Model For Heavy-ion Collisions Research Articles

Covariant formulation of spinodal decomposition in rapidly expanding quark gluon plasma

Quantum chromodynamics (QCD) is expected to have a first order phase transition between the confined hadron gas and the deconfined quark gluon plasma at high baryon densities. This will result in phase boundary effects in the metastable and unstable regions. It is important to include these effects in phenomenological models of heavy ion collisions to identify experimental signatures of a phase transition. This requires building intuition on phase separation in rapidly expanding fluids. In this work we present the covariant equations of relativistic hydrodynamics with a phase boundary, provide prescriptions to extend the equation of state to metastable and unstable regions, and show the effects of spinodal separation in a Bjorken flow. Published by the American Physical Society 2024

Evidence for universal flow and characteristics of early time thermalization in a scalar field model for heavy ion collisions

We study numerically the evolution of an expanding strongly self-coupled real scalar field. We use a conformally invariant action that gives a traceless energy-momentum tensor and is better suited to model the early time behavior of a system such as QCD, whose action is also conformally invariant. We consider asymmetric initial conditions and observe that when the system is initialized with nonzero spatial eccentricity, the eccentricity decreases and the elliptic flow coefficient increases. This behavior is characteristic of a hydrodynamic system in which pressure gradients are converted into fluid velocities, and therefore spatial anisotropy decreases while momentum anisotropy is generated. We look at a measure of transverse pressure asymmetry that has been shown to behave similarly to the elliptic flow coefficient in hydrodynamic systems and show that in our system their behavior is strikingly similar. We show that the derivative of the transverse velocity is proportional to the gradient of the energy in Milne coordinates and argue that this result means that transverse velocity initially develops in the same way that it does in hydrodynamic systems. We conclude that some aspects of the early onset of hydrodynamic behavior that has been observed in quark-gluon plasmas are seen in our numerical simulation of strongly coupled scalar fields. Published by the American Physical Society 2024

Two-Pion Bose–Einstein Correlations in Au+Au Collisions at sNN = 3 GeV in the STAR Experiment

The correlation femtoscopy technique makes it possible to estimate the geometric dimensions and lifetime of the particle emission region after the collision of ions. Measurements of the emission region characteristics not only at midrapidity but also at backward (forward) rapidity can provide new information about the source and make it possible to impose constraints on the heavy-ion collision models. This work is devoted to revealing the dependence of the spatial and temporal parameters of the emission region of identical pions in Au+Au collisions at sNN = 3 GeV from the fixed-target program of the STAR experiment. The extracted femtoscopic radii, Rout, Rside, Rlong, Rout−long2, and the correlation strength, λ, are presented as a function of collision centrality, pair rapidity, and transverse momentum. Physics implications will be discussed.

The dynamic hadronization of charm quarks in heavy-ion collisions

The Pythia8/Angantyr model for heavy ion collisions was recently updated with a mechanism for global colour reconnection. The colour reconnection model used is QCD colour algebra inspired and enhances baryon production due to the formation of string junctions. In this paper, we present updates to the junction formation and string fragmentation mechanisms, connected to heavy quark fragmentation. This allows for the simulation of heavy quark fragmentation, using junction formation, in heavy ion collisions. The framework is validated for proton collisions, and we show results for charm baryon production in proton-lead collisions.

First study of the initial gluonic fluctuations using UPCs with ALICE

Incoherent and dissociative J/ψ photoproduction is sensitive to fluctuations of the gluonic structure of the target. Thus, the measurement of Jψ photoproduction of the colliding hadron sheds light on the initial state of QCD and provides important constraints on the initial conditions used in hydrodynamical models of heavy-ion collisions. The first measurement of the transverse momentum dependence of both coherent and incoherent Jψ photoproduction in ultraperipheral Pb–Pb collisions at midrapidity is presented. These new results provide, a clear indication of subnucleonic fluctuations of the lead target. We also present the new measurement of dissociative Jψ photoproduction cross section as a function of energy, in p–Pb collisions at forward rapidity. Dissociative results do not show any indication of saturation and agree with previous data.

Determination of the Neutron Skin of ^{208}Pb from Ultrarelativistic Nuclear Collisions.

Emergent bulk properties of matter governed by the strong nuclear force give rise to physical phenomena across vastly different scales, ranging from the shape of atomic nuclei to the masses and radii of neutron stars. They can be accessed on Earth by measuring the spatial extent of the outer skin made of neutrons that characterizes the surface of heavy nuclei. The isotope ^{208}Pb, owing to its simple structure and neutron excess, has been in this context the target of many dedicated efforts. Here, we determine the neutron skin from measurements of particle distributions and their collective flow in ^{208}Pb+^{208}Pb collisions at ultrarelativistic energy performed at the Large Hadron Collider, which are mediated by interactions of gluons and thus sensitive to the overall size of the colliding ^{208}Pb ions. By means of state-of-the-art global analysis tools within the hydrodynamic model of heavy-ion collisions, we infer a neutron skin Δr_{np}=0.217±0.058 fm, consistent with nuclear theory predictions, and competitive in accuracy with a recent determination from parity-violating asymmetries in polarized electron scattering. We establish thus a new experimental method to systematically measure neutron distributions in the ground state of atomic nuclei.

Hydrodynamic model of heavy-ion collisions with low momentum components

Relativistic heavy-ion collisions suggest that low-momentum regions of the observed particle spectra are thermal and hydrodynamic, while medium-high momentum regions are non-thermal and perturbative. In this study, I construct a hydrodynamic model of heavy-ion collisions by cutting off the medium-high momentum contributions and investigate the phenomenological consequences. Numerical simulations indicate that the temperature of the quark matter can be higher at earlier times owing to the modification of the equation of state. It is also suggested that direct photon elliptic flow can be sensitive to the momentum dependence of thermalization.

A spatially constrained QCD colour reconnection in textrm{pp}, textrm{p}A, and AA collisions in the Pythia8/Angantyr model

We present an updated version of the QCD-based colour reconnection model in Pythia8, where we constrain the range in impact parameter for which reconnections are allowed. In this way, we can introduce more realistic colour reconnections in the Angantyr model for heavy ion collisions, where previously only reconnections within separate nucleon sub-collisions have been allowed. We investigate how the new impact parameter constraint influences final states in textrm{pp} collisions, and retune parameters of the multi-parton interaction parameters in Pythia to compensate so that minimum bias data are reproduced. We also study multiplicity distributions in textrm{p}A collisions and find that, in order to counteract the loss in multiplicity due to the introduction of global colour reconnections, we need to modify some parameters in the Angantyr model while keeping the parameters tuned to textrm{pp} fixed. With Angantyr we can then extrapolate to AA collisions without further parameter tuning and retaining a reasonable description of the basic multiplicity distributions.

Evidence of Hexadecapole Deformation in Uranium-238 at the Relativistic Heavy Ion Collider.

State-of-the-art hydrodynamic simulations of the quark-gluon plasma are unable to reproduce the elliptic flow of particles observed at the BNL Relativistic Heavy Ion Collider (RHIC) in relativistic ^{238}U+^{238}U collisions when they rely on information obtained from low-energy experiments for the implementation of deformation in the colliding ^{238}U ions. We show that this is due to an inappropriate treatment of well-deformed nuclei in the modeling of the initial conditions of the quark-gluon plasma. Past studies have identified the deformation of the nuclear surface with that of the nuclear volume, though these are different concepts. In particular, a volume quadrupole moment can be generated by both a surface hexadecapole and a surface quadrupole moment. This feature was so far neglected in the modeling of heavy-ion collisions, and is particularly relevant for nuclei like ^{238}U, which is both quadrupole deformed and hexadecapole deformed. With rigorous input from Skyrme density functional calculations, we show that correcting for such effects in the implementation of nuclear deformations in hydrodynamic simulations restores agreement with BNL RHIC data. This brings consistency to the results of nuclear experiments across energy scales, and demonstrates the impact of the hexadecapole deformation of ^{238}U on high-energy collisions.

Computational budget optimization for Bayesian parameter estimation in heavy-ion collisions

Bayesian parameter estimation provides a systematic approach to compare heavy-ion collision models with measurements, leading to constraints on the properties of nuclear matter with proper accounting of experimental and theoretical uncertainties. Aside from statistical and systematic model uncertainties, interpolation uncertainties can also play a role in Bayesian inference, if the model’s predictions can only be calculated at a limited set of model parameters. This uncertainty originates from using an emulator to interpolate the model’s prediction across a continuous space of parameters. In this work, we study the trade-offs between the emulator (interpolation) and statistical uncertainties. We perform the analysis using spatial eccentricities from the TRENTo model of initial conditions for nuclear collisions. Given a fixed computational budget, we study the optimal compromise between the number of parameter samples and the number of collisions simulated per parameter sample. For the observables and parameters used in the present study, we find that the best constraints are achieved when the number of parameter samples is slightly smaller than the number of collisions simulated per parameter sample.

Assessing the ultracentral flow puzzle in hydrodynamic modeling of heavy-ion collisions

An outstanding problem in heavy-ion collisions is the inability for models to accurately describe ultra-central experimental flow data, despite that being precisely the regime where a hydrodynamic description should be most applicable. We reassess the status of this puzzle by computing the flow in ultra-central collisions obtained from multiple recent Bayesian models that were tuned to various observables in different collision systems at typical centralities. While central data can now be described with better accuracy than in previous calculations, tension with experimental observation remains and worsens as one goes to ultra-central collisions. Tuning the model parameters cannot remove this tension without destroying the fit at other centralities. As such, new elements are likely needed in the standard modeling of heavy-ion collisions.

In-medium nucleon-nucleon cross section in nuclear matter

In-medium nucleon-nucleon ($NN$) cross sections at various densities and isospin asymmetries are investigated systematically in the framework of the Brueckner-Hartree-Fock approach. The calculations are base on the exact treatment of the center-of-mass momentum instead of the total momentum approximation employed in previous works. The neutron-proton in-medium cross section is shown to exhibit nearly isospin asymmetry independence. For convenience in application, analytical formulas embodying the medium correction to free $NN$ cross section with parameters calibrated to the calculated results have been provided. Using these formulas, the transverse and elliptic flows of emitted nucleons in heavy-ion collisions are studied within the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model. We find the medium effect of the cross section from the $G$ matrix contributes to the transverse and elliptic flows oppositely to and obviously smaller than that from the effective mass. In addition, the present microscopic in-medium cross sections can significantly revise the predictions of the transverse and elliptic flows compared to the in-medium cross sections previously adopted in transport models for heavy-ion collisions.

Extending a scaling equation of state to QCD

Whether Quantum Chromodynamics (QCD) exhibits a phase transition at finite temperature and density is an open question. It is important for hydrodynamic modeling of heavy ion collisions and neutron star mergers. Lattice QCD simulations have definitively shown that the transition from hadrons to quarks and gluons is a crossover when the baryon chemical potential is zero or small. We combine the parametric scaling equation of state, usually associated with the 3D Ising model, with a background equation of state based on a smooth crossover from hadrons to quarks and gluons. Comparison to experimental data from the Beam Energy Scan II at the Relativistic Heavy Ion Collider or in heavy ion experiments at other accelerators may allow the critical exponents and amplitudes in the scaling equation of state to be determined for QCD if a critical point exists.

Embedding a critical point in a hadron to quark-gluon crossover equation of state

Lattice QCD simulations have shown unequivocally that the transition from hadrons to quarks and gluons is a crossover when the baryon chemical potential is zero or small. Many model calculations predict the existence of a critical point at a value of the chemical potential where current lattice simulations are unreliable. We show how to embed a critical point in a smooth background equation of state so as to yield the critical exponents and critical amplitude ratios expected of a transition in the same universality class as the liquid-gas phase transition and the three-dimensional Ising model. There are only two independent critical exponents; the relations $\ensuremath{\alpha}+2\ensuremath{\beta}+\ensuremath{\gamma}=2$ and $\ensuremath{\beta}(\ensuremath{\delta}\ensuremath{-}1)=\ensuremath{\gamma}$ arise automatically, as does a relation between the two critical amplitudes. The resulting equation of state has parameters that may be inferred by hydrodynamic modeling of heavy-ion collisions in the Beam Energy Scan II at the BNL Relativistic Heavy Ion Collider or in experiments at other accelerators.

Machine-learning model-driven prediction of the initial geometry in heavy-ion collision experiments

We demonstrate high prediction accuracy of three important properties that determine the initial geometry of the heavy-ion collision (HIC) experiments by using supervised Machine Learning (ML) methods. These properties are the impact parameter, the eccentricity and the participant eccentricity. Though ML techniques have been used previously to determine the impact parameter of these collisions, we study multiple ML algorithms, their error spectrum, and sampling methods using exhaustive parameter scans and ablation studies to determine a combination of efficient algorithm and tuned training set that gives multi-fold improvement in accuracy for all three different heavy-ion collision models. The three models chosen are a transport model, a hydrodynamic model and a hybrid model. The motivation of using three different heavy-ion collision models was to show that even if the model is trained using a transport model, it gives accurate results for a hydrodynamic model as well as a hybrid model. We show that the accuracy of the impact parameter prediction depends on the centrality of the collision. With the standard application of ML training methods, prediction accuracy is considerable low for central collisions. Our method increases this accuracy by multiple folds. We also show that the eccentricity prediction accuracy can be improved by inclusion of the impact parameter as a feature in all these algorithms. We discuss how the errors can be minimized and the accuracy can be improved to a great extent in all the ranges of impact parameter and eccentricity predictions.

Prehydrodynamic evolution and its impact on quark-gluon plasma signatures

State-of-the-art hydrodynamic models of heavy-ion collisions have considerable theoretical model uncertainties in the description of the very early pre-hydrodynamic stage. We add a new computational module, K$_\mathrm{T}$Iso, that describes the pre-hydrodynamic evolution kinetically, based on the relativistic Boltzmann equation with collisions treated in the Isotropization Time Approximation. As a novelty, K$_\mathrm{T}$Iso allows for the inclusion and evolution of initial-state momentum anisotropies. To maintain computational efficiency K$_\mathrm{T}$Iso assumes strict longitudinal boost invariance and allows collisions to isotropize only the transverse momenta. We use it to explore the sensitivity of hadronic observables measured in relativistic heavy-ion collisions to initial-state momentum anisotropies and microscopic scattering during the pre-hydrodynamic stage.

A large-N expansion for minimum bias

Despite being the overwhelming majority of events produced in hadron or heavy ion collisions, minimum bias events do not enjoy a robust first-principles theoretical description as their dynamics are dominated by low-energy quantum chromodynamics. In this paper, we present a novel expansion scheme of the cross section for minimum bias events that exploits an ergodic hypothesis for particles in the events and events in an ensemble of data. We identify power counting rules and symmetries of minimum bias from which the form of the squared matrix element can be expanded in symmetric polynomials of the phase space coordinates. This expansion is entirely defined in terms of observable quantities, in contrast to models of heavy ion collisions that rely on unmeasurable quantities like the number of nucleons participating in the collision, or tunes of parton shower parameters to describe the underlying event in proton collisions. The expansion parameter that we identify from our power counting is the number of detected particles N and as N → ∞ the variance of the squared matrix element about its mean, constant value on phase space vanishes. With this expansion, we show that the transverse momentum distribution of particles takes a universal form that only depends on a single parameter, has a fractional dispersion relation, and agrees with data in its realm of validity. We show that the constraint of positivity of the squared matrix element requires that all azimuthal correlations vanish in the N → ∞ limit at fixed center-of-mass energy, as observed in data. The approach we follow allows for a unified treatment of small and large system collective behavior, being equally applicable to describe, e.g., elliptic flow in PbPb collisions and the “ridge” in pp collisions. We also briefly comment on power counting and symmetries for minimum bias events in other collider environments and show that a possible ridge in e+e− collisions is highly suppressed as a consequence of its symmetries.

Hadronic rescattering in pA and AA collisions

In a recent article we presented a model for hadronic rescattering, and some results were shown for mathrm {p}mathrm {p} collisions at LHC energies. In order to extend the studies to mathrm {p}mathrm {A} and mathrm {A}mathrm {A} collisions, the Angantyr model for heavy-ion collisions is taken as the starting point. Both these models are implemented within the general-purpose Monte Carlo event generator Pythia, which makes the matching reasonably straightforward, and allows for detailed studies of the full space–time evolution. The rescattering rate is significantly higher than in mathrm {p}mathrm {p}, especially for central mathrm {A}mathrm {A} collisions, where the typical primary hadron rescatters several times. We study the impact of rescattering on a number of distributions, such as p_{perp } and eta spectra, and the space–time evolution of the whole collision process. Notably rescattering is shown to give a significant contribution to elliptic flow in mathrm {XeXe} and mathrm {PbPb}, and to give a nontrivial impact on charm production.

Bayesian analysis of heavy ion collisions with the heavy ion computational framework Trajectum

We introduce a model for heavy ion collisions named Trajectum, which includes an expanded initial stage with a variable free streaming velocity $v_{\rm fs}$ and a hydrodynamic stage with three varying second order transport coefficients. We describe how to obtain a Gaussian Emulator for this 20-parameter model and show results for key observables. This emulator can be used to obtain Bayesian posterior estimates on the parameters, which we test by an elaborate closure test as well as a convergence study. Lastly, we employ the optimal values of the parameters found in [1] to perform a detailed comparison to experimental data from PbPb and $p$Pb collisions. This includes both observables that have been used to obtain these values as well as wider transverse momentum ranges and new observables such as correlations of event-plane angles.

Multisystem Bayesian constraints on the transport coefficients of QCD matter

We study the properties of the strongly-coupled quark-gluon plasma with a multistage model of heavy ion collisions that combines the T$_\mathrm{R}$ENTo initial condition ansatz, free-streaming, viscous relativistic hydrodynamics, and a relativistic hadronic transport. A model-to-data comparison with Bayesian inference is performed, revisiting assumptions made in previous studies. The role of parameter priors is studied in light of their importance towards the interpretation of results. We emphasize the use of closure tests to perform extensive validation of the analysis workflow before comparison with observations. Our study combines measurements from the Large Hadron Collider and the Relativistic Heavy Ion Collider, achieving a good simultaneous description of a wide range of hadronic observables from both colliders. The selected experimental data provide reasonable constraints on the shear and the bulk viscosities of the quark-gluon plasma at $T\sim$ 150-250 MeV, but their constraining power degrades at higher temperatures $T \gtrsim 250$ MeV. Furthermore, these viscosity constraints are found to depend significantly on how viscous corrections are handled in the transition from hydrodynamics to the hadronic transport. Several other model parameters, including the free-streaming time, show similar model sensitivity while the initial condition parameters associated with the T$_\mathrm{R}$ENTo ansatz are quite robust against variations of the particlization prescription. We also report on the sensitivity of individual observables to the various model parameters. Finally, Bayesian model selection is used to quantitatively compare the agreement with measurements for different sets of model assumptions, including different particlization models and different choices for which parameters are allowed to vary between RHIC and LHC energies.