Lattice Data Research Articles

Hospital Accessibility Catchment Areas as a Fuzzy Lattice Data Structure

Hospital Accessibility Catchment Areas as a Fuzzy Lattice Data Structure

Study of net-baryon higher moments in PNJL model and their expectation for net-proton using the subensemble acceptance method for the search of QCD critical point

The critical point is one of the most important aspects of the QCD phase diagram of strongly interacting matter. The nonmonotonic behavior of the higher-order moments of conserved quantities like net-baryon (ΔB), net-charge (ΔQ), and net-strangeness (ΔS) are believed to be the signatures of the QCD critical point as a function of energy. We study the effect of the QCD critical point on moments of net-baryon in the Polyakov loop enhanced Nambu-Jona-Lasinio (PNJL) model of QCD with six-quark and eight-quark interactions for finite and infinite volume systems. The study is performed at energies similar to Relativistic Heavy-Ion Collider beam energy scan. Experimentally measuring conserved quantities is difficult due to systematic limitations. Therefore, net-proton, net-pion, and net-kaon are measured as the proxy of ΔB, ΔQ, and ΔS. Recent studies in the subensemble acceptance method on the hadron resonance gas (HRG) model show the dependency of the measured higher-order moment on the experimental acceptance. We applied the subensemble acceptance method to analyze the behavior of κσ2 of net-baryon distribution within the subvolume system for various acceptance fractions. These results can be directly mapped to the subvolume (particle) percentage of the total volume (conserved quantities). Our findings are compared to the solenoidal tracker at RHIC (STAR) net-proton and proton data with different energies to investigate the presence of the critical point. Additionally, these results are also compared with the ultrarelativistic quantum molecular dynamics (UrQMD), HRG model, and available lattice data. Published by the American Physical Society 2024

Colour-Electric and Colour-Magnetic Confinement

The basic properties of the confinement mechanism in QCD—the temperature dependence of the spatial and temporal string tensions (\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\sigma }_{{\ ext{s}}}}(T)$$\\end{document} and \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\sigma }_{{\ ext{E}}}}(T)$$\\end{document})—are studied in the framework of the Field Correlator Method (FCM). It is shown that both functions are connected respectively to the spatial and temporal parts of the vacuum gluon energy \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\epsilon }_{{\ ext{s}}}}$$\\end{document} and \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\epsilon }_{{\ ext{E}}}}$$\\end{document} which define their equal values at \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T = 0$$\\end{document}. However at \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T > 0$$\\end{document} the spatial part is growing with T while the temporal part is destroyed by the hadronic pressure at \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T = {{T}_{{\ ext{c}}}}$$\\end{document} (the deconfinement). Both properties are derived within the same method and are in a good agreement with the corresponding lattice data.

Infrared gluon propagator in the refined Gribov-Zwanziger scenario at one-loop order in the Landau gauge

The refined Gribov-Zwanziger (RGZ) action in the Landau gauge provides a local and renormalizable framework to account for the existence of infinitesimal Gribov copies in the path integral together with other relevant infrared effects such as the formation of condensates. The properties of the tree-level gluon propagator obtained in this setup have been thoroughly investigated over the past decade. It accommodates important properties seen in lattice simulations such as a finite value at vanishing momentum and positivity violation. Yet a comprehensive study about the stability of such properties against quantum corrections was lacking. In this work, we compute the gluon propagator in the RGZ scenario at one-loop order and implement an appropriate renormalization scheme in order to compare our findings with lattice data. Remarkably, the qualitative properties of the tree-level gluon propagator are preserved. In particular, the fits with lattice data show evidence for positivity violation and the existence of complex poles for SU(2) and SU(3) gauge groups. We comment on the results for the ghost propagator as well. Published by the American Physical Society 2024

Valence quark PDFs of the proton from two-current correlations in lattice QCD

Following previous works on that topic, we consider Euclidean hadronic matrix elements in position space of two spatially separated local currents on the lattice, in order to extract the x dependence of parton distribution functions (PDFs). The corresponding approach is often referred to by the term . In this work we will consider valence quark PDFs of an unpolarized proton. We adapt the previously established formalism to our choice of operators. The calculation of the two-current matrix elements requires the evaluation of four-point functions. The corresponding calculation is carried out on a nf=2+1 gauge ensemble with lattice spacing a=0.0856 fm and pseudoscalar masses mπ=355 MeV and mK=441 MeV. The four-point functions have been evaluated in a previous project. The lattice data is converted to the MS¯ scheme at a scale μ=2 GeV and improved with respect to lattice artifacts. We use a common model as fit ansatz for the lattice data in order to extract the PDFs. Published by the American Physical Society 2024

Pion gravitational form factors in the QCD instanton vacuum. II

We revisit the hard QCD contributions to the pion gravitational form factors, in terms of the twist-2,3 pion distribution amplitudes (DAs), including novel semihard contributions from the instantons. The pion DAs are evaluated in the QCD instanton vacuum and then properly evolved to higher resolution. The results are compared to our recent results from the QCD instanton vacuum, as well as Bethe-Salpeter calculations and recent lattice data. The interpolated hard and soft contributions to the pion D form factor are used to derive the (gravitational) pressure and shear within the pion, with a clear delineation of their range. Published by the American Physical Society 2024

Forecasting Lattice and Point Spatial Data: Comparison of Unilateral and Multilateral SAR Models

Spatial auto-regressive (SAR) models are widely used in geosciences for data analysis; their main feature is the presence of weight (W) matrices, which define the neighboring relationships between the spatial units. The statistical properties of parameter and forecast estimates strongly depend on the structure of such matrices. The least squares (LS) method is the most flexible and can estimate systems of large dimensions; however, it is biased in the presence of multilateral (sparse) matrices. Instead, the unilateral specification of SAR models provides triangular weight matrices that allow consistent LS estimates and sequential prediction functions. These two properties are strictly related and depend on the linear and recursive nature of the system. In this paper, we show the better performance in out-of-sample forecasting of unilateral SAR (estimated with LS), compared to multilateral SAR (estimated with maximum likelihood, ML). This conclusion is supported by numerical simulations and applications to real geological data, both on regular lattices and irregularly distributed points.

On the (in)consistency of perturbation theory at finite temperature

A well-known difficulty of perturbative approaches to quantum field theory at finite temperature is the necessity to address theoretical constraints that are not present in the vacuum theory. In this work, we use lattice simulations of scalar correlation functions in massive ϕ4 theory to analyse the extent to which these constraints affect the perturbative predictions. We find that the standard perturbative predictions deteriorate even in the absence of infrared divergences at relatively low temperatures, and that this is directly connected to the analytic structure of the propagators used in the expansion. This suggests that the incorporation of non-perturbative thermal effects in the propagators is essential for a consistent perturbative formulation of scalar quantum field theories at finite temperature. By utilising the spectral constraints imposed on finite-temperature correlation functions, we explore how these effects manifest themselves in the lattice data, and discuss why the presence of distinct thermoparticle excitations provides a potential resolution to these issues.

Towards a Warm Holographic Equation of State by an Einstein–Maxwell-Dilaton Model

The holographic Einstein–Maxwell-dilaton model is employed to map state-of-the-art lattice QCD thermodynamics data from the temperature (T) axis towards the baryon–chemical potential (μB) axis and aims to gain a warm equation of state (EoS) of deconfined QCD matter which can be supplemented with a cool and confined part suitable for subsequent compact (neutron) star (merger) investigations. The model exhibits a critical end point (CEP) at TCEP=O(100) MeV and μBCEP=500…700 MeV with an emerging first-order phase transition (FOPT) curve which extends to large values of μB without approaching the μB axis. We consider the impact and peculiarities of the related phase structure on the EoS for the employed dilaton potential and dynamical coupling parameterizations. These seem to prevent the design of an overall trustable EoS without recourse to hybrid constructions.

Investigating two-dimensional adjoint QCD on the lattice

We present our investigations of SU(N) adjoint QCD in two dimensions with one Majorana fermion on the lattice. We determine the relevant parameter range for the simulations with Wilson fermions and present results for Polyakov loop, chiral condensate, and string tension. In the theory with massive fermions, all observables we checked show qualitative agreement between numerical lattice data and theory, while the massless limit is more subtle since chiral and non-invertible symmetry of the continuum theory are explicitly broken by lattice regularization. In thermal compactification, we observe N perturbative vacua for the holonomy potential at high-T with instanton events connecting them, and a unique vacuum at low-T. At finite-N, this is a cross-over and it turns to a phase transition at large-N thermodynamic limit. In circle compactification with periodic boundary conditions, we observe a unique center-symmetric minimum at any radius. In continuum, the instantons in the thermal case carry zero modes (for even N) and indeed, in the lattice simulations, we observe that chiral condensate is dominated by instanton centers, where zero modes are localized. We present lattice results on the issue of confinement vs. screening in the theory and comment on the roles of chiral symmetry and non-invertible symmetry.

A Bridge between Trace Anomalies and Deconfinement Phase Transitions

Inspired by the fact that both the dilaton potential encoding the trace anomalies of QCD and the Polyakov loop potential measuring the deconfinement phase transition can be expressed in the logarithmic forms, as well as the fact that the scale symmetry is expected to be restoring and colors are deconfined in extreme conditions such as high temperatures and/or densities, we conjecture a relation between the dilaton potential and the Polyakov loop potential. Explicitly, we start from the Coleman–Weinberg type potential of a real scalar field—a dilaton or conformal compensator—and make an ansatz of the relation between this scalar field and the Polyakov loop to obtain the Polyakov loop potential, which can be parameterized in Lattice QCD (LQCD) in the pure glue sector. We find that the coefficients of Polyakov potential fitted from Lattice data are automatically satisfied in this ansatz, the locations of deconfinement and scale restoration are locked to each other, and the first-order phase transition can be realized. Extensions to the low-energy effective quark models are also discussed. The conjectured relation may deepen our understanding of the evolution of the universe, the mechanism of electroweak symmetry breaking, the phase diagram of QCD matter, and the properties of neutron stars.

Pseudo-scalar meson spectral properties in the chiral crossover region of QCD

Determining the type of excitations that can exist in a thermal medium is key to understanding how hadronic matter behaves at extreme temperatures. In this work we study this question for pseudo-scalar mesons comprised of light-strange and strange-strange quarks, analysing how their low-energy spectral properties are modified as one passes through the high-temperature chiral crossover region between T = 145.6 MeV and 172.3 MeV. We utilise the non-perturbative constraints satisfied by correlation functions at finite temperature in order to extract the low-energy meson spectral function contributions from spatial correlator lattice data in Nf = 2 + 1 flavour QCD. The robustness of these contributions are tested by comparing their predictions with data for the corresponding temporal correlator at different momentum values. We find that around the pseudo-critical temperature Tpc the data in both the light-strange and strange-strange channels is consistent with the presence of a distinct stable particle-like ground state component, a so-called thermoparticle excitation. As the temperature increases this excitation undergoes collisional broadening, and this is qualitatively the same in both channels. These findings suggest that pseudo-scalar mesons in QCD have a bound-state-like structure at low energies within the chiral crossover region which is still strongly influenced by the vacuum states of the theory.

Revisiting O(N) σ model at unphysical pion masses and high temperatures

Roy-equation analysis on lattice data of ππ scattering phase shifts at mπ=391 MeV reveals that the lowest f0 meson becomes a bound state under this condition. In addition, there is a pair of complex poles below threshold generated by crossing symmetry [X.-H. Cao , ]. We use the N/D method to partially recover crossing symmetry of the O(N) σ model amplitude at leading order of 1/N expansion, and qualitatively reproduce the pole structure and pole trajectories with varying pion masses as revealed by Roy-equation analyses. The σ pole trajectory with varying temperature is also discussed and found to be similar to its properties when varying mπ. As the temperature increases, the complex σ poles firstly move from the second Riemann sheet to the real axis becoming two virtual state poles, and then one virtual state pole moves to the first sheet turning into a bound state pole and finally tends to the pion pole position at high temperature which is as expected from the chiral symmetry restoration. Our results provide further evidence that the lowest f0 state extracted from experiments and lattice data plays the role of the σ meson in the spontaneous breaking of chiral symmetry. Finally, we also briefly discuss the problems of the effective potential in the situation when mπ and the temperature become large. Published by the American Physical Society 2024

Unraveling generalized parton distributions through Lorentz symmetry and partial DGLAP knowledge

Relying on the polynomiality property of generalized parton distributions, which roots on Lorentz covariance, we prove that it is enough to know them at vanishing and low skewness within the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi region to obtain a unique extension to their entire support up to a D term. We put this idea in practice using two methods: reconstruction using artificial neural networks and finite-elements methods. We benchmark our results against standard models for generalized parton distributions. In agreement with the formal expectation, we obtain very a accurate reconstruction for a maximal value of the skewness as low as 20% of the longitudinal momentum fraction. This result might be relevant for reconstruction of generalized parton distribution from experimental and lattice QCD data, where computations are, for now, restricted in skewness. Published by the American Physical Society 2024

Four-gluon vertex from the Curci-Ferrari model at one-loop order

We compute the four-gluon vertex from the Curci-Ferrari model at one-loop order for a collinear configuration. Our results display a good agreement with the first lattice data for this vertex, released very recently []. A noteworthy novelty of our work is that we can provide analytical expressions for the four-gluon vertex in collinear configurations, together with a renormalization scheme that allows us to perform reliable perturbative computations even in the infrared regime. We observe an infrared suppression in the form factor associated with the tree-level four-gluon tensor with a possible zero crossing in the deep infrared which demands new lattice investigations to be confirmed. Moreover, we report an infrared divergence in the completely symmetric tensor form factor due to the ghost-loop contributions. These results come as predictions, since previous two-point correlations fix all the available parameters of the model, up to an overall constant factor. Published by the American Physical Society 2024

Solving the left-hand cut problem in lattice QCD: Tcc(3875)+ from finite volume energy levels

We discuss a novel effective-field-theory-based approach for extracting two-body scattering information from finite volume energies, serving as an alternative to Lüscher’s method. By explicitly incorporating one-pion exchange, we overcome the challenging left-hand cut problem in Lüscher’s method and can handle finite volume energy levels both below and above the left-hand cut. Applied to the lattice data for DD* scattering at a pion mass of 280 MeV, as an illustrative example, our results reveal the significant impact of the one-pion exchange on P-wave and S-wave phase shifts. The pole position of the Tcc(3875)+ state, extracted from the finite-volume energy levels at this pion mass while taking into account left-hand cut effects, range corrections and partial-wave mixing, is consistent with a near-threshold resonance. This study demonstrates, for the first time, that two-body scattering information can be reliably extracted from lattice spectra including the left-hand cut. Published by the American Physical Society 2024

Anisotropy and paramagnetism of QCD matter with an anomalous magnetic moment

We employ the Polyakov-loop enhanced Nambu–Jona-Lasinio model incorporating the quark anomalous magnetic moment to investigate the anisotropy structure and the renormalized magnetization of magnetized quark matter at finite temperature. The ultraviolet divergences and nonphysical oscillatory behavior are eliminated by the vacuum magnetic regularization scheme. With a parametrization of the anomalous magnetic moment that is proportional to the square of the chiral condensate, the renormalized magnetization is enlarged by the strong magnetic field so that the anisotropy becomes more apparent. The inflection point of the renormalized magnetization indicates the pseudocritical temperature for the chiral crossover. We find that the results with the anomalous magnetic moment are closer to the lattice quantum chromodynamics data. The connection between the paramagnetism and the chiral transition provides new insight into a magnetohydrodynamics description of hot and dense QCD matter produced in heavy-ion collisions.

Phase structure and critical phenomena in two-flavor QCD by holography

We explore the phase structure of quantum chromodynamics (QCD) with two dynamical quark flavors at finite temperature and baryon chemical potential, employing the nonperturbative gauge/gravity duality approach. Our gravitational model is tailored to align with state-of-the-art lattice data regarding the thermal properties of multiflavor QCD. Following a rigorous parameter calibration to match equations of state and the QCD trace anomaly at zero chemical potential derived from cutting-edge lattice QCD simulations, we investigate thermodynamic quantities and order parameters. We predict the location of the critical endpoint (CEP) at (μCEP,TCEP)=(219,182) MeV at which a line of first-order phase transitions terminate. We compute critical exponents associated with the CEP and find that they almost coincide with the critical exponents of the quantum 3D Ising model. Published by the American Physical Society 2024

Anomalous and linear holographic hard wall models for glueballs and the pomeron

In this work we propose improved holographic hard wall (HW) models by the inclusion of anomalous dimensions in the dual operators that describe glueballs inspired by the AdS/CFT correspondence. The anomalous dimensions come from well known semiclassical gauge/string duality analysis showing a dependence with the logarithm of spin S of the boundary states. We show that these logarithm anomalous dimensions of the high spin operators combined with the usual HW model allow us to match the pomeron trajectory and give glueball masses that are better than that of the original HW and soft wall models in comparison with lattice data. We also build up other anomalous HW models considering that the logarithm anomalous dimensions can be approximated by a truncated series of odd powers of the difference S−1/S. These models also fit the pomeron trajectory and produce good glueball masses. Then, we consider an anomalous dimension that is proportional to S, providing reasonable results. Finally, we propose an asymptotic linear anomalous HW model that effective dimensions for high spins operators are of the form Δ=aS+b, where a and b are constants to be fixed by comparison with the soft pomeron trajectory. In this last model, the Regge trajectory is asymptotically linear even for very high spins (J∼100) matching the soft pomeron trajectory accurately and generates glueball masses with deviations with respect to the lattice data better than the original HW and soft wall models. Published by the American Physical Society 2024

Evolution of parton distribution functions in the short-distance factorization scheme

Lattice QCD offers the possibility of computing parton distributions from first principles, although not in the usual MS¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{MS} $$\\end{document} factorization scheme. Calculations are therefore matched to MS¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{MS} $$\\end{document} using a perturbative procedure which is the source of significant uncertainty within the currently accessible kinematics. We present the possibility of computing the z2 evolution of non-singlet pseudo-parton distribution functions within the short factorization scheme in a numerically improvable way. The goal is to have tools to evolve a calculation to a scale where perturbative uncertainties are less pronounced. We compare a numerical extraction of the evolution operator from lattice data to the computation of z2 dependence in perturbation theory. Finally, we discuss how this numerical work may be extended to address the two-scale problem that arises when the Ioffe time range must be made large to extend the reach of the calculation of the pseudo-PDF to smaller values of the momentum fraction.