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This White Paper documents the discussion and consensus conclusions of the workshop "Software Infrastructure for Advanced Nuclear Physics Computing" (SANPC 24), which was held at Jefferson Lab on June 20-22, 2024. The workshop brought together members of the US Nuclear Physics community with data scientists and funding agency representatives to discuss the challenges and opportunities in advanced computing for Nuclear Physics in the coming decade. Opportunities for sustainable support and growth are identified within the context of existing and currently planned DOE and NSF programs., Comment: First draft. Open for NP community comment until Feb. 14, 2025. Please submit comments to the corresponding author (pmjacobs@lbl.gov)

Hot QCD physics studies the nuclear strong force under extreme temperature and densities. Experimentally these conditions are achieved via high-energy collisions of heavy ions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). In the past decade, a unique and substantial suite of data was collected at RHIC and the LHC, probing hydrodynamics at the nucleon scale, the temperature dependence of the transport properties of quark-gluon plasma, the phase diagram of nuclear matter, the interaction of quarks and gluons at different scales and much more. This document, as part of the 2023 nuclear science long range planning process, was written to review the progress in hot QCD since the 2015 Long Range Plan for Nuclear Science, as well as highlight the realization of previous recommendations, and present opportunities for the next decade, building on the accomplishments and investments made in theoretical developments and the construction of new detectors. Furthermore, this document provides additional context to support the recommendations voted on at the Joint Hot and Cold QCD Town Hall Meeting, which are reported in a separate document., Comment: 190 pages, 69 figures

This White Paper presents the community inputs and scientific conclusions from the Hot and Cold QCD Town Meeting that took place September 23-25, 2022 at MIT, as part of the Nuclear Science Advisory Committee (NSAC) 2023 Long Range Planning process. A total of 424 physicists registered for the meeting. The meeting highlighted progress in Quantum Chromodynamics (QCD) nuclear physics since the 2015 LRP (LRP15) and identified key questions and plausible paths to obtaining answers to those questions, defining priorities for our research over the coming decade. In defining the priority of outstanding physics opportunities for the future, both prospects for the short (~ 5 years) and longer term (5-10 years and beyond) are identified together with the facilities, personnel and other resources needed to maximize the discovery potential and maintain United States leadership in QCD physics worldwide. This White Paper is organized as follows: In the Executive Summary, we detail the Recommendations and Initiatives that were presented and discussed at the Town Meeting, and their supporting rationales. Section 2 highlights major progress and accomplishments of the past seven years. It is followed, in Section 3, by an overview of the physics opportunities for the immediate future, and in relation with the next QCD frontier: the EIC. Section 4 provides an overview of the physics motivations and goals associated with the EIC. Section 5 is devoted to the workforce development and support of diversity, equity and inclusion. This is followed by a dedicated section on computing in Section 6. Section 7 describes the national need for nuclear data science and the relevance to QCD research., Comment: QCD Town Meeting White Paper, as submitted to 2023 NSAC LRP committee on Feb. 28, 2023

We advocate for an active US participation in the international collaboration of the CBM experiment that will allow the US nuclear physics program to build on its successful exploration of the QCD phase diagram, use the expertise gained at RHIC to make complementary measurements at FAIR, and contribute to achieving the scientific goals of the beam energy scan (BES) program., Comment: 30 pages, 7 figures

The Beam Energy Scan Theory (BEST) collaboration's equation of state (EoS) incorporates a 3D Ising model critical point into the Quantum Chromodynamics (QCD) equation of state from lattice simulations. However, it contains 4 free parameters related to the size and location of the critical region in the QCD phase diagram. Certain combinations of the free parameters lead to acausal or unstable realizations of the EoS that should not be considered. In this work, we use an active learning framework to rule out pathological EoS efficiently. We find that checking stability and causality for a small portion of the parameters' range is sufficient to construct algorithms that perform with $>$96% accuracy across the entire parameter space. Though in this work we focus on a specific case, our approach can be generalized to any EoS containing a parameter space-class correspondence., Comment: 14 pages, 9 figures

We present a strangeness-neutral equation of state for QCD that exhibits critical behavior and matches lattice QCD results for the Taylor-expanded thermodynamic variables up to fourth-order in $\mu_B/T$. It is compatible with the SMASH hadronic transport approach and has a range of temperatures and baryonic chemical potentials relevant for phase II of the Beam Energy Scan at RHIC. We provide an updated version of the software BES-EoS, which produces an equation of state for QCD that includes a critical point in the 3D Ising model universality class. This new version also includes isentropic trejectories and the critical contribution to the correlation length. Since heavy-ion collisions have zero global net-strangeness density and a fixed ratio of electric charge to baryon number, the BES-EoS is more suitable to describe this system. Comparison with the previous version of the EoS is thoroughly discussed., Comment: 11 pages, 11 figures

Taylor expansion of the equation of state of QCD suffers from shortcomings at chemical potentials $\mu_B \geq (2-2.5)T$. First, one faces difficulties inherent in performing such an expansion with a limited number of coefficients; second, higher order coefficients determined from lattice calculations suffer from a poor signal-to-noise ratio. In this work, we present a novel scheme for extrapolating the equation of state of QCD to finite, real chemical potential that can extend its reach further than previous methods. We present continuum extrapolated lattice results for the new expansion coefficients and show the thermodynamic observables up to $\mu_B/T\le3.5$., Comment: 13 pages, 10 figures

In the context of the ongoing search for the QCD critical point at the Relativistic Heavy-Ion Collider, we study the equation of state near the critical point in the temperature and baryon chemical potential plane. We use the parametric representation introduced in earlier literature, which maps the universal 3D Ising equation of state onto the QCD phase diagram using several non-universal parameters. We focus on the quartic cumulant of the baryon number, or baryon number susceptibility~$\chi_4^B$, which can be accessed experimentally via net-proton fluctuation kurtosis measurements. It was originally predicted, through universality arguments based on the {\em leading} singular contribution, that $\chi_4^B$ and net-proton kurtosis should show a specific non-monotonic behavior due to the critical point. In particular, when following the freeze-out curve on the phase diagram by decreasing beam energy, the kurtosis is expected to dip, and then peak, when the beam energy scan passes close to the critical point. We study the effects of the non-universal and thus far unknown parameters of the Ising-to-QCD mapping on the behavior of~$\chi_4^B$. We find that, while the peak remains a solid feature, the presence of the critical point does not necessarily cause a dip in $\chi_4^B$ on the freezeout line {\em below} the transition temperature. The critical point contribution to the dip appears only for a narrow set of mapping parameters, when subleading singular terms are sufficiently suppressed., Comment: 10 pages, 4 figures

Detailed knowledge of the hadronic spectrum is still an open question, which has phenomenological consequences on the study of heavy-ion collisions. A previous lattice QCD study concluded that additional strange resonances are missing in the currently tabulated lists provided by the Particle Data Group (PDG). That study identified the list labeled PDG2016+ as the ideal spectrum to be used as an input in thermal-model-based analyses. In this work, we determine the effect of additional resonances on the freeze-out parameters of systems created in heavy-ion collisions. These parameters are obtained from thermal fits of particle yields and net-particle fluctuations. For a complete picture, we compare several hadron lists including both experimentally discovered and theoretically predicted states. We find that the inclusion of additional resonances mildly influences the extracted parameters -- with a general trend of progressively lowering the temperature -- but is not sufficient to close the gap in temperature between light and strange hadrons previously observed in the literature., Comment: 13 pages, 8 figures, v2: typos corrected, references updated

We construct an equation of state for Quantum Chromodynamics (QCD) at finite temperature and chemical potentials for baryon number $B$, electric charge $Q$ and strangeness $S$. We use the Taylor expansion method, up to the fourth power for the chemical potentials. This requires the knowledge of all diagonal and non-diagonal $BQS$ correlators up to fourth order: these results recently became available from lattice QCD simulations, albeit only at a finite lattice spacing $N_t=12$. We smoothly merge these results to the Hadron Resonance Gas (HRG) model, to be able to reach temperatures as low as 30 MeV; in the high temperature regime, we impose a smooth approach to the Stefan-Boltzmann limit. We provide a parameterization for each one of these $BQS$ correlators as functions of the temperature. We then calculate pressure, energy density, entropy density, baryonic, strangeness, electric charge densities and compare the two cases of strangeness neutrality and $\mu_S=\mu_Q=0$. We also calculate the isentropic trajectories and compare them in the two cases. Our equation of state can be readily used as an input of hydrodynamical simulations of matter created at the Relativistic Heavy Ion Collider (RHIC)., Comment: 14 pages, 6 figures; version published in Phys.Rev.C; clarified discussion of range of validity, added treatment of the speed of sound

We compare the mean-over-variance ratio of the net-kaon distribution calculated within a state-of-the-art hadron resonance gas model to the latest experimental data from the Beam Energy Scan at RHIC by the STAR collaboration. Our analysis indicates that it is not possible to reproduce the experimental results using the freeze-out parameters from the existing combined fit of net-proton and net-electric charge mean-over-variance. The strange mesons need about 10-15 MeV higher temperatures than the light hadrons at the highest collision energies. In view of the future $\Lambda$ fluctuation measurements, we predict the $\Lambda$ variance-over-mean and skewness-times-variance at the light and strange chemical freeze-out parameters. We observe that the $\Lambda$ fluctuations are sensitive to the difference in the freeze-out temperatures established in this analysis. Our results have implications for other phenomenological models in the field of relativistic heavy ion collisions., Comment: 5 pages, 3 figures

This Workshop brought top experts, researchers, postdocs, and students from high-energy heavy ion interactions, lattice QCD and hadronic physics communities together. YSTAR2016 discussed the impact of "missing" hyperon resonances on QCD thermodynamics, on freeze-out in heavy ion collisions, on the evolution of early universe, and on the spectroscopy of strange particles. Recent studies that compared lattice QCD predictions of thermodynamic properties of quark-gluon plasma at freeze-out with calculations based on statistical hadron resonance gas models as well as experimentally measured ratios between yields of different hadron species in heavy ion collisions provide indirect evidence for the presence of "missing" resonances in all of these contexts. The aim of the YSTAR2016 Workshop was to sharpen these comparisons and advance our understanding of the formation of strange hadrons from quarks and gluons microseconds after the Big Bang and in todays experiments at LHC and RHIC as well as at future facilities like FAIR, J-PARC and KL at JLab. It was concluded that the new initiative to create a secondary beam of neutral kaons at JLab will make a bridge between the hardron spectroscopy, heavy-ion experiments and lattice QCD studies addressing some major issues related to thermodynamics of the early universe and cosmology in general., Comment: 167 pages, Editors: M. Amaryan, E. Chudakov, K. Rajagopal, C. Ratti, J. Ritman, and I. Strakovsky One more contribution was added

We determine the equation of state of QCD at finite chemical potential, to order $(\mu_B/T)^6$, for a system of 2+1 quark flavors. The simulations are performed at the physical mass for the light and strange quarks on several lattice spacings; the results are continuum extrapolated using lattices of up to $N_t=16$ temporal resolution. The QCD pressure and interaction measure are calculated along the isentropic trajectories in the $(T,~\mu_B)$ plane corresponding to the RHIC Beam Energy Scan collision energies. Their behavior is determined through analytic continuation from imaginary chemical potentials of the baryonic density. We also determine the Taylor expansion coefficients around $\mu_B=0$ from the simulations at imaginary chemical potentials. Strangeness neutrality and charge conservation are imposed, to match the experimental conditions., Comment: 5 pages, 4 figures

The Future Circular Collider (FCC) Study is aimed at assessing the physics potential and the technical feasibility of a new collider with centre-of-mass energies, in the hadron-hadron collision mode, seven times larger than the nominal LHC energies. Operating such machine with heavy ions is an option that is being considered in the accelerator design studies. It would provide, for example, Pb-Pb and p-Pb collisions at sqrt{s_NN} = 39 and 63 TeV, respectively, per nucleon-nucleon collision, with integrated luminosities above 30 nb^-1 per month for Pb-Pb. This is a report by the working group on heavy-ion physics of the FCC Study. First ideas on the physics opportunities with heavy ions at the FCC are presented, covering the physics of the Quark-Gluon Plasma, of gluon saturation, of photon-induced collisions, as well as connections with other fields of high-energy physics., Comment: 57 pages, 28 figures. This document will be part of a CERN Yellow Report on Physics at FCC-hh

This document was prepared by the community that is active in Italy, within INFN (Istituto Nazionale di Fisica Nucleare), in the field of ultra-relativistic heavy-ion collisions. The experimental study of the phase diagram of strongly-interacting matter and of the Quark-Gluon Plasma (QGP) deconfined state will proceed, in the next 10-15 years, along two directions: the high-energy regime at RHIC and at the LHC, and the low-energy regime at FAIR, NICA, SPS and RHIC. The Italian community is strongly involved in the present and future programme of the ALICE experiment, the upgrade of which will open, in the 2020s, a new phase of high-precision characterisation of the QGP properties at the LHC. As a complement of this main activity, there is a growing interest in a possible future experiment at the SPS, which would target the search for the onset of deconfinement using dimuon measurements. On a longer timescale, the community looks with interest at the ongoing studies and discussions on a possible fixed-target programme using the LHC ion beams and on the Future Circular Collider., Comment: 99 pages, 56 figures

We calculate the QCD cross-over temperature, the equation of state and fluctuations of conserved charges at finite density by analytical continuation from imaginary to real chemical potentials. Our calculations are based on new continuum extrapolated lattice simulations using the 4stout staggered actions with a lattice resolution up to $N_t=16$. The simulation parameters are tuned such that the strangeness neutrality is maintained, as it is in heavy ion collisions., Comment: 4 pages, 2 figures, Proceedings of the Quark Matter 2015 conference, Kobe, Japan

We present the crossover line between the quark gluon plasma and the hadron gas phases for small real chemical potentials. First we determine the effect of imaginary values of the chemical potential on the transition temperature using lattice QCD simulations. Then we use various formulas to perform an analytic continuation to real values of the baryo-chemical potential. Our data set maintains strangeness neutrality to match the conditions of heavy ion physics. The systematic errors are under control up to $\mu_B\approx 300$ MeV. For the curvature of the transition line we find that there is an approximate agreement between values from three different observables: the chiral susceptibility, chiral condensate and strange quark susceptibility. The continuum extrapolation is based on $N_t=$ 10, 12 and 16 lattices. By combining the analysis for these three observables we find, for the curvature, the value $\kappa = 0.0149 \pm 0.0021$., Comment: 14 pages, 4 figures, revised version

We calculate second- and fourth-order cumulants of conserved charges in a temperature range stretching from the QCD transition region towards the realm of (resummed) perturbation theory. We perform lattice simulations with staggered quarks; the continuum extrapolation is based on $N_t=10\dots24$ in the crossover-region and $N_t=8\dots16$ at higher temperatures. We find that the Hadron Resonance Gas model predictions describe the lattice data rather well in the confined phase. At high temperatures (above $\sim$250 MeV) we find agreement with the three-loop Hard Thermal Loop results., Comment: 18 pages revtex, 13 figures

We discuss details of our thermal model applied to extract chemical freeze-out conditions from fluctuations in the net-electric charge and net-proton number measured at RHIC. A parametrization for these conditions as a function of the beam energy is given., Comment: Dec 18, 2014. 4 pp

This chapter examines the possibility to analyze and compare human activities in an urban environment based on the detection of mobile phone usage patterns. Thanks to an unprecedented collection of counter data recording the number of calls, SMS, and data transfers resolved both in time and space, we confirm the connection between temporal activity profile and land usage in three global cities: New York, London and Hong Kong. By comparing whole cities typical patterns, we provide insights on how cultural, technological and economical factors shape human dynamics. At a more local scale, we use clustering analysis to identify locations with similar patterns within a city. Our research reveals a universal structure of cities, with core financial centers all sharing similar activity patterns and commercial or residential areas with more city-specific patterns. These findings hint that as the economy becomes more global, common patterns emerge in business areas of different cities across the globe, while the impact of local conditions still remains recognizable on the level of routine people activity., Comment: 24 pages, 9 figures, book chapter to be published in "Computational Approaches for Urban Environments" (Springer Ed.), October 2014

Recent results for moments of multiplicity distributions of net-protons and net-electric charge from the STAR collaboration are compared to lattice QCD results for higher order fluctuations of baryon number and electric charge by the Wuppertal-Budapest collaboration, with the purpose of extracting the freeze-out temperature and chemical potential. All lattice simulations are performed for a system of 2+1 dynamical quark flavors, at the physical mass for light and strange quarks; all results are continuum extrapolated. We show that it is possible to extract an upper value for the freeze-out temperature, as well as precise baryo-chemical potential values corresponding to the four highest collision energies of the experimental beam energy scan. Consistency between the freeze-out parameters obtained from baryon number and electric charge fluctuations is found. The freeze-out chemical potentials are now in agreement with the statistical hadronization model., Comment: 5 pages, 4 figures, references added, discussion added to the introduction, results unchanged

We present continuum extrapolated lattice results for the higher order fluctuations of conserved charges in high temperature Quantum Chromodynamics. Through the matching of the grand canonical ensemble on the lattice to the net charge and net baryon distribution realized in heavy ion experiments the temperature and the chemical potential may be estimated at the time of chemical freeze-out, Comment: 7 pages, 5 figures, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, Germany

We extend a previous work on the study of heavy charmonia and bottomonia in a deconfined quark-gluon plasma by considering the Bc family of mesons. With the introduction of this bound state of a charm and a beauty quark, we investigate at finite temperature the behavior of the quarkonium, in an energy region between the {\psi} and the {\Upsilon} states., Comment: 6 pages, 8 figures

We present realistic equations of state for QCD matter at vanishing net-baryon density which embed recent lattice QCD results at high temperatures combined with a hadron resonance gas model in the low-temperature, confined phase. In the latter, we allow an implementation of partial chemical equilibrium, in which particle ratios are fixed at the chemical freeze-out, so that a description closer to the experimental situation is possible. Given the present uncertainty in the determination of the chemical freeze-out temperature from first-principle lattice QCD calculations, we consider different values within the expected range. The corresponding equations of state can be applied in the hydrodynamic modeling of relativistic heavy-ion collisions at the LHC and at the highest RHIC beam energies. Suitable parametrizations of our results as functions of the energy density are also provided., Comment: Updated journal version with refined EoS-parametrization. July 2014. 8 pp. 4 figs. 3 parametrization-tables and weblink Ref. [45]

We present our results for ratios of higher order fluctuations of electric charge as functions of the temperature. These results are obtained in a system of 2+1 quark flavors at physical quark masses and continuum extrapolated. We compare them to preliminary data on higher order moments of the net electric charge distribution from the STAR collaboration. This allows us to determine the freeze-out temperature and chemical potential from first principles. We also show continuum-extrapolated results for ratios of higher order fluctuations of baryon number. These will allow to test the consistency of the approach, by comparing them to the corresponding experimental data (once they become available) and thus extracting the freeze-out parameters in an independent way., Comment: 5 pages, 7 figures, revtex

We determine the equation of state of QCD for nonzero chemical potentials via a Taylor expansion of the pressure. The results are obtained for N_f=2+1 flavors of quarks with physical masses, on various lattice spacings. We present results for the pressure, interaction measure, energy density, entropy density, and the speed of sound for small chemical potentials. At low temperatures we compare our results with the Hadron Resonance Gas model. We also express our observables along trajectories of constant entropy over particle number. A simple parameterization is given (the Matlab/Octave script parameterization.m, submitted to the arXiv along with the paper), which can be used to reconstruct the observables as functions of T and mu, or as functions of T and S/N., Comment: 14 pages, 15 figures, version accepted for publication in JHEP

We study the interpretation of Lattice data about the thermodynamics of the deconfinement phase of SU(3) Yang-Mills theory, in terms of gluon quasiparticles propagating in a background of a Polyakov loop. A potential for the Polyakov loop, inspired by the strong coupling expansion of the QCD action, is introduced; the Polyakov loop is coupled to tranverse gluon quasiparticles by means of a gas-like effective potential. This study is useful to identify the effective degrees of freedom propagating in the gluon medium above the critical temperature. A main general finding is that a dominant part of the phase transition dynamics is accounted for by the Polyakov loop dynamics, hence the thermodynamics can be described without the need for diverging or exponentially increasing quasiparticle masses as $T \rightarrow T_c$, at variance respect to standard quasiparticle models., Comment: 8 pages, 9 figures

We analyze the anonymous communication patterns of 2.5 million customers of a Belgian mobile phone operator. Grouping customers by billing address, we build a social network of cities, that consists of communications between 571 cities in Belgium. We show that inter-city communication intensity is characterized by a gravity model: the communication intensity between two cities is proportional to the product of their sizes divided by the square of their distance.

We formulate the Polyakov-Nambu-Jona-Lasinio (PNJL) model in 0+1 dimensions. The thermodynamics captured by the partition function yields a bulk pressure, as well as quark susceptibilities versus temperature that are similar to the ones in 3+1 dimensions. Around the transition temperature the behavior in the pressure and quark susceptibilities follows from the interplay between the lowest Matsubara frequency and the Polyakov line. The reduction to the lowest Matsubara frequency yields a matrix Model. In the presence of the Polyakov line the UV part of the Dirac spectrum features oscillations when close to the transition temperature., Comment: 18 pages, 13 figures

We investigate the behavior of a pair of heavy fermions, denoted by $Q$ and $\bar{Q}$, in a hot/dense medium. Although we have in mind the situation where $Q$ and $\bar{Q}$ denote heavy quarks, our treatment will be limited to simplified models, which bear only some general similarities with QCD. We study in particular the limiting case where the mass of the heavy fermions is infinite. Then a number of results can be derived exactly: a Schr\"odinger equation can be established for the correlator of the heavy quarks; the interaction effects exponentiate, leading to a simple instantaneous effective potential for this Schr\"odinger equation. We consider simple models for the medium in which the $Q\bar Q$ pair propagates. In the case where the medium is a plasma of photons and light charged fermions, an imaginary part develops in this effective potential. We discuss the physical interpretation of this imaginary part in terms of the collisions between the heavy particles and the light fermions of the medium; the same collisions also determine the damping rate of the heavy fermions. Finally we study the connection between the real-time propagator of the heavy fermion pair and its Euclidean counterpart, and show that the real part of the potential entering the Schr\"odinger equation for the real-time propagator is the free energy calculated in the imaginary-time formalism., Comment: 32 pages, 8 figures

QCD thermodynamics is investigated by means of the Polyakov-loop-extended Nambu Jona-Lasinio (PNJL) model, in which quarks couple simultaneously to the chiral condensate and to a background temporal gauge field representing Polyakov loop dynamics. The behaviour of the Polyakov loop as a function of temperature is obtained by minimizing the thermodynamic potential of the system. A Taylor series expansion of the pressure is performed. Pressure difference and quark number density are then evaluated up to sixth order in quark chemical potential, and compared to the corresponding lattice data. The validity of the Taylor expansion is discussed within our model, through a comparison between the full results and the truncated ones., Comment: 6 pages, 5 figures, Talk given at the Workshop for Young Scientists on the Physics of Ultrarelativistic Nucleus-Nucleus Collisions (Hot Quarks 2006), Villasimius, Italy, 15-20 May 2006

We investigate the properties of scalar and pseudo-scalar mesons at finite temperature and quark chemical potential in the framework of the Nambu-Jona-Lasinio (NJL) model coupled to the Polyakov loop (PNJL model) with the aim of taking into account features of both chiral symmetry breaking and deconfinement. The mesonic correlators are obtained by solving the Schwinger-Dyson equation in the RPA approximation with the Hartree (mean field) quark propagator at finite temperature and density. In the phase of broken chiral symmetry a narrower width for the sigma meson is obtained with respect to the NJL case; on the other hand, the pion still behaves as a Goldstone boson. When chiral symmetry is restored, the pion and sigma spectral functions tend to merge. The Mott temperature for the pion is also computed., Comment: 24 pages, 9 figures, version to appear in Phys. Rev. D

We investigate three-colour QCD thermodynamics at finite quark chemical potential. Lattice QCD results are compared with a generalized Nambu Jona-Lasinio model in which quarks couple simultaneously to the chiral condensate and to a background temporal gauge field representing Polyakov loop dynamics. This so-called PNJL model thus includes features of both deconfinement and chiral symmetry restoration. The parameters of the Polyakov loop effective potential are fixed in the pure gauge sector. The chiral condensate and the Polyakov loop as functions of temperature and quark chemical potential are calculated by minimizing the thermodynamic potential of the system. The resulting equation of state, (scaled) pressure difference and quark number density at finite quark chemical potential are then confronted with corresponding Lattice QCD data., Comment: 20 pages, 10 figures, version to appear in Phys. Rev. D