A relativistic hadronic transport approach

Download: Pb-Pb collision with 17.3 GeV center-of-mass energy (by J. Mohs)

SMASH is a relativistic hadronic transport approach including all well-established hadrons up to a mass of ~ 2 GeV as degrees of freedom. Electromagnetic emission is treated perturbatively. It constitutes an effective solution of the relativistic Boltzmann equation with binary interactions. Most interactions proceed via resonance excitation and decay at lower energies or string excitation and fragmentation at higher energies. The following applications have been well tested:

- Dynamical description of heavy-ion collisions at low beam energies (0.4 to 2.0 AGeV kinetic energy)
- Infinite matter calculations to investigate equilibrium properties
- Afterburner for dilute non-equilibrium stages of high beam energy heavy-ion reactions
- Expansion of a spherically symmetric system

The SMASH analysis suite serves as a python-based add-on to the transport code. It contains various tools and scripts to compute observables from the SMASH output. Among these are:

- Angular distributions
- Cross sections
- Detailed balance tests
- Dilepton invariant mass spectra
- Scattering rates
- Particle spectra over a large range of collision energies
- FOPI pion spectra

In this article SMASH is introduced and applied to study the production of nonstrange particles in heavy-ion reactions at E_{Kin}=0.4A–2A GeV. First, the model is described including details about the collision criterion, the initial conditions and the resonance formation and decays. To validate the approach, equilibrium properties such as detailed balance are presented and the results are compared to experimental data for elementary cross sections. Finally, results for pion and proton production in C+C and Au+Au collisions are confronted with data from the high-acceptance dielectron spectrometer (HADES) and FOPI. Predictions for particle production in π+A collisions are made.

In this work SMASH is applied to study the first four anisotropic flow coefficients in Au+Au collisions at 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.

INSPIREWe develop a flexible, relativistically covariant parameterization of dense nuclear matter equation of state suited for inclusion in computationally demanding hadronic transport simulations. Within an implementation in the hadronic transport code SMASH, we show that effects due to bulk thermodynamic behavior are reproduced in dynamic hadronic systems, demonstrating that hadronic transport can be used to study critical behavior in dense nuclear matter, both at and away from equilibrium. We also show that two-particle correlations calculated from hadronic transport simulation data follow theoretical expectations based on the second order cumulant ratio, and constitute a clear signature of crossing the phase diagram above the critical point.

INSPIRE PaperWe study the properties of the strongly-coupled quark-gluon plasma with a multistage model of heavy ion collisions that combines the Trento 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. 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.

INSPIRE Paper INSPIRE LetterIn March 2019, the HADES collaboration has taken data for AgAg collisions and in this work, we provide predictions for particle production within SMASH. The multiplicities of strange and non-strange particles follow the expected trends as a function of system size. In particular, in ArKCl (and pNb) 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 Ξ baryons via rare decays of high mass N* resonances and predict the multiplicities. In addition, we predict the 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, a hint that the smaller system at a higher energy behaves very similar to the larger system at lower beam energy.

INSPIREThe temperature dependence of the bulk viscosity in a relativistic hadron gas. Employing the Green-Kubo formalism in the SMASH transport approach, we study different hadronic systems in increasing order of complexity. We analyze the (in)validity of the single exponential relaxation ansatz for the bulk-channel correlation function and the strong influence of the resonances and their lifetimes. We discuss the difference between the inclusive bulk viscosity of an equilibrated, long-lived system, and the effective bulk viscosity of a short-lived mixture like the hadronic phase of relativistic heavy-ion collisions, where the processes whose inverse relaxation rate are larger than the fireball duration are excluded from the analysis. We compare our final results with previous hadron gas calculations and confirm a decreasing trend of the inclusive bulk viscosity over entropy density as temperature increases, whereas the effective bulk viscosity to entropy ratio, while being lower than the inclusive one, shows no strong dependence to temperature.

INSPIREIn 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 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.

INSPIREThe 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 1.7 GeV kinetic energy. 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. 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.

INSPIREThe 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 this work, the effect of the late stage hadronic interactions are explored. 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 for such an observable 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 qtilde and etilde 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.

INSPIREThe stopping of baryons in heavy ion collisions at beam momenta of p_{lab}= 20−160A GeV is lacking a quantitative description within theoretical calculations. 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. 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. In the future, the presented approach can be used to create event-by-event initial conditions for hybrid calculations.

The unambiguous observation of a Chiral Magnetic Effect (CME)-driven charge separation is the core aim of the isobar program at RHIC consisting of Zr+Zr and Ru+Ru collisions at E_{CM}= 200A GeV. We quantify the role of the spatial distributions of the nucleons in the isobars on both eccentricity and magnetic field strength. In particular, we introduce isospin-dependent nucleon-nucleon spatial correlations in the geometric description of both nuclei, deformation for Ru and the so-called neutron skin effect for the neutron-rich isobar i.e. Zr. The main result of this study is a reduction of the magnetic field strength difference between Ru+Ru and Zr+Zr by a factor of 2, from 10\% to 5\% in peripheral collisions when the neutron-skin effect is included.

The performance of SMASH is studied in the transport code comparison project: The pion production via NN↔N∆ and ∆↔Nπ processes in structinized, detailed balance is tested and the yields and collision rates are compared to a numerical (not Monte-Carlo) solution of the relativistic Boltzmann equation.

INSPIREThe production of direct photons from hadronic scatterings is implemented and validated within SMASH. Cross sections for photon production in binary, mesonic scattering processes are derived from chiral field theory and applied to describe photon production in equilibrated hadronic systems. The sensitivity of the thermal photon rate to incorporating form factors and describing non-stable ρ mesons is further investigated. It is found that photon processes involving ω mesons provide a major contribution to the total photon production and that considering non-stable ρ mesons results in a significant enhancement of photon production at low photon energies. This benchmark is the first step towards a consistent treatment of photon emission in hybrid hydrodynamics+transport approaches and a genuine dynamical description.

INSPIREMotivated 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 SMASH to 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.

INSPIREProduction of strange hadrons in elementary and heavy-ion reactions is studied within SMASH. The poorly known branching ratios of the relevant hadronic resonances are constrained from the known elementary hadronic cross sections and from invariant mass spectra of dileptons. The constrained model is employed as a baseline to compare to heavy-ion-collision experiments at low energies (E_{kin} = 1−2AGeV) and to predict some of the upcoming pion-beam results by HADES, which are expected to be sensitive to the resonance properties. The employed vacuum-resonance approach proves to be viable for small systems at these energies, but for large systems additional in-medium effects might be required.

The deuteron yield in Pb+Pb collisions at center-of-mass energies of 2.76 TeV is consistent with thermal production at a freeze-out temperature of T=155 MeV. The existence of deuterons with binding energy of 2.2 MeV at this temperature was described as "snowballs in hell". We provide a microscopic explanation of this phenomenon, utilizing relativistic hydrodynamics and switching to a hadronic afterburner at the above mentioned temperature of T=155 MeV.

INSPIRE APS Physics SynopsisThe dilepton emission in heavy-ion reactions at low beam energies is examined within SMASH. The calculations are systematically confronted with HADES data in the kinetic energy range of 1−3.5A GeV for elementary, proton-nucleus and nucleus-nucleus reactions. The present approach employing a resonance treatment based on vacuum properties is validated by an excellent agreement with experimental data up to system sizes of carbon-carbon collisions. After establishing this well-understood baseline in elementary and small systems, the significance of in-medium effects is investigated with a coarse-graining approach based on the same hadronic evolution.

INSPIRESimulations by transport codes are indispensable to extract valuable physical information from heavy-ion collisions. In order to understand the origins of discrepancies among different widely used transport codes, we compare 15 such codes under controlled conditions of a system confined to a box with periodic boundary, initialized with Fermi-Dirac distributions at saturation density and temperatures of either 0 or 5 MeV. In such calculations, one is able to check separately the different ingredients of a transport code. In this second publication of the code evaluation project, we only consider the two-body collision term; i.e., we perform cascade calculations.

INSPIREWe address a discrepancy between different computations of η/s (shear viscosity over entropy density) of hadronic matter. Substantial deviations of this coefficient are found between transport approaches mainly based on resonance propagation with finite lifetime and other (semianalytical) approaches with energy-dependent cross sections, where interactions do not introduce a timescale. We provide an independent extraction of this coefficient by using SMASH, which is an example of a mainly resonance-based approach. Our conclusion is that the hadron interaction via resonance formation/decay strongly affects the transport properties of the system, resulting in significant differences in η/s with respect to other approaches where binary collisions dominate.

INSPIREMotivated by a recent finding of an exact solution of the relativistic Boltzmann equation in a Friedmann–Robertson–Walker spacetime, we implement this metric into SMASH. We study the numerical solution of the transport equation and compare it to this exact solution for massless particles. Having passed these checks for the SMASH code, we study a gas of massive particles within the same spacetime, where the particle decoupling is forced by the Hubble expansion. The results might be of interest for their potential application to relativistic heavy-ion collisions, for the characterization of the freeze-out process in terms of hadron properties.

INSPIREAt high densities, the assumption of binary interactions often used in hadronic transport approaches may not be applicable anymore. Therefore, we effectively simulate the high-density regime using the local forced canonical thermalization. This framework provides the opportunity to interpolate in a dynamical way between two different limits of kinetic theory: the dilute gas approximation and the ideal fluid case. This approach will be important for studies of the dynamical evolution of heavy ion collisions at low and intermediate energies as experimentally investigated at the beam energy scan program at RHIC, and in the future at FAIR and NICA.

INSPIRETalk by Hannah Petersen at Quark Matter 2018 on May 5th 2018

Microscopic transport approaches are the tool to describe the non-equilibrium evolution in low energy collisions as well as in the late dilute stages of high energy collisions. In this talk, a newly developed hadronic transport approach is introduced.

SlidesTalk by Anna Schäfer at DPG Spring Meeting 2019 on March 22nd 2019

In this talk, a novel hadronic transport approach, SMASH, is presented. It can be applied to microscopically describe the non-equilibrium evolution of low-energy heavy-ion collisions and the late-stage rescattering phase of high-energy collisions.

SlidesTalk by Hannah Elfner at Beijing Seminar Series on September 22nd 2020

In this talk, all ingredients of SMASH are explained, an overview over the validation procedure is given as well as results for particle production at SIS-18 energies are reviewed. The current findings on electromagnetic probes are presented as well as the results for several transport coefficients are discussed. An outlook on future developments is included in addition.

Slides- Download the code on our GitHub page
- File bugs and feature request as issues on GitHub
- For everything else:
*elfner(at)itp.uni-frankfurt.de*(Prof. H. Elfner)