the fractional powers of the fermion determinants in the ensemble generation. We have found that f_\pi = 127(4) MeV, f_K = 157(5) MeV and f_K/f_\pi = 1.24(2), where the errors are statistical only, which are in good agreement with the experimental values.

We present results for the static interquark potential, light meson and baryon masses, and light pseudoscalar meson decay constants obtained from simulations of domain wall QCD with one dynamical flavour approximating the s quark, and two degenerate dynamical flavours with input bare masses ranging from m{sub s} to m{sub s}/4 approximating the u and d quarks. We compare these quantities obtained using the Iwasaki and DBW2 improved gauge actions, and actions with larger rectangle coefficients, on 16{sup 3}x32 lattices. We seek parameter values at which both the chiral symmetry breaking residual mass due to the finite lattice extent in the fifth dimension and the Monte Carlo time history for topological charge are acceptable for this set of quark masses at lattice spacings above 0.1 fm. We find that the Iwasaki gauge action is best, demonstrating the feasibility of using QCDOC to generate ensembles which are good representations of the QCD path integral on lattices of up to 3 fm in spatial extent with lattice spacings in the range 0.09-0.13 fm. Despite large residual masses and a limited number of sea quark-mass values with which to perform chiral extrapolations, our results for light hadronic physics scale and agree with experimental measurementsmore » within our statistical uncertainties.« less

We study the finite temperature transition in QCD with three flavors of equal masses using the R and RHMC algorithms on lattices with temporal extent ${N}_{\ensuremath{\tau}}=4$ and 6. For the transition temperature in the continuum limit we find ${r}_{0}{T}_{c}=0.429(8)$ for the light pseudoscalar mass corresponding to the endpoint of the 1st order transition region. When comparing the results obtained with the R and RHMC algorithms for p4fat3 action we see no significant step-size errors down to a lightest pseudoscalar mass of ${m}_{\mathrm{ps}}{r}_{0}=0.4$.

We present a detailed calculation of the transition temperature in QCD with two light and one heavier (strange) quark mass on lattices with temporal extent N_t =4 and 6. Calculations with improved staggered fermions have been performed for various light to strange quark mass ratios in the range, 0.05 0) and continuum (aT = 1/N_t -> 0) limits we find for the transition temperature at the physical point T_c r_0 = 0.457(7) where the scale is set by the Sommer-scale parameter r_0 defined as the distance in the static quark potential at which the slope takes on the value, (dV_qq(r)/dr)_r=r_0 = 1.65/r_0^2. Using the currently best known value for r_0 this translates to a transition temperature T_c = 192(7)(4)MeV. The transition temperature in the chiral limit is about 3% smaller. We discuss current ambiguities in the determination of T_c in physical units and also comment on the universal scaling behavior of thermodynamic quantities in the chiral limit.

Numerical simulations of full QCD on anisotropic lattices provide a convenient way to study QCD thermodynamics with fixed physics scales and reduced lattice spacing errors. We report results from calculations with two flavors of dynamical staggered fermions, where all bare parameters and the renormalized anisotropy are kept constant and the temperature is changed in small steps by varying only the number of time slices. Including results from zero-temperature scale setting simulations, which determine the Karsch coefficients, allows for the calculation of the equation of state at finite temperatures., Comment: 27 pages, 11 figures, 8 tables

We find the renormalisation coefficients of the quark field and the flavour non-singlet fermion bilinear operators for the domain wall fermion action, in the regularisation independent (RI) renormalisation scheme. Our results are from a quenched simulation, on a 16^3x32 lattice, with beta=6.0 and an extent in the fifth dimension of 16. We also discuss the expected effects of the residual chiral symmetry breaking inherent in a domain wall fermion simulation with a finite fifth dimension, and study the evidence for both explicit and spontaneous chiral symmetry breaking effects in our numerical results. We find that the relations between different renormalisation factors predicted by chiral symmetry are, to a good approximation, satisfied by our results and that systematic effects due to the (low energy) spontaneous chiral symmetry breaking and zero-modes can be controlled. Our results are compared against the perturbative predictions for both their absolute value and renormalisation scale dependence., Comment: 53 pages, 21 figures, revtex

The domain wall approach to lattice fermions employs an additional dimension, in which gauge fields are merely replicated, to separate the chiral components of a Dirac fermion. It is known that in the limit of infinite separation in this new dimension, domain wall fermions have exact zero modes, even for gauge fields which are not smooth. We explore the effects of finite extent in the fifth dimension on the zero modes for both smooth and non-smooth topological configurations and find that a fifth dimension of around ten sites is sufficient to clearly show zero mode effects. This small value for the extent of the fifth dimension indicates the practical utility of this technique for numerical simulations of QCD., Updated fig. 3-7, small changes in sect. 3, added fig. 8, added more references

We calculate the QCD equation of state for temperatures corresponding to the transition region with physical mass values for two degenerate light quark flavors and a strange quark using an improved staggered fermion action (p4-action) on lattices with temporal extent N_tau=8. We compare our results with previous calculations performed at twice larger values of the light quark masses as well as with results obtained from a resonance gas model calculation. We also discuss the deconfining and chiral aspects of the QCD transition in terms of renormalized Polyakov loop, strangeness fluctuations and subtracted chiral condensate. We show that compared to the calculations performed at twice larger value of the light quark mass the transition region shifts by about 5 MeV toward smaller temperatures, Comment: 7 pages, LaTeX, 6 figures; minor corrections, typos corrected, references added

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 doubly blocked Wilson (DBW2), are studied and compared to the Wilson action. All improved gauge actions studied show a reduction in the additive residual quark mass, $\mres$. Remarkably, in the DBW2 case $\mres$ is roughly two orders of magnitude smaller than the Wilson gauge action at $a^{-1}=2$ GeV and $L_s=16$. Significant reduction in $\mres$ is also realized at stronger gauge coupling corresponding to $a^{-1}=1.3$ 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., 50 pages, 25 figures, RevTeX formated, minor corrections