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At fine lattice spacings, Markov chain Monte Carlo simulations of QCD and other gauge theories with or without fermions are plagued by slow modes that give rise to large autocorrelation times. This can lead to simulation runs that are effectively stuck in one topological sector, a problem known as topological freezing. Here, we demonstrate that for a relevant set of parameters, Metadynamics can be used to unfreeze 4-dimensional SU(3) gauge theory. However, compared to local update algorithms and the Hybrid Monte Carlo algorithm, the computational overhead is significant in pure gauge theory, and the required reweighting procedure may considerably reduce the effective sample size. To deal with the latter problem, we propose modifications to the Metadynamics bias potential and the combination of Metadynamics with parallel tempering. We test the new algorithm in 4-dimensional SU(3) gauge theory and find that it can achieve topological unfreezing without compromising the effective sample size, thereby reducing the autocorrelation times of topological observables by at least two orders of magnitude compared to conventional update algorithms. Additionally, we observe significantly improved scaling of autocorrelation times with the lattice spacing in 2-dimensional U(1) gauge theory., Comment: 23 pages, 12 figures, 8 tables. v2: Matches published version

The automatic fine-tuning of isospin breaking effects by conformal coalescence found by Georgi in the 2-flavor Schwinger model is studied. The analytical results obtained for the bosonic correlators are elaborated and the mass splitting parameter in leading order determined. Numerical investigation of meson mass splitting confirms the exponential suppression of symmetry breaking effects even for mass differences $\delta m$ near the fermion mass $m_f$., Comment: 7 pages. Proceedings of the 39th International Symposium on Lattice Field Theory, LATTICE2022 8th-13th August, 2022, University of Bonn, Germany. Matches PoS version

Topological freezing is a well known problem in lattice simulations: with shrinking lattice spacing a transition between topological sectors becomes increasingly improbable, leading to a problematic increase of the autocorrelation time regarding several observables. We present our investigation of metadynamics as a solution for topological freezing in the Schwinger model. Specifically, we take a closer look at the collective variable and its scaling behaviour, visualize the effects of topological freezing and how metadynamics helps in that respect and explore alternatives for a more efficient building process. Possible implications for and differences to four-dimensional SU(3) theory are briefly discussed., Comment: 10 pages, 7 figures, 1 table

At fine lattice spacings, lattice simulations are plagued by slow (topological) modes that give rise to large autocorrelation times. These, in turn, lead to statistical and systematic errors that are difficult to estimate. We study the problem and possible algorithmic solutions in 4-dimensional SU(3) gauge theory, with special focus on instanton updates and Metadynamics., Comment: 10 pages, 4 figures, 3 tables. Proceedings of the 39th International Symposium on Lattice Field Theory, LATTICE2022 8th-13th August, 2022, University of Bonn, Germany v2: Added references and slightly expanded discussion. Matches PoS version

We give an explicit proof for the locality of staggered overlap operators. The proof covers the original two flavor construction by Adams as well as a single flavor version. As in the case of Neuberger's operator, an admissibility condition for the gauge fields is required., Comment: 15 pages, no figures, v2: matches PRD version

In modern lattice simulations, conventional update algorithms do not allow for tunneling between topological sectors at fine lattice spacings. We compare the viability of multiple less commonly used algorithms (metadynamics, instanton updates, and multiscale thermalization) with respect to proper sampling of all topological sectors in the Schwinger model. We briefly comment on the prospects of applying these methods to 4-dimensional SU(3) simulations., Comment: 10 pages, 5 figures, 1 table. Proceedings of the 38th International Symposium on Lattice Field Theory, LATTICE2021 26th-30th July, 2021, Zoom/Gather@Massachusetts Institute of Technology

We present a new formalism for numerically treating the semiclassical gravitational collapse of a scalar quantum field in the radially symmetric case. Our formalism is time reversal invariant and the evolution of the scalar fields is unitary. We present some first results in the angular momentum $l=0$ approximation for an initially coherent state of a massless field and briefly discuss future prospects., Comment: 9 pages, 4 figures, talk presented at the 38th International Symposium on Lattice Field Theory - LATTICE2021, 26th-30th, July, 2021, Zoom/Gather@Massachusetts Institute of Technology

We present a method to study the semiclassical gravitational collapse of a radially symmetric scalar quantum field in a coherent initial state. The formalism utilizes a Fock space basis in the initial metric, is unitary and time reversal invariant up to numerical precision. It maintains exact compatibility of the metric with the expectation values of the energy momentum tensor in the scalar field coherent state throughout the entire time evolution. We find a simple criterion for the smallness of discretization effects, which is violated when a horizon forms. As a first example, we study the collapse of a specific state in the angular momentum $l=0$ approximation. Outside the simulated volume it produces a Schwarzschild metric with $r_s \sim 3.5 \ell_p$. We see behaviour that is compatible with the onset of horizon formation both in the semiclassical and corresponding classical cases in a regime where we see no evidence for large discretization artefacts. In our example setting, we see that quantum effects accelerate the possible horizon formation and move it radially outward. We find that this effect is robust against variations of the radial resolution, the time step, the volume, the initial position and shape of the inmoving state, the vacuum subtraction, the discretization of the time evolution operator and the integration scheme of the metric. We briefly discuss potential improvements of the method and the possibility of applying it to black hole evaporation. We also briefly touch on the extension of our formalism to higher angular momenta, but leave the details and numerics for a forthcoming publication., Comment: v2: 54 pages, 32 figures. Version to appear in PRD

We construct domain wall fermions with a staggered kernel and investigate their spectral and chiral properties numerically in the Schwinger model. In some relevant cases we see an improvement of chirality by more than an order of magnitude as compared to usual domain wall fermions. Moreover, we present first results for four-dimensional quantum chromodynamics, where we also observe significant reductions of chiral symmetry violations for staggered domain wall fermions., Comment: 7 pages, 4 figures; v2: Added references; Proceedings for the 34th International Symposium on Lattice Field Theory, University of Southampton, UK, 24-30 July 2016

We follow up on a suggestion by Adams and construct explicit domain wall fermion operators with staggered kernels. We compare different domain wall formulations, namely the standard construction as well as Borici's modified and Chiu's optimal construction, utilizing both Wilson and staggered kernels. In the process, we generalize the staggered kernels to arbitrary even dimensions and introduce both truncated and optimal staggered domain wall fermions. Some numerical investigations are carried out in the (1+1)-dimensional setting of the Schwinger model, where we explore spectral properties of the bulk, effective and overlap Dirac operators in the free-field case, on quenched thermalized gauge configurations and on smooth topological configurations. We compare different formulations using the effective mass, deviations from normality and violations of the Ginsparg-Wilson relation as measures of chirality., Comment: 23 pages, 22 figures, 2 tables; major revision, matches published version

We present a calculation of the leptonic decay-constant ratio $f_K/f_\pi$ in 2+1 flavor QCD. Our data set includes five lattice spacings and pion masses reaching down below the physical one. Special emphasis is placed on a careful study of all systematic uncertainties, especially the continuum extrapolation. Our result is perfectly compatible with the first-row unitarity constraint of the Standard Model., Comment: 19 pages, 6 figures, 3 tables; v2: added supplementary analysis, version published in Phys. Rev. D

We present preliminary results of a 2+1-flavor study of finite-volume effects in the lattice QCD computation of the leading-order hadronic contribution to the muon anomalous magnetic moment. We also present methods for obtaining directly the invariant hadronic polarization function, $\Pi(Q^2)$, and the Adler function at all discrete lattice values of $Q^2$, including $Q^2=0$. Results are obtained with HEX-smeared clover fermions., Comment: 7 pages, 2 figures, Contribution to the Proceedings of the 32nd International Symposium on Lattice Field Theory (Lattice 2014), 23-28 June 2014, Columbia University, New York, NY, USA

We report on a continuum extrapolated result (arXiv:1309.5258) for the equation of state (EoS) of QCD with $N_f=2+1$ dynamical quark flavors and discuss preliminary results obtained with an additional dynamical charm quark ($N_f=2+1+1$). For all our final results, the systematics are controlled, quark masses are set to their physical values, and the continuum limit is taken using at least three lattice spacings corresponding to temporal extents up to $N_t=16$., Comment: Conference proceedings: The 32nd International Symposium on Lattice Field Theory - Lattice 2014, June 23-28, 2014, Columbia University, New York, New York

Finite temperature charmonium spectral functions in the pseudoscalar(PS) and vector(V) channels are studied in lattice QCD with 2+1 flavours of dynamical Wilson quarks, on fine isotropic lattices (with a lattice spacing of 0.057fm), with a non-physical pion mass of 545MeV. The highest temperature studied is approximately 1.4Tc. Up to this temperature no significant variation of the spectral function is seen in the PS channel. The V channel shows some temperature dependence, which seems to be consistent with a temperature dependent low frequency peak related to heavy quark transport, plus a temperature independent term at omega > 0. These results are in accord with previous calculations using the quenched approximation., Comment: Conference proceedings: The 32nd International Symposium on Lattice Field Theory - Lattice 2014 June 23-28, 2014 Columbia University, New York, New York This conference contribution draws heavily from the paper: arXiv:1401.5940 [hep-lat]

I give a brief introduction to lattice QCD for non-specialists., Comment: Lecture notes, based on lectures at the 54th Cracow School of Theoretical Physics (Zakopane, Poland), the Helmholtz international summer school "Lattice QCD, Hadron Structure and Hadronic Matter" (Dubna, Russia) and the 26th Belgian-Dutch-German graduate school in particle physics (Kerkerade, Netherlands). 67 pages, 36 figures v2: changed layout and reference style. one typo corrected

Finite temperature charmonium spectral functions in the pseudoscalar and vector channels are studied in lattice QCD with 2+1 flavours of dynamical Wilson quarks, on fine isotropic lattices (with a lattice spacing of 0.057 fm), with a non-physical pion mass of $m_{\pi} \approx$ 545 MeV. The highest temperature studied is approximately $1.4 T_c$. Up to this temperature no significant variation of the spectral function is seen in the pseudoscalar channel. The vector channel shows some temperature dependence, which seems to be consistent with a temperature dependent low frequency peak related to heavy quark transport, plus a temperature independent term at \omega>0. These results are in accord with previous calculations using the quenched approximation., Comment: 17 pages, 9 figures, 2 tables

We report on a continuum extrapolated result [arXiv:1309.5258] for the equation of state (EoS) of QCD with $N_f=2+1$ dynamical quark flavors. In this study, all systematics are controlled, quark masses are set to their physical values, and the continuum limit is taken using at least three lattice spacings corresponding to temporal extents up to $N_t=16$. A Symanzik improved gauge and stout-link improved staggered fermion action is used. Our results are available online [ancillary file to arXiv:1309.5258]., Comment: Conference proceedings, 7 pages, 4 figures. Talk presented at 31st International Symposium on Lattice Field Theory (LATTICE 2013), July 29 - August 3, 2013, Mainz, Germany

We present preliminary lattice results for the leading-order hadronic contribution to the muon anomalous magnetic moment, calculated with HEX-smeared clover fermions. In our calculation we include 2+1-flavor ensembles with pions at the physical mass., Comment: 7 pages, 10 figures, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, Germany. Two references added

We perform a detailed, fully-correlated study of the chiral behavior of the pion mass and decay constant, based on 2+1 flavor lattice QCD simulations. These calculations are implemented using tree-level, O(a)-improved Wilson fermions, at four values of the lattice spacing down to 0.054 fm and all the way down to below the physical value of the pion mass. They allow a sharp comparison with the predictions of SU(2) chiral perturbation theory (\chi PT) and a determination of some of its low energy constants. In particular, we systematically explore the range of applicability of NLO SU(2) \chi PT in two different expansions: the first in quark mass (x-expansion), and the second in pion mass (\xi-expansion). We find that these expansions begin showing signs of failure around M_\pi=300 MeV for the typical percent-level precision of our N_f=2+1 lattice results. We further determine the LO low energy constants (LECs), F=88.0 \pm 1.3\pm 0.3 and B^\msbar(2 GeV)=2.58 \pm 0.07 \pm 0.02 GeV, and the related quark condensate, \Sigma^\msbar(2 GeV)=(271\pm 4\pm 1 MeV)^3, as well as the NLO ones, l_3=2.5 \pm 0.5 \pm 0.4 and l_4=3.8 \pm 0.4 \pm 0.2, with fully controlled uncertainties. We also explore the NNLO expansions and the values of NNLO LECs. In addition, we show that the lattice results favor the presence of chiral logarithms. We further demonstrate how the absence of lattice results with pion masses below 200 MeV can lead to misleading results and conclusions. Our calculations allow a fully controlled, ab initio determination of the pion decay constant with a total 1% error, which is in excellent agreement with experiment.

We present a full result for the 2+1 flavor QCD equation of state. All the systematics are controlled, the quark masses are set to their physical values, and the continuum extrapolation is carried out. This extends our previous studies [JHEP 0601:089 (2006); 1011:077 (2010)] to even finer lattices and now includes ensembles with Nt = 6,8,10,12 up to Nt = 16. We use a Symanzik improved gauge and a stout-link improved staggered fermion action. Our findings confirm our earlier results. In order to facilitate the direct use of our equation of state we make our tabulated results available for download., Comment: 10 pages, 9 figures

We present results for the light quark masses and the neutral kaon mixing parameter $B_K$ from lattice QCD. Our data set includes lighter than physical light quark masses and 5 lattice spacings so that chiral extrapolation is not necessary and cutoff effects are fully under control. We obtain fully nonperturbative predictions for $m_{ud}=(m_u+m_d)/2$, $m_s$ and $B_K$ in the RI scheme with $M_\pi$, $M_K$ and $M_\Omega$ as the only input quantities. Using perturbative 4-loop respectively 2-loop running and dispersive input from $\eta\rightarrow 3\pi$, we obtain $m_u^\mathrm{\bar{MS}}(2 \mathrm{GeV})=2.17(4)(10) \mathrm{MeV}$, $m_d^\mathrm{\bar{MS}}(2 \mathrm{GeV})=4.79(7)(12) \mathrm{MeV}$, $m_s^\mathrm{\bar{MS}}(2 \mathrm{GeV})=95.5(1.1)(1.5) \mathrm{MeV}$ and $\hat{B}_K=0.773(8)(8)$ where the first error is statistical and the second systematic., Comment: 6 pages, 6 figures. Contribution to the proceedings of the 47th recontres de Moriond, EW session

This article reviews lattice QCD results for the light hadron spectrum. We give an overview of different formulations of lattice QCD, with discussions on the fermion doubling problem and improvement programs. We summarize recent developments in algorithms and analysis techniques, that render calculations with light, dynamical quarks feasible on present day computer resources. Finally, we summarize spectrum results for ground state hadrons and resonances using various actions., Comment: 53 pages, 24 figures, one table; Rev.Mod.Phys. (published version); v2: corrected typo

At the precision reached in current lattice QCD calculations, electromagnetic effects are becoming numerically relevant. Here, electromagnetic effects are included by superimposing $\mathrm{U}(1)$ degrees of freedom on $N_f = 2+1$ QCD configurations from the Budapest-Marseille-Wuppertal Collaboration. We present preliminary results for the electromagnetic corrections to light pseudoscalars mesons masses and discuss some of the associated systematic errors., Comment: 7 pages, 2 figures, The XXIX International Symposium on Lattice Field Theory, July 10-16, 2011, Squaw Valley, Lake Tahoe, California, USA

QCD is investigated at finite temperature using Wilson fermions in the fixed scale approach. A 2+1 flavor stout and clover improved action is used at four lattice spacings allowing for control over discretization errors. The light quark masses in this first study are fixed to heavier than physical values. The renormalized chiral condensate, quark number susceptibility and the Polyakov loop is measured and the results are compared with the staggered formulation in the fixed N_t approach. The Wilson results at the finest lattice spacing agree with the staggered results at the highest N_t., Comment: 7 pages, Talk presented at the XXIX International Symposium on Lattice Field Theory (Lattice 2011), July 10-16, 2011, Squaw Valley, Lake Tahoe, California, USA

The QCD transition is studied on lattices up to $N_t=16$. The chiral condensate is presented as a function of the temperature, and the corresponding transition temperature is extracted. The equation of state is determined on lattices with $N_t=6,8,10$ and at some temperature values with $N_t=12$. The pressure and the trace anomaly are presented as functions of the temperature in the range 100 ...1000 MeV . Using the same configurations we determine the continuum extrapolated phase diagram of QCD on the $\mu-T$ plane for small to moderate chemical potentials. Two transition lines are defined with two quantities, the chiral condensate and the strange quark number susceptibility., Comment: 4 pages, 2 figures, Proceedings for Quark Matter 2011

I review recent lattice QCD results on light hadron spectroscopy and pseudoscalar decay constants., Comment: 21 pages, 10 figures, 1 table. Review talk given at the XXVIII International Symposium on Lattice Field Theory, June 14-19 2010, Villasimius, Italy. (V2: typos corrected)

We present our most recent investigations on the QCD cross-over transition temperatures with 2+1 staggered flavours and one-link stout improvement [JHEP 1009:073, 2010]. We extend our previous two studies [Phys. Lett. B643 (2006) 46, JHEP 0906:088 (2009)] by choosing even finer lattices ($N_t$=16) and we work again with physical quark masses. All these results are confronted with the predictions of the Hadron Resonance Gas model and Chiral Perturbation Theory for temperatures below the transition region. Our results can be reproduced by using the physical spectrum in these analytic calculations. A comparison with the results of the hotQCD collaboration is also discussed., Comment: 4 pages, 3 figures, Presented at the 4th International Conference Hard Probes 2010

We conclude our investigations on the QCD cross-over transition temperatures with 2+1 staggered flavours and one-link stout improvement. We extend our previous two studies [Phys. Lett. B643 (2006) 46, JHEP 0906:088 (2009)] by choosing even finer lattices (N_t=16) and we work again with physical quark masses. These new results [for details see JHEP 1009:073,2010] support our earlier findings. We compare them with the published results of the hotQCD collaboration. All these results are confronted with the predictions of the Hadron Resonance Gas model and Chiral Perturbation Theory for temperatures below the transition region. Our results can be reproduced by using the physical spectrum. The findings of the hotQCD collaboration can be recovered only by using a distorted spectrum. This analysis provides a simple explanation for the observed discrepancy in the transition T between our and the hotQCD collaborations., Comment: presented at the XXVIII. International Symposium on Lattice Field Theory, June 14-19,2010, Villasimius, Sardinia Italy

The goal of this study is to investigate the scaling behaviour of our 2 HEX action. For this purpose, we compute the $N_f=3$ spectrum and compare the results to our 6 EXP action. We find a large scaling window up to $\sim 0.15\,\mathrm{fm}$ along with small scaling corrections at the 2%-level and full compatibility with our previous study. As a second important observable to be tested for scaling, we chose the non-perturbatively renormalized quenched strange quark mass. Here we find a fairly flat scaling with a broad scaling range up to $\simeq 0.15\,\mathrm{fm}$ and perfect agreement with the literature., Comment: PoS for the XXVIII International Symposium on Lattice Field Theory, Lattice2010, 7 pages, 4 figures

Based on recent work by Adams, I construct a lattice fermion operator that fully lifts the staggered flavor degeneracy. The resulting operator is of Wilson type but smaller by a factor of 4, better conditioned and contains 3 instead of 15 doublers. It is further suggested that this operator may be used as a candidate kernel operator to an overlap construction. Prospects for practical applications and potential problems of the new discretizations are briefly discussed., Comment: 9 pages, 1 table, 1 figure. Referencing slightly modified. Final version, to appear in Phys.Lett.B

The present paper concludes our investigations on the QCD cross-over transition temperatures with 2+1 staggered flavours and one-link stout improvement. We extend our previous two studies [Phys. Lett. B643 (2006) 46, JHEP 0906:088 (2009)] by choosing even finer lattices ($N_t$=16) and we work again with physical quark masses. The new results on this broad cross-over are in complete agreement with our earlier ones. We compare our findings with the published results of the hotQCD collaboration. All these results are confronted with the predictions of the Hadron Resonance Gas model and Chiral Perturbation Theory for temperatures below the transition region. Our results can be reproduced by using the physical spectrum in these analytic calculations. The findings of the hotQCD collaboration can be recovered by using a distorted spectrum which takes into account lattice discretization artifacts and heavier than physical quark masses. This analysis provides a simple explanation for the observed discrepancy in the transition temperatures between our and the hotQCD collaborations., Comment: 25 pages, 10 figures and 3 tables

We evaluate baryon wave functions in both the Coulomb and Landau gauge in lattice QCD. These are constructed from quark propagators calculated with the overlap Dirac operator on quenched gauge configurations at beta = 6. By comparing baryon states that differ in their diquark content, we find evidence for enhanced correlation in the scalar diquark channel, as favored by quark models. We also summarize earlier results for diquark masses in the Landau gauge, casting them in a form more easily compared with subsequent studies., Comment: 9 pages, 12 figures, v2 as appears in PRD

We determine the topological susceptibility in the SU(3) pure gauge theory. We perform a series of high-statistics lattice studies and take the combined continuum and infinite volume limit. We find chi_{top}r_0^4=0.0524(7)(6) which translates into chi_{top}^{1/4}=193(1)(8)MeV with the second error exclusively due to the intrinsic scale ambiguity., Comment: 13 pages, 7 figures. v2: several new footnotes, one figure augmented, 9 Refs added, 1 Ref corrected; matches published version

The speed, bandwidth and cost characteristics of today's PC graphics cards make them an attractive target as general purpose computational platforms. High performance can be achieved also for lattice simulations but the actual implementation can be cumbersome. This paper outlines the architecture and programming model of modern graphics cards for the lattice practitioner with the goal of exploiting these chips for Monte Carlo simulations. Sample code is also given., Comment: 11 pages, 2 figures, sample code, new benchmarks added

We present results for B_K and selected matrix elements for beyond the standard model interactions obtained in quenched QCD with overlap fermions. We also illustrate results on baryon wave-functions and diquark correlations within baryons in the Coulomb and Landau gauge., Comment: 7 pages, 6 figures. Contribution to Lattice 2006, Tucson, Arizona, 23-28 July 2006

We investigate filtered clover fermions, built from fat gauge links, both in one-loop perturbation theory and in numerical simulations. We use a variety of filtering recipes (APE, HYP, EXP, HEX), some of which are suitable for a HMC with dynamical fermions. A generic filtering together with a (fat-link) clover term yields fermions with much reduced chiral symmetry breaking., Comment: 7 pages, Lattice 2006 (Quark Masses, Gauge Couplings, and Renormalization)

We study the contributions Sigma_0 and Sigma_1, proportional to a^0 and a^1, to the fermion self-energy in Wilson's formulation of lattice QCD with UV-filtering in the fermion action. We derive results for m_{crit} and the renormalization factors Z_S, Z_P, Z_V, Z_A to 1-loop order in perturbation theory for several filtering recipes (APE, HYP, EXP, HEX), both with and without a clover term. The perturbative series is much better behaved with filtering, in particular tadpole resummation proves irrelevant. Our non-perturbative data for m_{crit} and Z_A/(Z_m*Z_P) show that the combination of filtering and clover improvement efficiently reduces the amount of chiral symmetry breaking -- we find residual masses am_{res}=O(10^{-2})., Comment: 25 pages, 4 figures; v2: typo in eqn. (37) fixed [agrees with published version]

We present results for the \Delta S=2 matrix elements which are required to study neutral kaon mixing in the standard model (SM) and beyond (BSM). We also provide leading chiral order results for the matrix elements of the electroweak penguin operators which give the dominant \Delta I=3/2 contribution to direct CP violation in K->\pi\pi decays. Our calculations were performed with Neuberger fermions on two sets of quenched Wilson gauge configurations at inverse lattice spacings of approximately 2.2 GeV and 1.5 GeV. All renormalizations were implemented non-perturbatively in the RI/MOM scheme, where we accounted for sub-leading operator product expansion corrections and discretization errors. We find ratios of non-SM to SM matrix elements which are roughly twice as large as in the only other dedicated lattice study of these amplitudes. On the other hand, our results for the electroweak penguin matrix elements are in good agreement with two recent domain-wall fermion calculations. As a by-product of our study, we determine the strange quark mass. Our main results are summarized and discussed in Sec. VII. Within our statistics, we find no evidence for scaling violations., Comment: 37 pages (REVTeX 4), 11 figures