Search

We aim to constrain the equation of state of nuclear matter by comparing calculations with the SMASH transport model to directed and elliptic flow measurements for protons and deuterons performed by the HADES collaboration in a systematic way. A momentum-dependent term is included in the potential for which we show that it is needed to describe flow data. We further incorporate a simple symmetry potential in the transport model and present constraints on the stiffness of the equation of state of nuclear matter at saturation density and on the symmetry potential. The constraints are obtained by performing a Bayesian analysis such that we can also provide an uncertainty for the estimated parameters. The posterior distribution is obtained by Markov chain Monte Carlo sampling for which we emulate the transport model with a Gaussian process to lower computational costs. We find that a relatively stiff equation of state is favoured in our analysis with a small uncertainty whereas the constraints obtained for the symmetry potential are rather loose., Comment: 11 pages, 11 figures

The production of light nuclei in heavy -ion collisions is an excellent probe for studying the phase diagram of quantum chromodynamics and for the search of a critical end point. In this work we apply a hybrid approach in which we study the light nuclei production in the afterburner stage of central Au+Au collisions at $\sqrt{s}_{NN}=7.7$, 14.5 and 19.6 GeV. In this stage, light nuclei are produced dynamically in $4\leftrightarrow 2$ catalysis reactions. A comparison of the dynamic production and a coalescence approach is presented for transverse momentum spectra of deuterons, tritons, $^3\rm He$ nuclei and hypertritons and ratios of light nuclei yields. A good agreement with the experimentally measured yield of nuclei is found and we proceed to further investigate the production mechanisms of light nuclei by calculating the rates of the important channels for the formation and disintegration. We find that the afterburner stage is essential for the description of light nuclei formation in heavy-ion collisions, as light nuclei undergo a large number of interactions., Comment: 15 pages, 25 figures

We present calculations of dielectron anisotropic flow in heavy-ion collisions at HADES beam energies from a hadronic transport approach. The ongoing experimental analysis employs the traditional reaction plane method to evaluate the flow coefficients $v_n$ and claims to see isotropic radiation from the thermal quark-gluon plasma. We show in this work, that in the region above the pion mass, the dilepton flow measurement might suffer from cancellation effects that mask the complicated underlying dynamics. Contributions from different baryonic and mesonic resonances show collective behaviour with different signs and lead to an overall vanishing elliptic flow. To differentiate the different contributions, we propose to employ the scalar product method, which exploits the previously measured hadronic flow to create different reference planes. As a proof of concept, we calculate the $v_2$ of dielectrons for Ag+Ag collisions at $\sqrt{s_{NN}}=2.55$ $\mathrm{GeV}$ with both methods and investigate the contribution of each source, concluding that the scalar product method provides the proton and pion tagged flow coefficients as two distinct measurements, disentangling the various dilepton sources., Comment: 10 pages, 7 figures

We present a comparison of directed and elliptic flow data by the FOPI collaboration in Au-Au, Xe-CsI, and Ni-Ni collisions at beam kinetic energies from 0.25 to 1.5 GeV per nucleon to simulations using the SMASH hadronic transport model. The Equation of State is parameterized as a function of nuclear density and momentum dependent potentials are newly introduced in SMASH. With a statistical analysis, we show that the collective flow data at lower energies is in best agreement with a soft momentum dependent potential, while the elliptic flow at higher energies requires a harder momentum dependent Equation of State.

We present BHAC-QGP, a new numerical code to simulate the evolution of matter created in heavy-ion collisions. BHAC-QGP is based on the Black Hole Accretion Code (BHAC), which has been designed to model astrophysical processes through the solution of the equations of general-relativistic magnetohydrodynamics. Like the mother code, BHAC-QGP uses Adaptive Mesh Refinement (AMR), which allows for a dynamic adjustment of the resolution in regions of the computational domain where a particularly high accuracy is needed. We here discuss a number of applications of BHAC-QGP to Au-Au collisions at Relativistic Heavy-Ion Collider (RHIC) energies and show that the code is able to reproduce results of other simulations of these scenarios, but with much higher accuracy., Comment: 17 pages, 18 figures

We present BHAC-QGP, a new numerical code to simulate the evolution of matter created in heavy-ion collisions in the presence of electromagnetic fields. It is derived from the Black Hole Accretion Code (BHAC), which has been designed to model astrophysical processes in a general-relativistic magnetohydrodynamical description. As the original Black Hole Accretion Code, BHAC-QGP benefits from the use of Adaptive Mesh Refinement (AMR), which allows us to dynamically adjust the resolution where necessary, and makes use of time-dependent Milne coordinates and the ultrarelativistic equation of state, $P = e/3$. We demonstrate that BHAC-QGP accurately passes a number of systematic and rigorous tests., Comment: 18 pages, 7 figures

Considerable information about the early-stage dynamics of heavy-ion collisions is encoded in the rapidity dependence of measurements. To leverage the large amount of experimental data, we perform a systematic analysis using three-dimensional hydrodynamic simulations of multiple collision systems -- large and small, symmetric and asymmetric. Specifically, we perform fully 3D multi-stage hydrodynamic simulations initialized by a parameterized model for rapidity-dependent energy deposition, which we calibrate on the hadron multiplicity and anisotropic flow coefficients. We utilize Bayesian inference to constrain properties of the early- and late- time dynamics of the system, and highlight the impact of enforcing global energy conservation in our 3D model.

The purpose of this work is to study the effect of exchanging initial condition models in a modular hybrid approach. The focus lies on the event-by-event correlations of elliptic and triangular flow. This study is performed in the hybrid approach SMASH-vHLLE, composed of the hadronic transport approach SMASH and the (3+1)d viscous hydrodynamic code vHLLE. The initial condition models investigated are SMASH IC, Trento and IP-Glasma. Correlations are calculated on an event-by-event basis between the eccentricities and momentum anisotropies of the initial state as well as the momentum anisotropies in the final state, both for ultra-central and off-central collisions for AuAu collisions at $\sqrt{s_{NN}} = 200$ GeV. This work demonstrates that, although averaged values for the eccentricities of these models are very similar, substantial differences exist both in the distributions of eccentricities, the correlations amongst the initial state properties as well as in the correlations between initial state and final state properties. Notably, whereas initial state momentum anisotropy is shown to not affect the final state flow, the presence of radial flow affects the emergence of final state momentum anisotropies. Inclusion of radial flow in the linear fit improves the prediction of final state flow from initial state properties. The presence of momentum in the initial state has an effect on the emergence of flow and is therefore a relevant part of initial state models, challenging the common understanding of final state momentum anisotropies being a linear response to initial state eccentricity only., Comment: 17 pages, 12 figures. Raw data of figures is provided in the supplemental material

Anisotropic flow emerges in all three of hybrid approaches: initial conditions, viscous relativistic hydrodynamics as well as hadronic transport. Previous works focus mainly on a constant or temperature dependent shear viscosity $\eta/s$. Here instead, we study qualitatively the effect of a generalized $\eta/s(T,\mu_B)$ in the hybrid approach SMASH-vHLLE-hybrid. The parameterization takes into account the constraints of matching to the transport coefficients in the hadronic phase, as well as of recent Bayesian analysis results. We compare the effect of the different parameterizations in the intermediate energy region of $\sqrt{s_{NN}}$=7.7 - 39.0 GeV. We observe that using the energy density dependent parameterization decreases the effect of the point of particlization. In addition, we quantify the uncertainty due to different initial state profiles, including the SMASH initial conditions as well as TrENTo and IP-Glasma profiles. It can be shown that the initial state transverse momentum impacts final state momentum anisotropy., Comment: 4 pages, 3 figures. Presented at Hot Quarks 2022 Workshop for Young Scientists on the Physics of Ultrarelativistic Nucleus-Nucleus Collisions, Estes Park, USA

In this short note we present aspects of the energy and charge deposition within the McDIPPER, a novel 3D resolved model for the initial state of ultrarelativistic Heavy-Ion collisions based on the $k_\perp$-factorized Color Glass Condensate hybrid approach. This framework is a initial-state Monte Carlo event generator which deposits the relevant conserved charges (energy, charge and baryon densities) both in the midrapidity and forward/backward regions of the collision. The event-by-event generator computes the gluon and (anti-) quark phase-space densities using the IP-Sat model, from where the conserved charges can be extracted directly. In this work we present the centrality and collision energy dependence for the deposited conserved quantities at midrapidity and the full event, the so-called $4\pi$ solid angle range.

In this talk we review jet production in a large variety of collision systems using the JETSCAPE event generator and Hybrid Hadronization. Hybrid Hadronization combines quark recombination, applicable when distances between partons in phase space are small, and string fragmentation appropriate for dilute parton systems. It can therefore smoothly describe the transition from very dilute parton systems like $e^++e^-$ to full $A+A$ collisions. We test this picture by using JETSCAPE to generate jets in various systems. Comparison to experimental data in $e^++e^-$ and $p+p$ collisions allows for a precise tuning of vacuum baseline parameters in JETSCAPE and Hybrid Hadronization. Proceeding to systems with jets embedded in a medium, we study in-medium hadronization for jet showers. We quantify the effects of an ambient medium, focusing in particular on the dependence on the collective flow and size of the medium. Our results clarify the effects we expect from in-medium hadronization of jets on observables like fragmentation functions, hadron chemistry and jet shape., Comment: 6 pages, 4 figures, Hard Probes 2023 conference, accepted for publication in Proceedings of Science: version 2, references added, typos fixed

The photon emission from the late stages of the dynamical evolution of heavy-ion reactions at the highest RHIC and LHC energies is investigated. A comparison between a calculation from hadronic rates from a fluid dynamic evolution down to temperatures of 120 MeV and a full non-equilibrium hadronic transport approach is performed. The photon yields are very similar in both cases while the elliptic flow is slightly smaller in the non-equilibrium scenario. This study is important, since it is crucial to apply the same dynamical evolution model for hadronic and electromagnetic observables., Comment: 6 pages, 4 figures, accepted in PoS for Hard Probes 2023

We study the evolution of critical fluctuations in an expanding system within a hadronic transport approach. The initialization of the system with critical fluctuations is achieved by coupling the ideal hadron resonance gas cumulants to the ones from the 3d Ising model and generating the net and total particle number distribution from the principle of maximum entropy. These distributions are then evolved using realistic hadronic interactions. We systematically investigate the evolution of the critical fluctuations initialized at various temperatures and chemical potentials along a freeze-out line. We find that resonance regeneration and isospin randomization processes have the strongest influence on the evolution of the fluctuations. Additionally, the sets of particles coupled to the critical mode are modified to assess the strength of the propagation of correlations through interactions. We find that in the scaling region of the critical point correlations are propagated through the whole collisional history and are still present after the kinetic freeze-out of the matter if the coupling strength is large enough.

Hadron lists based on experimental studies summarized by the Particle Data Group (PDG) are a crucial input for the equation of state and thermal models used in the study of strongly-interacting matter produced in heavy-ion collisions. Modeling of these strongly-interacting systems is carried out via hydrodynamical simulations, which are followed by hadronic transport codes that also require a hadronic list as input. To remain consistent throughout the different stages of modeling of a heavy-ion collision, the same hadron list with its corresponding decays must be used at each step. It has been shown that even the most uncertain states listed in the PDG from 2016 are required to reproduce partial pressures and susceptibilities from Lattice Quantum Chromodynamics with the hadronic list known as the PDG2016+. Here, we update the hadronic list for use in heavy-ion collision modeling by including the latest experimental information for all states listed in the Particle Data Booklet in 2021. We then compare our new list, called PDG2021+, to Lattice Quantum Chromodynamics results and find that it achieves even better agreement with the first principles calculations than the PDG2016+ list. Furthermore, we develop a novel scheme based on intermediate decay channels that allows for only binary decays, such that PDG2021+ will be compatible with the hadronic transport framework SMASH. Finally, we use these results to make comparisons to experimental data and discuss the impact on particle yields and spectra., Comment: 17 pages, 16 figures, 2 tables

We present a new 3D resolved model for the initial state of ultrarelativistic heavy-ion collisions, based on the $k_\perp$-factorized Color Glass Condensate hybrid approach. The McDIPPER framework responds to the need for a rapidity-resolved initial-state Monte Carlo event generator which can deposit the relevant conserved charges (energy, charge and baryon densities) both in the midrapidity and forward/backward regions of the collision. This event-by-event generator computes the gluon and (anti-) quark phase-space densities using the IP-Sat model, from where the relevant conserved charges can be computed directly. In the present work we have included the leading order contributions to the light flavor parton densities. As a feature, the model can be systematically improved in the future by adding next-to-leading order calculations (in the CGC hybrid framework), and extended to lower energies by including sub-eikonal corrections the channels included. We present relevant observables, such as the eccentricities and flow decorrelation, as tests of this new approach., Comment: 18 pages, 11 figures

Understanding the modification of jets and high-$p_T$ probes in small systems requires the integration of soft and hard physics. We present recent developments in extending the JETSCAPE framework to build an event generator, which includes correlations between soft and hard partons, to study jet observables in small systems. The multi-scale physics of the collision is separated into different stages. Hard scatterings are first sampled at binary collision positions provided by the Glauber geometry. They are then propagated backward in space-time following an initial-state shower to obtain the initiating partons' energies and momenta before the collision. These energies and momenta are then subtracted from the incoming colliding nucleons for soft-particle production, modeled by the 3D-Glauber + hydrodynamics + hadronic transport framework. This new hybrid approach (X-SCAPE) includes non-trivial correlations between jet and soft particle productions in small systems. We calibrate this framework with the final state hadrons' $p_T$-spectra from low to high $p_T$ in $p$-$p$, and and then compare with the spectra in $p$-$Pb$ collisions from the LHC. We also present results for additional observables such as the distributions of event activity as a function of the hardest jet $p_T$ in forward and mid-rapidity for both $p$-$p$ and $p$-$Pb$ collisions., Comment: 6 pages, 6 figures, Proceedings of Hard Probes 2023, 26-31 March 2023 Aschaffenburg, Germany

In this work the shear viscosity $\eta$ and the diffusion coefficients of conserved charges $\kappa_{ij}$ with $i,j\in\{B,Q,S\}$ of hadronic matter are investigated within the hadronic transport approach SMASH. We systematically study the effect of multi-particle reactions, angular distributions and additional elastic cross sections via the additive quark model description, the numbers of degrees of freedom and the baryon density on the transport coefficients using the Green-Kubo formalism. We find that multi-particle reactions decrease the shear viscosity in a simplified hadron gas whereas the electric charge diffusion coefficient is not modified. Furthermore, additional elastic cross sections have a strong impact on both $\eta$ and $\kappa_{ij}$ whereas anisotropic scatterings enhance the shear viscosity in the full hadron gas. When increasing the number of degrees of freedom the shear viscosity is only slightly modified in comparison to the diffusion coefficients. Finally, the calculation within a finite baryon chemical potential reveals that the shear viscosity itself does not depend on $\mu_B$ but on the ratio $\eta / s$. The diffusion coefficients show a strong dependency which we compare to Chapman-Enskog calculations.

This review aims at providing an extensive discussion of modern constraints relevant for dense and hot strongly interacting matter. It includes theoretical first-principle results from lattice and perturbative QCD, as well as chiral effective field theory results. From the experimental side, it includes heavy-ion collision and low-energy nuclear physics results, as well as observations from neutron stars and their mergers. The validity of different constraints, concerning specific conditions and ranges of applicability, is also provided.

The nuclear equation of state (EOS) is at the center of numerous theoretical and experimental efforts in nuclear physics. With advances in microscopic theories for nuclear interactions, the availability of experiments probing nuclear matter under conditions not reached before, endeavors to develop sophisticated and reliable transport simulations to interpret these experiments, and the advent of multi-messenger astronomy, the next decade will bring new opportunities for determining the nuclear matter EOS, elucidating its dependence on density, temperature, and isospin asymmetry. Among controlled terrestrial experiments, collisions of heavy nuclei at intermediate beam energies (from a few tens of MeV/nucleon to about 25 GeV/nucleon in the fixed-target frame) probe the widest ranges of baryon density and temperature, enabling studies of nuclear matter from a few tenths to about 5 times the nuclear saturation density and for temperatures from a few to well above a hundred MeV, respectively. Collisions of neutron-rich isotopes further bring the opportunity to probe effects due to the isospin asymmetry. However, capitalizing on the enormous scientific effort aimed at uncovering the dense nuclear matter EOS, both at RHIC and at FRIB as well as at other international facilities, depends on the continued development of state-of-the-art hadronic transport simulations. This white paper highlights the essential role that heavy-ion collision experiments and hadronic transport simulations play in understanding strong interactions in dense nuclear matter, with an emphasis on how these efforts can be used together with microscopic approaches and neutron star studies to uncover the nuclear EOS., Comment: White paper prepared for the 2023 Long Range Plan. v3: Updated version as published in Progress in Particle and Nuclear Physics. Note: the published version does not include the executive summary; in the updated arXiv version, the executive summary is included as an appendix. v4: Corrected list of authors

In 2017, the STAR collaboration at the Relativistic Heavy Ion Collider (RHIC) has measured finite global angular momentum in heavy-ion collisions through a spin polarization measurement of $\Lambda$ hyperons. This measurement revealed a high angular momentum of the heavy ions and provided experimental evidence for vorticity in the quark-gluon plasma (QGP) for the first time. In order to investigate the underlying mechanisms, a dynamic description of the transfer of angular momentum is required. In this work, the microscopic non-equilibrium transport approach SMASH (Simulating Many Accelerated Strongly-interacting Hadrons) is applied to study the generation of global angular momentum by the interaction of two nuclei. As SMASH provides access to the whole phase-space evolution of every particle at any given time, it allows to assess the fraction of angular momentum generated in the fireball by all participants. We confirm the previous modeling by Becattini \textit{et al} within a geometric Glauber model approach, which found that the angular momentum transfer reaches a unique maximum in mid-central collisions during time evolution. The corresponding impact parameter is around $b=4-6$ fm for all beam energies from $\sqrt{s_{\rm NN}}=2.41-200$ GeV. Even though angular momentum is not conserved locally in the transport approach a priori, we identify the contributions to the conservation violation and propose optimal setups for different energy regimes that recover conservation, based upon the test particle method and the treatment of Fermi motion. Furthermore, the system size and centrality dependence are investigated., Comment: 8 pages, 6 figures

Since the release of the 2015 Long Range Plan in Nuclear Physics, major events have occurred that reshaped our understanding of quantum chromodynamics (QCD) and nuclear matter at large densities, in and out of equilibrium. The US nuclear community has an opportunity to capitalize on advances in astrophysical observations and nuclear experiments and engage in an interdisciplinary effort in the theory of dense baryonic matter that connects low- and high-energy nuclear physics, astrophysics, gravitational waves physics, and data science, Comment: 70 pages, 3 figures, White Paper for the Long Range Plan for Nuclear Science

This article summarizes our present knowledge about nuclear matter at the highest energy densities and its formation in relativistic heavy ion collisions. We review what is known about the structure and properties of the quark-gluon plasma and survey the observables that are used to glean information about it from experimental data., Comment: 110 pages

In this work, the qualitative impact of the net baryochemical potential dependence of the shear viscosity to entropy density ratio $\eta/s$ in hydrodynamical simulations is studied. The effect of a predicted non-constant $\eta/s$($\mu_B$) is largely unexplored in hydrodynamic simulations. Previous studies focus only on a temperature dependence or even only a constant effective shear viscosity. This work addresses this issue by studying qualitatively the effect of a generalized $\eta/s$($T,\mu_B$) in the hybrid approach SMASH-vHLLE, composed of the hadronic transport approach SMASH and the (3+1)d viscous hydrodynamic code vHLLE. In order to reduce the bias of the result on the equation of state used in the hydrodynamic part of the model, $\eta/s$ is parameterized directly in the energy density and net baryon number density. The parameterization takes into account the constraints of matching to the transport coefficients in the hadronic phase, as well as pQCD results. This work compares the impact of the density dependence for different system sizes and energies and compares the observables with experimental results in the RHIC - BES region $\sqrt{s_{NN}}$ =7.7 - 39.0 GeV, as the effect of this generalization is especially relevant for intermediate collision energies, for which the system is in equilibrium for a relevant amount of time, but the net baryochemical potential does not vanish. It is shown that the effect of an explicit net baryon number dependence on the elliptic flow is negligible and only relevant in the early stages of the collision. Additionally, we find that the proposed parameterization could be a good proxy for the shear viscosity in the non-equilibrium hadronic transport stage., Comment: 11 pages, 12 figures

Effective spectral functions of the $\rho$ meson are reconstructed by considering the lifetimes inside different media using the hadronic transport SMASH (Simulating Many Accelerated Strongly-interacting Hadrons). Due to inelastic scatterings, resonance lifetimes are dynamically shortened (collisional broadening), even though the employed approach assumes vacuum resonance properties. Analyzing the $\rho$ meson lifetimes allows to quantify an effective broadening of the decay width and spectral function, which is important in order to distinguish dynamical effects from additional genuine medium modifications to the spectral functions, indicating e.g. an onset of chiral symmetry restoration. The broadening of the spectral function in a thermalized system is shown to be consistent with other theoretical calculations. The effective $\rho$ meson spectral function is also presented for the dynamical evolution of heavy-ion collisions, finding a clear correlation of the broadening to system size, which is explained by an observed dependence of the width on the local hadron density. Furthermore, the difference in the results between the thermal system and full collision dynamics is explored, which may point to non-equilibrium effects., Comment: 9 pages, 12 figures. Ancillary files divided by system

Understanding the phase diagram of QCD by measuring fluctuations of conserved charges in heavy-ion collision is one of the main goals of the beam energy scan program at RHIC. Within this work, we calculate the role of hadronic interactions and momentum cuts on cumulants of conserved charges up to fourth order in a system in equilibrium within a hadronic transport approach (SMASH). In our model the net baryon, net charge and net strangeness is perfectly conserved on an event-by-event basis and the cumulants are calculated as a function of subvolume sizes and compared to analytic expectations. We find a modification of the kurtosis due to charge annihilation processes in systems with simplified degrees of freedom. Furthermore the result of the full SMASH hadron gas for the net baryon and net proton number fluctuations is presented for systems with zero and finite values of baryon chemical potential. Additionally we find that due to dynamical correlations the cumulants of the net baryon number cannot easily be recovered from the net protons. Finally the influence of deuteron cluster formation on the net proton and net baryon fluctuations in a simplified system is shown. This analysis is important to better understand the relation between measurements of fluctuations in heavy-ion collisions and theoretical calculation which are often performed in a grand canonical ensemble.

Transport models are the main method to obtain physics information from low to relativistic-energy heavy-ion collisions. The Transport Model Evaluation Project (TMEP) has been pursued to test the robustness of transport model predictions in reaching consistent conclusions from the same type of physical model. Calculations under controlled conditions of physical input and set-up were performed with various participating codes. These included both calculations of nuclear matter in a box with periodic boundary conditions, and more realistic calculations of heavy-ion collisions. In this intermediate review, we summarize and discuss the present status of the project. We also provide condensed descriptions of the 26 participating codes, which contributed to some part of the project. These include the major codes in use today. We review the main results of the studies completed so far. They show, that in box calculations the differences between the codes can be well understood and a convergence of the results can be reached. These studies also highlight the systematic differences between the two families of transport codes, known as BUU and QMD type codes. However, when the codes were compared in full heavy-ion collisions using different physical models, as recently for pion production, they still yielded substantially different results. This calls for further comparisons of heavy-ion collisions with controlled models and of box comparisons of important ingredients, like momentum-dependent fields, which are currently underway. We often indicate improved strategies in performing transport simulations and thus provide guidance to code developers. Results of transport simulations of heavy-ion collisions from a given code will have more significance if the code can be validated against benchmark calculations such as the ones summarized in this review., Comment: 114 pages, 14 figures, 479 references, accepted for publication in Progress of Particle and Nuclear Phsics

To assess the degree of equilibration of the matter created in heavy-ion reactions at low to intermediate beam energies, a hadronic transport approach (SMASH) is employed. By using a coarse-graining method, we compute the energy momentum tensor of the system at fixed time steps and evaluate the degree of isotropy of the diagonal terms and the relative magnitude of the off-diagonal terms. This study focuses mostly on Au+Au collisions in the energy range $\sqrt{s_{\rm NN}}$ = 2.4-7.7 GeV, but central collisions of lighter ions like C+C, Ar+KCl and Ag+Ag are considered as well. We find that the conditions concerning local equilibration for a hydrodynamic description are reasonably satisfied in a large portion of the system for a significant amount of time (several fm/c) when considering the average evolution of many events, yet they are rarely fulfilled on an event by event basis. This is relevant for the application of hybrid approaches at low beam energies as they are or will be reached by the HADES experiment at GSI, the future CBM experiment at FAIR as well as the beam energy scan program at RHIC., Comment: Ancillary files with plots data and workflow provided. Version 2 corresponding to version accepted for publication by EPJC

In this work, we assess the importance of non-equilibrium dynamics in the production of photons from the late stages of relativistic heavy-ion collisions. The p$_\mathrm{T}$-differential spectra and $v_2$ of photons from the late hadronic stage are computed within a non-equilibrium hadron transport approach, and compared to the results of a local equilibrium evolution using ideal relativistic hydrodynamics. It is found that non-equilibrium dynamics enhance the late-stage photon production at low p$_\mathrm{T}$ and decreases it at higher p$_\mathrm{T}$ compared to the estimate from hydrodynamics. This same comparison points to a significant increase in the momentum anisotropies of these photons due to non-equilibrium dynamics. Once combined with photons produced above the particlization temperature in the hydrodynamics evolution, the differences between the two approaches appear modest in what concerns the p$_\mathrm{T}$ differential spectra, but are clearly noticeable at low p$_\mathrm{T}$ for the elliptic flow: non-equilibrium dynamics enhance the photon $v_2$ below p$_\mathrm{T}$ $\approx 1.4$ GeV., Comment: Data is available in the anc directory

Heavy-ion collisions covering a wide range of collision energies provide a vast amount of observables characterizing the properties of strongly-interacting matter. In particular collisions towards the high baryon-density regime of the QCD phase-diagram have become of interest to study the postulated first order phase transition and to locate a possible critical end point. In this work, the SMASH-vHLLE-hybrid is presented as a novel hybrid model to theoretically describe such heavy-ion collisions. In addition, the SMASH hadron resonance gas equation of state is introduced. The accuracy of the latter is shown to be of fundamental importance in order to conserve energy, baryon number and electric charge throughout the different stages of the hybrid model. Furthermore, the impact of an inaccurate equation of state on final state observables is discussed. This work constitutes a first validation of the SMASH-vHLLE-hybrid in terms of conservation laws and excitation functions. It is expected to be applied to a broader range of observables in the future., Comment: Proceedings CPOD 2021

The Beam Energy Scan Theory (BEST) Collaboration was formed with the goal of providing a theoretical framework for analyzing data from the Beam Energy Scan (BES) program at the relativistic heavy ion collider (RHIC) at Brookhaven National Laboratory. The physics goal of the BES program is the search for a conjectured QCD critical point as well as for manifestations of the chiral magnetic effect. We describe progress that has been made over the previous five years. This includes studies of the equation of state and equilibrium susceptibilities, the development of suitable initial state models, progress in constructing a hydrodynamic framework that includes fluctuations and anomalous transport effects, as well as the development of freezeout prescriptions and hadronic transport models. Finally, we address the challenge of integrating these components into a complete analysis framework. This document describes the collective effort of the BEST Collaboration and its collaborators around the world., Comment: 103 pages

We investigate the long-standing question of the effect of proton-antiproton annihilation on the (anti-)proton yield, while respecting detailed balance for the 5-body back-reaction for the first time in a full microscopic description of the late stages of heavy-ion collisions. This is achieved by employing a stochastic collision criterion in a hadronic transport approach (SMASH), which allows to treat arbitrary multi-particle reactions. It is used to account for the regeneration of (anti-)protons via $5\pi\rightarrow p\bar{p}$. Our results show that a back-reaction happens for a fraction of 15-20\% of all annihilations. Within a viscous hybrid approach Au+Au/Pb+Pb collisions from $\sqrt{s_{NN}}=17.3$ GeV$-5.02$ TeV are investigated and the quoted fraction is independent of the beam energy or centrality of the collision. Taking the back-reaction into account results in regeneration of half of the (anti-)proton yield that is lost due to annihilations at midrapidity. We also find that, concerning the multiplicities, treating the back-reaction as a chain of 2-body reactions is equivalent to a single 5-to-2 reaction., Comment: 6 pages, 4 figures

We study the deuteron production via the deuteron pion and nucleon catalysis reactions, $\pi p n \leftrightarrow \pi d$ and $N p n \leftrightarrow N d$, by employing stochastic multi-particle reactions in the hadronic transport approach SMASH for the first time. This is an improvement compared to previous studies, which introduced an artificial fake resonance $d'$ to simulate these $3 \leftrightarrow 2$ reactions as a chain of $2\leftrightarrow 2$ reactions. The derivation of the stochastic criterion for multi-particle reactions is presented in a comprehensive fashion and its implementation is tested against an analytic expression for the scattering rate and the equilibrating particle yields in box calculations. We then study Au + Au collisions at $\sqrt{s_{\mathrm{NN}}} = 7.7$ GeV, where we find that multi-particle collisions substantially reduce the time required for deuterons to reach partial chemical equilibrium with nucleons. Subsequently, the final yield of $d$ is practically independent from the number of $d$ at particlization, confirming the results of previous studies. The mean transverse momentum and the integrated elliptic flow as a function of centrality are rather insensitive to the exact realization of the $2\leftrightarrow 3$ reactions., Comment: 14 pages, 10 figures; included text files with the data to reproduce the figures; replaced with published version; additional appendix about grid setup

Within the transport model evaluation project (TMEP) of simulations for heavy-ion collisions, the mean-field response is examined here. Specifically, zero-sound propagation is considered for neutron-proton symmetric matter enclosed in a periodic box, at zero temperature and around normal density. The results of several transport codes belonging to two families (BUU-like and QMD-like) are compared among each other and to exact calculations. For BUU-like codes, employing the test particle method, the results depend on the combination of the number of test particles and the spread of the profile functions that weight integration over space. These parameters can be properly adapted to give a good reproduction of the analytical zero-sound features. QMD-like codes, using molecular dynamics methods, are characterized by large damping effects, attributable to the fluctuations inherent in their phase-space representation. Moreover, for a given nuclear effective interaction, they generally lead to slower density oscillations, as compared to BUU-like codes. The latter problem is mitigated in the more recent lattice formulation of some of the QMD codes. The significance of these results for the description of real heavy-ion collisions is discussed.

Collective flow observables are known to be a sensitive tool to gain insights on the equation of state of nuclear matter from heavy-ion collision observations. Towards more quantitative constraints one has to carefully assess other influences on the collective behaviour. In this work a hadronic transport approach SMASH (Simulating Many Accelerated Strongly-interacting Hadrons) is applied to study the first four anisotropic flow coefficients in Au+Au collisions at $E_{\rm lab}=1.23A$ GeV in the context of the recently measured data by the HADES collaboration. In particular, the formation of light nuclei is important in this energy regime. Two different approaches are contrasted to each other: A clustering algorithm inspired by coalescence as well as microscopic formation of deuterons via explicit cross-sections. The sensitivity of directed and elliptic flow observables to the strength of the Skyrme mean field is explored. In addition, it is demonstrated that the rapidity-odd $v_3$ coefficient is practically zero in this energy regime and the ratio of $v_4/v_2^2$ is close to the value of 0.5 expected from hydrodynamic behaviour. This study establishes the current understanding of collective behaviour within the SMASH approach and lays the ground for future more quantitative constraints on the equation of state of nuclear matter within improved mean field calculations., Comment: Tables for all plotted calculations can be found in the anc folder

In the past two decades, pions created in the high density regions of heavy ion collisions have been predicted to be sensitive at high densities to the symmetry energy term in the nuclear equation of state, a property that is key to our understanding of neutron stars. In a new experiment designed to study the symmetry energy, the multiplicities of negatively and positively charged pions have been measured with high accuracy for central $^{132}$Sn+$^{124}$Sn, $^{112}$Sn+$^{124}$Sn, and $^{108}$Sn+$^{112}$Sn collisions at $E/A=270~\mathrm{MeV}$ with the S$\pi$RIT Time Projection Chamber. While the uncertainties of individual pion multiplicities are measured to 4\%, those of the charged pion multiplicity ratios are measured to 2\%. We compare these data to predictions from seven major transport models. The calculations reproduce qualitatively the dependence of the multiplicities and their ratios on the total neutron to proton number in the colliding systems. However, the predictions of the transport models from different codes differ too much to allow extraction of reliable constraints on the symmetry energy from the data. This finding may explain previous contradictory conclusions on symmetry energy constraints obtained from pion data in Au+Au system. These new results call for better understanding of the differences among transport codes, and new observables that are more sensitive to the density dependence of the symmetry energy., Comment: 8 pages, 4 figures, 1 table (accepted for publication in PLB)

In most calculations of hard particle suppression in heavy-ion reactions the hadronic stage has been neglected due to formation time arguments. Most of the hard particle shower exits the hot and dense medium before the system enters the hadronic evolution. In this contribution, a first assessment within the hadronic transport approach SMASH (Simulating Many Accelerated Strongly-interacting Hadrons) of rescattering effects on hard particles is presented. In particular, it is shown that the hadronic energy loss depends on the particle species as well as the energy of the probe. A parametrization for the $\langle \tilde{q} \rangle$ parameter as a function of temperature and particle energy is given for pions. Overall, major effects of the hadronic stage are expected in the transverse momentum range from 2-10 GeV and therefore jet sub-structure analysis and (hard-soft) correlation observables might be affected., Comment: 5 pages, 4 figures, Proceedings for HardProbes2020, 1-6 June 2020, Austin, Texas (virtual)

Heavy-ion collisions at low beam energies explore the high density regime of strongly-interacting matter. The dynamical evolution of these collisions can be successfully described by hadronic transport approaches. In March 2019, the HADES collaboration has taken data for AgAg collisions at $E_{\rm Kin}=1.58A$ GeV and in this work, we provide predictions for particle production and spectra within the Simulating Many Accelerated Strongly-interacting Hadrons (SMASH) approach. The multiplicities and spectra of strange and non-strange particles follow the expected trends as a function of system size. In particular, in AuAu collisions, much higher yields of double-strange baryons were observed experimentally than expected from a thermal model. Therefore, we incorporate a previously suggested mechanism to produce $\Xi$ baryons via rare decays of high mass $N^*$ resonances and predict the multiplicities. In addition, we predict the invariant mass spectrum for dilepton emission and explore the most important sources of dileptons above 1 GeV, that are expected to indicate the temperature of the medium. Interestingly, the overall dilepton emission is very similar to the one in AuAu collisions at $1.23 A$ GeV, a hint that the smaller system at a higher energy behaves very similar to the larger system at lower beam energy., Comment: 13 pages, 13 figures, text files with the data to reproduce the figures provided in source; replaced with published version, only minor changes and 1 figure removed

In general, the constituents of the bulk matter produced in heavy-ion collisions carry, besides electric charge, multiple other conserved quantum numbers like baryon number and strangeness. Therefore, an electric field will not only generate an electric current but, at the same time, also currents in baryon number and strangeness. We propose that the impact of the electric field on these conserved currents should be characterized by additional transport coefficients, which we call cross-conductivities. In this paper, we introduce and present a calculation of these cross-conductivities from the Green-Kubo formalism within the transport code SMASH for different chemical compositions of hadron resonance gases. We find that the coefficients underlie an ordering in the active degrees of freedom and that thus the chemical composition of the system plays a crucial role. Further, we argue that in future comparisons of lattice QCD calculations with these findings, one could constrain which degrees of freedom and their corresponding charge properties are relevant for the QCD dynamics of the system., Comment: 6 pages, 5 figures

Cross sections for photon production in hadronic scattering processes have been calculated according to an effective chiral field theory. For $\pi + \rho \to \pi + \gamma$ and $\pi + \pi \to \rho + \gamma$ processes, these cross sections have been implemented into a novel hadronic transport approach (SMASH), which is suitable for collisions at low and intermediate energies. The implementation is verified by systematically comparing the thermal photon rate to theoretical expectations. The photon rates we obtain are compared to previous works, where scattering processes mediated by $\omega$ mesons are found to contribute significantly to the total photon production. Finally, the impact of considering the finite width of the $\rho$ meson is investigated, and a significant enhancement of photon production in the low-energy region is observed. This work is the first step towards a consistent treatment of photon emission in hybrid hydrodynamics+transport approaches. The quantification of the importance of the hadronic stage for the resolution of the direct photon flow puzzle is a next step and can be applied to identify equilibrium and non-equilibrium effects in the hadronic afterburner., Comment: 4 pages, 3 figures, proceedings of Quark Matter 2019

Hadronic interactions are crucial for the dynamical description of heavy-ion reactions at low collision energies and in the late dilute stages at high collision energies. In particular, the properties and decay channels of resonances are an essential ingredient of hadronic transport approaches. The HADES collaboration measured particle production in collisions of pions with carbon and tungsten nuclei at $E_\text{kin} = 1.7\,\text{GeV}$. Such reactions are of high interest, because they allow to probe the properties of baryonic resonances produced in a much cleaner environment than the usual nucleus-nucleus collisions. We study these reactions with two transport approaches: SMASH (Simulating Many Accelerated Strongly-interacting Hadrons) and UrQMD (Ultra relativistic Quantum Molecular Dynamics) which follow the same underlying concept but with different implementations. The differential spectra in rapidity and transverse momentum are used to show how model parameters, as the decay channels of high mass resonances and angular distributions of kaon elastic scattering, can be constrained. It is found that the data favor the production of more particles with lower momentum over the production of few particles with higher momentum in these decays. In addition, the shape of the rapidity distribution of the kaons strongly depends on the angular distribution of the elastic kaon-nucleon cross section., Comment: 15 pages, 3 figures

The suppression of high momentum particles in heavy-ion collisions in comparison to elementary reactions is one of the main indications for the formation of a quark-gluon plasma. In recent studies, full jets are being reconstructed and substructure observables are gaining importance in assessing the medium modifications of hard probes. In this work, the effect of the late stage hadronic interactions are explored within the hadronic transport approach SMASH (Simulating Many Accelerated Strongly-interacting Hadrons). High momentum particles are incorporated in a radially expanding hadron gas to analyse the corresponding angular distributions, also refered to as `jet shape' observables. We find that the full hadron gas can be approximated with a pion gas with constant elastic cross-sections of 100 mb. In addition, the temperature and probe energy dependence of diffusion coefficients $\tilde{q}$ and $\tilde{e}$ quantifying the transverse and parallel momentum transfers are extracted. The species dependence and the importance of different interaction types are investigated. Parametrizations are presented that can be employed in future jet quenching calculations to include the effect of the hadronic phase., Comment: 8 pages, 5 figures

The stopping of baryons in heavy ion collisions at beam momenta of $p_{\rm lab} = 20-160A$ GeV is lacking a quantitative description within theoretical calculations. Heavy ion reactions at these energies are experimentally explored at the Super Proton Synchrotron (SPS) and the Relativistic Heavy Ion Collider (RHIC) and will be studied at future facilities such as FAIR and NICA. Since the net baryon density is determined by the amount of stopping, this is the pre-requisiste for any investigation of other observables related to structures in the QCD phase diagram such as a first-order phase transition or a critical endpoint. In this work we employ a string model for treating hadron-hadron interactions within a hadronic transport approach (SMASH, Simulating Many Accelerated Strongly-interacting Hadrons). Free parameters of the string excitation and decay are tuned to match experimental measurements in elementary proton-proton collisions, where some mismatch in the $x_F$ distribution of protons is still present. Afterwards, the model is applied to heavy ion collisions, where the experimentally observed change of the shape of the proton rapidity spectrum from a single peak structure to a double peak structure with increasing beam energy is reproduced. Heavy ion collisions provide the opportunity to study the formation process of string fragments in terms of formation times and reduced interaction cross-sections for pre-formed hadrons. A good agreement with the measured rapidity spectra of protons and pions is achieved while insights on the fragmentation process are obtained. In the future, the presented approach can be used to create event-by-event initial conditions for hybrid calculations., Comment: As accepted in Journal of Physics G, added a subsection on the multi-parameter problem and minor changes. J. Phys. G: Nucl. Part. Phys (2020)

The unambiguous observation of a Chiral Magnetic Effect (CME)-driven charge separation is the core aim of the isobar program at RHIC consisting of ${^{96}_{40}}$Zr+${^{96}_{40}}$Zr and ${^{96}_{44}}$Ru+${^{96}_{44}}$Ru collisions at $\sqrt {s_{\rm NN}}\!=\!200$ GeV. We quantify the role of the spatial distributions of the nucleons in the isobars on both eccentricity and magnetic field strength within a relativistic hadronic transport approach (SMASH, Simulating Many Accelerated Strongly-interacting Hadrons). In particular, we introduce isospin-dependent nucleon-nucleon spatial correlations in the geometric description of both nuclei, deformation for ${^{96}_{44}}$Ru and the so-called neutron skin effect for the neutron-rich isobar i.e. ${^{96}_{40}}$Zr. The main result of this study is a reduction of the magnetic field strength difference between ${^{96}_{44}}$Ru+${^{96}_{44}}$Ru and ${^{96}_{40}}$Zr+${^{96}_{40}}$Zr by a factor of 2, from $10\%$ to $5\%$ in peripheral collisions when the neutron-skin effect is included. Further, we find an increase of eccentricity by up to 10$\%$ when deformation is taken into account while neither the neutron skin effect nor the nucleon-nucleon correlations result into a significant modification of this observable with respect to the traditional Woods-Saxon modeling. Our results suggest a significantly smaller CME signal to background ratio for the experimental charge separation measurement in peripheral collisions with the isobar systems than previously expected., Comment: 6 pages, 3 figures, v2: bug in the implementation of the deformation has been fixed. Conclusions remain intact

We compare ten transport codes for a system confined in a box, aiming at improved handling of the production of $\Delta$ resonances and pions, which is indispensable for constraining high-density symmetry energy from observables such as the $\pi^-/\pi^+$ yield ratio in heavy-ion collisions. The system in a box is initialized with nucleons at saturation density and at 60 MeV temperature. The reactions $NN\leftrightarrow N\Delta$ and $\Delta\leftrightarrow N\pi$ are implemented, but the Pauli blocking and the mean-field potential are deactivated in the present comparison. Results are compared to those from the two reference cases of a chemically equilibrated ideal gas mixture and of the rate equation. In the results of the numbers of $\Delta$ and $\pi$, deviations from the reference values are observed in many codes, and they depend significantly on the size of the time step. These deviations are tied to different ways in ordering the sequence of collisions and decays, that take place in the same time step. Better agreements are seen in the reaction rates and the number ratios among the isospin species of $\Delta$ and $\pi$. These are, however, affected by the correlations, which are absent in the Boltzmann equation, but are induced by the way particle scatterings are treated in transport calculations. The uncertainty in the transport-code predictions of the $\pi^-/\pi^+$ ratio for the system initialized at n/p = 1.5, after letting the existing $\Delta$ resonances decay, is found to be within a few percent, which is sufficiently small so that it does not strongly impact constraining the high-density symmetry energy from heavy-ion collisions. Most of the sources of uncertainties have been understood, and individual codes may be further improved. This investigation will be extended in the future to heavy-ion collisions to ensure the problems identified here remain under control., Comment: 36 pages, 27 figures; a new Fig. 21 and revised results from some codes, achieving improved and consistent understanding

In this work, the production of photons through binary scattering processes is investigated for equilibrated hadronic systems. More precisely, a non-equilibrium hadronic transport approach to describe relativistic heavy-ion collisions is benchmarked with respect to photon emission. Cross sections for photon production in $\pi + \rho \to \pi + \gamma$ and $\pi + \pi \to \rho + \gamma$ scattering processes are derived from an effective chiral field theory and implemented into the hadronic transport approach, SMASH (Simulating Many Accelerated Strongly-interacting Hadrons). The implementation is verified by systematically comparing the thermal photon rate to theoretical expectations. Further, the impact of form factors is discussed, scattering processes mediated by $\omega$ mesons are found to contribute significantly to the total photon production. Several comparisons of the yielded photon rates are performed: to parametrizations of the very same rates, as used in hydrodynamic simulations, to previous works relying on different cross sections for the production of direct photons from the hadronic stage, and to partonic rates. Finally, the impact of considering the finite width of the $\rho$ meson is investigated, where a significant enhancement of photon production in the low-energy region is observed. This benchmark is the first step towards a consistent treatment of photon emission in hybrid hydrodynamics+transport approaches and a genuine dynamical description., Comment: 14 pages, 15 figures

The deuteron binding energy is only 2.2 MeV. At the same time, its yield in Pb+Pb collisions at $\sqrt{s_{NN}} = $2.76 TeV corresponds to a thermal yield at the temperature around 155 MeV, which is too hot to keep deuterons bound. This puzzle is not completely resolved yet. In general, the mechanism of light nuclei production in ultra-high energy heavy ion collisions remains under debate. In a previous work [1] we suggest a microscopic explanation of the deuteron production in central ultra-relativistic Pb+Pb collisions, the main mechanism being $\pi pn \leftrightarrow \pi d$ reactions in the hadronic phase of the collision. We use a state-of-the-art hybrid approach, combining relativistic hydrodynamics for the hot and dense stage and hadronic transport for a later, more dilute stage. Deuteron rescattering in the hadronic stage is implemented explicitly, using its experimentally measured vacuum cross-sections. In these proceedings we extend our previous work to non-central collisions, keeping exactly the same methodology and parameters. We find that our approach leads to a good description of the measured deuteron transverse momentum spectra at centralities up to 40%, and underestimates the amount of deuterons at low transverse momentum at higher centralities. Nevertheless, the coalescence parameter $B_2$, measured by ALICE collaboration, is reproduced well in our approach even for peripheral collisions., Comment: Proceedings of Hot Quarks 2018, 4 pages, 2 figures

Motivated by the theory of relativistic hydrodynamic fluctuations we make use of the Green-Kubo formula to compute the electrical conductivity and the (second-order) relaxation time of the electric current of an interacting hadron gas. We use the recently developed transport code SMASH to numerically solve the coupled set of Boltzmann equations implementing realistic hadronic interactions. In particular, we explore the role of the resonance lifetimes in the determination of the electrical relaxation time. As opposed to a previous calculation of the shear viscosity we observe that the presence of resonances with lifetimes of the order of the mean-free time does not appreciably affect the relaxation of the electric current fluctuations. We compare our results to other approaches describing similar systems, and provide the value of the electrical conductivity and the relaxation time for a hadron gas at temperatures between T=60 MeV and T=150 MeV., Comment: 29 pages, 11 figures. Typos corrected, new references incorporated and minor clarifications added. Version to be published by the Physical Review D journal