We carry out lattice simulations of two-color QCD and spectroscopy at finite density with two flavors of rooted-staggered quarks and a diquark source term. As in a previous four-flavor study, for small values of the inverse gauge coupling we observe a Goldstone spectrum which reflects the symmetry-breaking pattern of a Gaussian symplectic chiral random-matrix ensemble (GSE) with Dyson index $β_D=4$, which corresponds to any-color QCD with adjoint quarks in the continuum instead of QC$_2$D wih fundamental quarks. We show that this unphysical behavior occurs only inside of the bulk phase of $SU(2)$ gauge theory, where the density of $Z_2$ monopoles is high. Using an improved gauge action and a somewhat larger inverse coupling to suppress these monopoles, we demonstrate that the continuum Goldstone spectrum of two-color QCD, corresponding to a Gaussian orthogonal ensemble (GOE) with Dyson index $β_D=1$, is recovered also with rooted-staggered quarks once simulations are performed away from the bulk phase. We further demonstrate how this change of random-matrix ensemble is reflected in the distribution of eigenvalues of the Dirac operator. By computing the unfolded level spacings inside and outside of the bulk phase, we demonstrate that, starting with the low-lying eigenmodes which determine the infrared physics, the distribution of eigenmodes continuously changes from the GSE to the GOE one as monopoles are suppressed.
We calculate the axial current decay constants of taste non-Goldstone pions and kaons in staggered chiral perturbation theory through next-to-leading order. The results are a simple generalization of the results for the taste Goldstone case. New low-energy couplings are limited to analytic corrections that vanish in the continuum limit; certain coefficients of the chiral logarithms are modified, but they contain no new couplings. We report results for quenched, fully dynamical, and partially quenched cases of interest in the chiral SU(3) and SU(2) theories.
We calculate the masses of taste non-Goldstone pions and kaons in staggered chiral perturbation theory through next-to-leading order in the standard power counting. The results can be used to quantitatively understand taste violations in existing lattice data generated with staggered fermions and to extract the $u$, $d$, and $s$ quark masses and Gasser-Leutwyler parameters from the experimentally observed spectrum. The expressions for the non-Goldstone masses contain low-energy couplings unique to the non-Goldstone sector. With two exceptions these enter as coefficients of analytic terms; all …
We present results of the masses of taste non-Goldstone $(F \ne ξ_5)$ pions and kaons calculated up to the next-to-leading order in the SU(3) staggered chiral perturbation theory (SChPT). The results can be used to fit data and to understand taste symmetry breaking effect quantitatively. The final expressions for the non-Goldstone masses contain 20 low energy constants unique to the non-Goldstone sector. We have calculated the several cases such as the full QCD, partially quenched QCD, and quenched QCD in the $N_f=1+1+1$ flavor and $N_f=2+1$ flavor cases in the SU(3) and SU(2) SChPT. In this p…
We calculate the next-to-leading order axial current decay constants of taste non-Goldstone pions and kaons in staggered chiral perturbation theory. This is an extension of the taste Goldstone decay constants calculation to that of the non-Goldstone tastes. We present results for the partially quenched case in the SU(3) and SU(2) staggered chiral perturbation theories and discuss the difference between the taste Goldstone and non-Goldstone cases.
We report on exploratory studies of heavy-light meson semileptonic decays using Asqtad light quarks, NRQCD heavy quarks and Symanzik improved glue on coarse quenched lattices. Oscillatory contributions to three-point correlators coming from the staggered light quarks are found to be handled well by Bayesian fitting methods. B meson decays to both the Goldstone pion and to one of the point-split non-Goldstone pions are investigated. One-loop perturbative matching of NRQCD/Asqtad heavy-light currents is incorporated.
We investigate a class of actions for lattice QCD with staggered quarks aimed at reducing the flavour symmetry violations associated with using staggered fermions. These actions replace the gauge field link fields in the quark action with covariantly smeared fields. As such they are an extension of actions considered by the MILC collaboration. We show that such actions systematically reduce flavour symmetry violations in the weak coupling limit. Using the mass splitting between Goldstone and non-Goldstone pions as a measure of flavour symmetry violations we find that these actions have conside…
We investigate the continuum limit of the rooted staggered determinant in the 2-dimensional Schwinger model. We match both the unrooted and rooted staggered determinant with an overlap fermion determinant of two (one) flavors and a local pure gauge effective action by fitting the coefficients of the effective action and the mass of the overlap operator. The residue of this fit measures the difference of the staggered and overlap fermion actions. We show that this residue scales at least as O(a^2), implying that any difference, be it local or non-local, between the staggered and overlap actions…
Evaluation of the continuum limit of the axial anomaly and index is sketched for the staggered overlap Dirac operator. There are new complications compared to the usual overlap case due to the distribution of the spin and flavor components around lattice hypercubes in the staggered formalism. The index is found to correctly reproduce the continuum index, but for the axial anomaly this is only true after averaging over the sites of a lattice hypercube.
In this talk, I will give an overview of the theoretical status of staggered Lattice QCD with the "fourth-root trick." In this regularization of QCD, a separate staggered quark field is used for each physical flavor, and the inherent four-fold multiplicity that comes with the use of staggered fermions is removed by taking the fourth root of the staggered determinant for each flavor. At nonzero lattice spacing, the resulting theory is nonlocal and not unitary, but there are now strong arguments that this disease is cured in the continuum limit. In addition, the approach to the continuum limit c…
We explore the possibility of a trivial continuum limit of strongly coupled quenched QED4 by contrasting our results with a Nambu--Jona Lasinio equation of state. The data does not compare favorably with such scenario. We study in detail the interplay of chiral symmetry breaking with the Goldstone mechanism, and clarify some puzzling features of past results.
We report on recent progress in the calculation of $B_K$ using HYP-smeared staggered fermions on the MILC asqtad lattices. Our main focus is on the continuum extrapolation, which is done using (up to) four different lattice spacings---$a\approx$ 0.12, 0.09, 0.06 and 0.045 fm. Since Lattice 2010, we have reduced the statistical errors on the $a\approx 0.09\;$fm lattices by a factor of $\sim 3$, and roughly doubled the size of the $a\approx0.045\;$fm ensemble. We find that these improvements have a very significant impact on the continuum extrapolation, with the $a\approx 0.12\;$fm data lying ou…
We match continuum and lattice heavy-light four-fermion operators at one loop in perturbation theory. For the heavy quarks we use nonrelativistic QCD and for the massless light quarks the highly improved staggered quark action. We include the full set of $ΔB=2$ operators relevant to neutral $B$ mixing both within and beyond the Standard Model and match through order $α_s$, $Λ_{\mathrm{QCD}}/M_b$, and $α_s/(aM_b)$.
We extend previous work on finite-size effects with dynamical staggered quarks to the quenched approximation. We again emphasize the large volume limit that is of interest for spectrum calculations which may hope to approach the experimental values. Relying on new calculations at $6/g^2=5.7$ and recent work with weaker couplings, we extrapolate to the continuum limit and find a nucleon to rho mass ratio in close agreement with the experimental value and the value obtained by extrapolations from calculations with Wilson quarks. Additional calculations that should be done to improve the reliabil…
Durr and Hoelbling recently observed that the continuum and chiral limits do not commute in the two dimensional, one flavor, Schwinger model with staggered fermions. I point out that such lack of commutativity can also be seen in four-dimensional staggered chiral perturbation theory (SChPT) in quenched or partially quenched quantities constructed to be particularly sensitive to the chiral limit. Although the physics involved in the SChPT examples is quite different from that in the Schwinger model, neither singularity seems to be connected to the trick of taking the nth root of the fermion det…
In confining lattice gauge theories in which part of the flavor group is coupled weakly to additional gauge fields, both the dynamics of the weak gauge fields as well as lattice artifacts may have non-trivial effects on the orientation of the vacuum in flavor space. Here we discuss this issue for lattice gauge theories employing staggered fermions. Staggered fermions break flavor symmetries to a much smaller group on the lattice, and orientations in flavor space that are equivalent in the continuum may be distinct on the lattice. Assuming universality, we show that in the continuum limit the w…
Staggered fermions with 4 tastes are expected to describe 4-flavor QCD in the continuum limit, therefore at finite lattice spacing the staggered determinant should be equivalent to an SU(4) flavor-symmetric system up to lattice artifacts. This equivalence is the starting point of the 4th root trick used to reduce the number of fermion flavors and provides the only consistent description of 2 or 1 flavor systems. In this paper we argue that the quark mass of the underlying flavor symmetric theory differs from the staggered mass by an additive term due to the taste breaking of the staggered acti…
We present results on the chiral and deconfinement properties of the QCD transition at finite temperature. We performed calculations using asqtad and HISQ/tree actions using lattices with temporal extent N_tau=6, 8 and 12 allowing to control the approach to the continuum limit. We analyze the chiral transition in terms of universal O(N) scaling functions. From peaks in the scaling functions we perform a simultaneous continuum extrapolation for HISQ/tree and asqtad to derive the critical temperature, T_c= 157 +/- 6 MeV.
We present preliminary results for $B_K$ calculated using improved staggered fermions with a mixed action (HYP-smeared staggered valence quarks and AsqTad staggered sea quarks). We investigate the effect of non-degenerate quarks on $B_K$ and attempt to estimate the ${\cal O}(a^2)$ effect due to non-Goldstone pions in loops. We fit the data to continuum partially quenched chiral perturbation theory. We find that the quality of fit for $B_K$ improves if we include non-degenerate quark mass combinations. We also observe, however, that the fitting curve deviates from the data points in the light q…
One exciting possibility of new physics beyond the Standard Model is that the fundamental Higgs sector is replaced by a strongly-interacting gauge theory, known as technicolor. A viable theory must break chiral symmetry dynamically, like in QCD, to generate Goldstone bosons which become the longitudinal components of the W and Z. By measuring the eigenvalues of the Dirac operator, one can determine if chiral symmetry is in fact spontaneously broken. We simulate SU(3) gauge theory with n_s=2 and 3 staggered flavors in the fundamental representation, corresponding to N_f=8 and 12 flavors in the …
We investigate the properties of staggered-fermion lattice QCD in which the fourth root of the fermion determinant is taken. We show that this theory is non-local at non-zero lattice spacing $a$, and that the non-locality is caused by the breaking of taste symmetry at $a\ne 0$. We then present a renormalization-group based argument that the theory restores taste symmetry in the continuum limit. As a consequence the theory is local in that limit, and falls into the correct universality class. Finally, we argue that the correct effective theory for the physics of Goldstone bosons at $a\ne 0$ is …
Different versions of improved staggered fermions can be used as valence quarks to reduce discretization effects in lattice QCD calculations while increasing statistics on existing staggered gauge ensembles. Such mixed-action simulations can be used to improve determinations of light quark masses, Gasser-Leutwyler couplings, decay constants, and other parameters relevant to particle phenomenology. We recall the generalization of ordinary, unmixed staggered chiral perturbation theory required to describe data from lattice calculations with a mixed action such as with HYP staggered valence quark…
The QCD light quark mass renormalized at a 1 GeV scale in the $ \overline{MS} $ scheme is obtained from the numerical results of the lattice QCD simulation with staggered fermions. The primary emphasis is given to the connection between the lattice and continuum parameters. The results are compared with those from the QCD sum rule.
As a first step towards constructing chiral models on the lattice with staggered fermions, we study a U(1) model with axial-vector coupling to an external gauge field in two dimensions. In our approach gauge invariance is broken, but it is restored in the classical continuum limit. We find that the continuum divergence relations for the vector and axial-vector currents are reproduced, up to contact terms, which we determine analytically. The current divergence relations are also studied numerically for smooth external gauge fields with topological charge zero. We furthermore investigate the ef…
We discuss the Schrödinger functional in lattice QCD with staggered fermions including its order $O(a)$ boundary counterterms. We relate it, in the classical continuum limit, to the Schrödinger functional as obtained in the same limit with Wilson fermions. We compute the strong coupling constant defined via the Schrödinger functional with staggered fermions at one loop and show that it agrees with the continuum running coupling constant in the Schrödinger functional formalism.
Growing evidence indicates that in the continuum limit the rooted staggered action is in the correct QCD universality class, the non-local terms arising from taste breaking can be viewed as lattice artifacts. In this paper we consider the 2-flavor Asqtad staggered action at a lattice spacing of approximately 0.13 fm and probe the properties of the staggered configurations by an overlap valence Dirac operator. By comparing the distribution of the overlap eigenmodes to continuum QCD predictions we investigate if/when the lattice artifacts are small as a function of the staggered quark mass. We d…
A popular approximation in lattice gauge theory is an extrapolation in the number of fermion species away from the four fold degeneracy natural with the staggered fermions formulation. I show that at finite lattice spacing and for an odd number of flavors this extrapolation misses terms which, on general principles, must be present in the continuum theory. For a correct continuum limit, this forces unphysical singularities in parameter regions where continuum physics is smooth and all physical particles are massive. These singularities are not expected with other lattice regulators. Finally, I…
I develop a renormalization-group blocking framework for lattice QCD with staggered fermions. Under plausible, and testable, assumptions, I then argue that the fourth-root recipe used in numerical simulations is valid in the continuum limit. The taste-symmetry violating terms, which give rise to non-local effects in the fourth-root theory when the lattice spacing is non-zero, vanish in the continuum limit. A key role is played by reweighted theories that are local and renormalizable on the one hand, and that approximate the fourth-root theory better and better as the continuum limit is approac…
In hep-lat/0701018, Creutz claims that the rooting trick used in simulations of staggered fermions to reduce the number of tastes misses key physics whenever the desired theory has an odd number of continuum flavors, and uses this argument to call into question the rooting trick in general. Here we show that his argument fails as the continuum limit is approached, and therefore does not imply any problem for staggered simulations. We also show that the cancellations necessary to restore unitarity in physical correlators in the continuum limit are a straightforward consequence of the restoratio…
We have extended our previous study of the lattice QCD spectrum with 2 flavors of staggered dynamical quarks at $6/g^2=5.6$ and $am_q=0.025$ and 0.01 to larger lattices, with better statistics and with additional sources for the propagators. The additional sources allowed us to estimate the $Δ$ mass and to measure the masses of all mesons whose operators are local in time. These mesons show good evidence for flavor symmetry restoration, except for the masses of the Goldstone and non-Goldstone pions. PCAC is observed in that $m_π^2 \propto m_q$, and $f_π$ is estimated. Use of undoubled lattices…
We report preliminary results on the chiral and deconfinement aspects of the QCD transition at finite temperature using the Highly Improved Staggered Quark (HISQ) action on lattices with temporal extent of N_τ=6 and 8. The chiral aspects of the transition are studied in terms of quark condensates and the disconnected chiral susceptibility. We study the deconfinement transition in terms of the strange quark number susceptibility and the renormalized Polyakov loop. We made continuum estimates for some quantities and find reasonably good agreement between our results and the recent continuum extr…
A recent numerical lattice calculation of the kaon mixing matrix elements of general $ΔS=2$ four-fermion operators using staggered fermions relied on two auxiliary theoretical calculations. Here we describe the methodology and present the results of these two calculations. The first concerns one-loop matching coefficients between staggered lattice operators and the corresponding continuum operators. Previous calculations with staggered fermions have used a non-standard regularization scheme for the continuum operators, and here we provide the additional matching factors needed to connect to th…
I describe a calculation of B meson mixing at one-loop in staggered chiral perturbation theory, for the complete set of Standard Model and beyond-the-Standard Model operators. The particular lattice representation of the continuum operators used by the Fermilab Lattice/MILC collaborations (and earlier by the HPQCD collaboration) turns out to be important, and results in the presence of "wrong-spin" operators, whose contributions however vanish in the continuum limit. The relation between staggered and naive fermions also plays a key role.
We investigate the continuum limit of the rooted staggered action in the 2-dimensional Schwinger model. We match both the unrooted and rooted staggered determinants with an overlap fermion determinant of two (one) flavors and a local pure gauge effective action by fitting the coefficients of the effective action and the mass of the overlap operator. The residue of this fit measures the difference of the staggered and overlap fermion actions. We show that this residue scales at least as O(a^2), implying that any difference, be it local or non-local, between the staggered and overlap actions bec…
We describe a proposal for constructing a lattice theory that we argue may be capable of yielding free Weyl fermions in the continuum limit. The model employs reduced staggered fermions and uses site parity dependent Yukawa interactions of Fidkowski-Kitaev type to gap a subset of the lattice fermions without breaking symmetries. The possibility for such symmetric mass generation is tied to the cancellation of certain discrete anomalies arising in the continuum limit. The latter place strong constraints on the number of lattice fermions -- constraints that are satisfied by this model. We presen…
Lattice QCD calculations with different staggered valence and sea quarks can be used to improve determinations of quark masses, Gasser-Leutwyler couplings, and other parameters relevant to phenomenology. We calculate the masses and decay constants of flavored pions and kaons through next-to-leading order in staggered-valence, staggered-sea mixed-action chiral perturbation theory. We present the results in the valence-valence and valence-sea sectors, for all tastes. As in unmixed theories, the taste-pseudoscalar, valence-valence mesons are exact Goldstone bosons in the chiral limit, at non-zero…
We study the finite temperature transition in QCD with two flavors of dynamical fermions at a pseudoscalar pion mass of about 350 MeV. We use lattices with temporal extent of $N_t$=8, 10 and 12. For the first time in the literature a continuum limit is carried out for several observables with dynamical overlap fermions. These findings are compared with results obtained within the staggered fermion formalism at the same pion masses and extrapolated to the continuum limit. The presented results correspond to fixed topology and its effect is studied in the staggered case. Nice agreement is found …
We calculate the light quark spectrum of lattice QCD in the quenched approximation using Kogut-Susskind quarks. By combining results for different lattice spacings, several volumes and five quark masses, we are able to take the light quark mass, infinite volume, continuum limit. When we use non-linear chiral extrapolations, we find that the nucleon to rho mass ratio is 1.254 +- 0.018 +- 0.027, where the errors are statistical and systematic (within the quenched approximation), respectively. This should be compared with the experimental value of 1.22. Our results indicate that the error due to …
We present results for kaon mixing parameter $B_K$ calculated using HYP-smeared improved staggered fermions on the MILC asqtad lattices. We use three lattice spacings ($a\approx 0.12$, $0.09$ and $0.06\;$fm), ten different valence quark masses ($m\approx m_s/10-m_s$), and several light sea-quark masses in order to control the continuum and chiral extrapolations. We derive the next-to-leading order staggered chiral perturbation theory (SChPT) results necessary to fit our data, and use these results to do extrapolations based both on SU(2) and SU(3) SChPT. The SU(2) fitting is particularly strai…
We study various improved staggered quark Dirac operators on quenched gluon backgrounds in lattice QCD. We find a clear separation of the spectrum of eigenvalues into high chirality, would-be zero modes and others, in accordance with the Index Theorem. We find the expected clustering of the non-zero modes into quartets as we approach the continuum limit. The predictions of random matrix theory for the epsilon regime are well reproduced. We conclude that improved staggered quarks near the continuum limit respond correctly to QCD topology.
We discuss the properties of 't Hooft vertices in partially quenched and rooted versions of QCD in the continuum. These theories have a physical subspace, equivalent to ordinary QCD, that is contained within a larger space that includes many unphysical correlation functions. We find that the 't Hooft vertices in the physical subspace have the expected form, despite the presence of unphysical 't Hooft vertices appearing in correlation functions that have an excess of valence quarks (or ghost quarks). We resolve an apparent paradox that arises when one uses rooted staggered fermions to study one…
The staggered fermion determinant is complex when the quark chemical potential mu is nonzero. Its fourth root, used in simulations with dynamical fermions, will have phase ambiguities that become acute when Re mu is sufficiently large. We show how to resolve these ambiguities, but our prescription only works very close to the continuum limit. We argue that this regime is far from current capabilities. Other procedures require being even closer to the continuum limit, or fail altogether, because of unphysical discontinuities in the measure. At zero temperature the breakdown is expected when Re …
We compute O(alpha_s) lattice-to-continuum perturbative matching coefficients for the Delta S=2 flavor changing four-quark operators for the Asqtad improved staggered action. In conjunction with lattice simulations with three flavors of light, dynamical quarks, our results yield an unquenched determination of B_K, the parameter that determines the amount of indirect CP violation in the neutral kaon system. Its value is an important input for the unitarity triangle analysis of weak decays.
We calculate the kaon mixing B-parameters for operators arising generically in theories of physics beyond the standard model. We use HYP-smeared improved staggered fermions on the $N_f = 2+1$ MILC asqtad lattices. Operator matching is done perturbatively at one-loop order. Chiral extrapolations are done using "golden combinations" in which one-loop chiral logarithms are absent. For the combined sea-quark mass and continuum extrapolation, we use three lattice spacings: $a \approx 0.045, 0.06$ and $0.09 \text{fm}$. Our results have a total error of 5-6%, which is dominated by the systematic erro…
In the staggered fermion formulation of lattice QCD, we construct diquark operators to be embedded in singly heavy baryons. The group theoretical connections between the continuum and lattice staggered diquark representations are established.
We present a scaling analysis in the 1-flavor Schwinger model with the full overlap and the rooted staggered determinant. In the latter case the chiral and continuum limit of the scalar condensate do not commute, while for overlap fermions they do. For the topological susceptibility a universal continuum limit is suggested, as is for the partition function and the Leutwyler-Smilga sum rule. In the heavy-quark force no difference is visible even at finite coupling. Finally, a direct comparison between the complete overlap and the rooted staggered determinant yields evidence that their ratio is …
We consider the Schrödinger functional with staggered one-component fermions on a fine lattice of size $(L/a)^3 \times (T/a)$ where $T/a$ must be an odd number. In order to reconstruct the four-component spinors, two different set-ups are proposed, corresponding to the coarse lattice having size $(L/2a)^3 \times (T'/2a)$, with $T' = T \pm a$. The continuum limit is then defined at fixed $T'/L$. Both cases have previously been investigated in the pure gauge theory. Here we define fermionic correlation functions and study their approach to the continuum limit at tree-level of perturbation theory…
We extend our recent unquenched ($N_f=2+1$ flavor) calculation of $B_K$ using improved staggered fermions by including in the fits the finite volume shift predicted by one-loop staggered chiral perturbation theory. The net result is to lower the result in the continuum limit by 0.6%. This shift is slightly smaller than our previous estimate of finite volume effects based on a direct comparison between different volumes. To include the finite volume effects in a reasonable time, we found it necessary to calculate them using Graphics Processing Units.
We show that the use of the fourth-root trick in lattice QCD with staggered fermions corresponds to a non-local theory at non-zero lattice spacing, but argue that the non-local behavior is likely to go away in the continuum limit. We give examples of this non-local behavior in the free theory, and for the case of a fixed topologically non-trivial background gauge field. In both special cases, the non-local behavior indeed disappears in the continuum limit. Our results invalidate a recent claim that at non-zero lattice spacing an additive mass renormalization is needed because of taste-symmetry…
In the staggered fermion formulation of lattice QCD, we construct diquark operators which are to be embedded in singly heavy baryons. The group theoretical connections between continuum and lattice staggered diquark representations are established.
We investigate the use of two kinds of staggered fermion operators, smeared and unsmeared. The smeared operators extend over a $4^4$ hypercube, and tend to have smaller perturbative corrections than the corresponding unsmeared operators. We use these operators to calculate kaon weak matrix elements on quenched ensembles at $β=6.0$, 6.2 and 6.4. Extrapolating to the continuum limit, we find $B_K(NDR, 2 GeV)= 0.62\pm 0.02(stat)\pm 0.02(syst)$. The systematic error is dominated by the uncertainty in the matching between lattice and continuum operators due to the truncation of perturbation theory …
Many results from lattice QCD of broad importance to particle and nuclear physics are obtained with 2+1 flavors of staggered sea quarks. In the continuum limit, staggered fermions yield four species, called tastes. To reduce the number of tastes to one (per flavor), the simulation employs the fourth root of the four-taste staggered fermion determinant. This talk surveys evidence in favor of this procedure, refutes recent criticisms, and reviews recent algorithmic and technical improvements. Physics results are covered in other plenary talks.
The MILC collaboration has been performing realistic simulations of full QCD with 2+1 flavors of improved staggered quarks. Our simulations allow for controlled continuum and chiral extrapolations. I present results for the light pseudoscalar sector: masses and decay constants, quark masses and Gasser-Leutwyler low-energy constants. In addition I will present some results for heavy-light mesons, decay constants and semileptonic form factors, obtained in collaboration with the HPQCD and Fermilab lattice collaborations. Such calculations will help in the extraction of CKM matrix elements from ex…
We have extended our program of QCD simulations with an improved Kogut-Susskind quark action to a smaller lattice spacing, approximately 0.09 fm. Also, the simulations with a approximately 0.12 fm have been extended to smaller quark masses. In this paper we describe the new simulations and computations of the static quark potential and light hadron spectrum. These results give information about the remaining dependences on the lattice spacing. We examine the dependence of computed quantities on the spatial size of the lattice, on the numerical precision in the computations, and on the step siz…
We numerically compute renormalized expectation values of quadratic operators in a quantum field theory (QFT) of free Dirac fermions in curved two-dimensional (Lorentzian) spacetime. First, we use a staggered-fermion discretization to generate a sequence of lattice theories yielding the desired QFT in the continuum limit. Numerically-computed lattice correlators are then used to approximate, through extrapolation, those in the continuum. Finally, we use so-called point-splitting regularization and Hadamard renormalization to remove divergences, and thus obtain finite, renormalized expectation …
We present results from our simulations of quantum chromodynamics (QCD) with four flavors of quarks: u, d, s, and c. These simulations are performed with a one-loop Symanzik improved gauge action, and the highly improved staggered quark (HISQ) action. We are generating gauge configurations with four values of the lattice spacing ranging from 0.06 fm to 0.15 fm, and three values of the light quark mass, including the value for which the Goldstone pion mass is equal to the physical pion mass. We discuss simulation algorithms, scale setting, taste symmetry breaking, and the autocorrelations of va…
