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 an add-on for the SMASH transport code. It is python-based and 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 Ekin=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.

INSPIREThe 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.

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