Collision term dependence of the hadronic shear viscosity and diffusion coefficients

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

Multi-particle interactions in hadronic transport approaches

The topic of this thesis is the theoretical description of the hadron gas stages in heavy-ion collisions. The overall addressed question hereby is: How does the hadronic medium evolve i.e. what are the relevant microscopic reaction mechanisms and the properties of the involved degrees of freedom? The main goal is to address this question specifically for hadronic multi-particle interactions. For this goal, the hadronic transport approach SMASH is extended with stochastic rates, which allow to include detailed balance fulfilling multi-particle reactions in the approach. Three types of reactions are newly-accounted for: 3-to-1, 3-to-2 and 5-to-2 reactions. After extensive verifications of the stochastic rates approach, they are used to study the effect of multi-particle interactions, particularly in afterburner calculations. These studies follow complementary results for the dilepton and strangeness production with only binary reactions, which show that hadronic transport approaches are capable of describing observables when employed for the entire evolution of low-energy heavy-ion collisions. This is illustrated by the agreement of dilepton and strangeness production for smaller systems with SMASH calculations. It is, in particular, possible to match the measured strangeness production of phi and Xi hadrons via additional heavy nucleon resonance decay channels. For larger systems or higher energies, hadronic transport cascade calculations with vacuum resonance properties can point to medium effects. This is demonstrated extensively for the dilepton emission in comparisons to the full set of HADES dielectron data. The dilepton invariant mass spectra are sensitive to a medium modification of the vector meson spectral function for large collision systems already at low beam energies. The sensitivity to medium modifications is mapped out in detail by comparisons to a coarse-graining approach, which employs medium-modified spectral functions and is based on the same evolution. The theoretical foundation of stochastic rates are collision probabilities derived from the Boltzmann equation's collision term with the assumption of a constant matrix element. This derivation is presented in a comprehensive and pedagogical fashion. The derived collision probabilities are employed for a stochastic collision criterion and various detailed-balance fulfilling multi-particle reactions: the mesonic Dalitz decay back-reaction (3-to-1), the deuteron catalysis (3-to-2) and the proton-antiproton annihilation back-reaction (5-to-2). The introduced stochastic rates approach is extensively verified by studies of the numerical stability and comparisons to previous results and analytic expectations. The stochastic rates results agree perfectly with the respective analytic results. Physically, multi-particle reactions are demonstrated to be significant for different observables, most notably the yield of the partaking particles, even in the late dilute stage of heavy-ion reactions. They lead to a faster equilibration of the system than equivalent binary multi-step treatments. The difference in equilibration consequently influences the yield in afterburner calculations. Interestingly, the interpretation of results is not dependent on employing multi-particle or multi-step treatments, which a posteriori validates the latter. As the first test case of multi-particle reactions in heavy-ion reactions, the mesonic 3-to-1 Dalitz decay is found to be dominated by the omega Dalitz decay back-reaction. While the effect on the medium is found to be negligible overall, the regeneration is found to be sizable: up to a quarter of Dalitz decays are regenerated. Non-equilibrium rescattering effects are shown to be relevant for late collision stages for two particle species: deuteron and protons. In both cases, the relevant rescatterings involve multiple particles. The deuteron pion and nucleon catalysis reactions equilibrate quickly in the afterburner stage at intermediate energies. The constant formation and destruction keeps the yield constant and microscopically explains the "snowballs in hell"-paradox. The yield is also generated with no d present at early times, which explains why coalescence models can also match the multiplicity. New is the study of the 5-body back-reaction of proton-antiproton annihilations. This work marks the first realization of microscopic 5-body reactions in a transport approach to fulfill detailed balance for such reactions. A sizable regeneration due to the back-reaction of up to half of the proton-antiproton pairs lost due to annihilations is found. Consequently, both annihilation and regeneration in the late non-equilibrium stage are shown to have a significant effect on the p yield

Bulk Observables within a Hybrid Approach for Heavy Ion Collisions with SMASH Afterburner

We present a model of the dynamical evolution of relativistic heavy ion collisions, which combines second-order viscous hydrodynamics and microscopic transport. In particular, we present a hybrid approach with MUSIC hydrodynamics, and SMASH (Simulating Many Accelerated Strongly-interacting Hadrons) afterburner. In this work, we focus on low- p T hadronic observables—identified hadron p T spectra and anisotropic flow coefficients. We also demonstrate how the hadronic chemistry is altered by the hadronic non-equilibrium dynamics, for example by baryon-antibaryon annihilation. The new MUSIC + SMASH hybrid approach is also compared to existing MUSIC + UrQMD results

Effective spectral function of vector mesons via lifetime analysis

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 syste

Particle production in AgAg collisions at EKin_{Kin} = 1.58 A GeV within a hadronic transport approach

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 took data for AgAg collisions at EKin=1.58AGeV, 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 nonstrange 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 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 1.23AGeV, a hint that the smaller system at a higher energy behaves very similarly to the larger system at lower beam energy

Effective spectral function of vector mesons via lifetime analysis

Effective spectral functions of the ρ 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 ρ 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 ρ 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

Strangeness Production in Nucleus-Nucleus Collisions at SIS Energies

Simulating Many Accelerated Strongly-interacting Hadrons (SMASH) is a new hadronic transport approach designed to describe the non-equilibrium evolution of heavy-ion collisions. The production of strange particles in such systems is enhanced compared to elementary reactions (Blume and Markert 2011), providing an interesting signal to study. Two different strangeness production mechanisms are discussed: one based on resonances and another using forced canonical thermalization. Comparisons to experimental data from elementary collisions are shown

Dilepton production and resonance properties within a new hadronic transport approach in the context of the GSI-HADES experimental data

The dilepton emission in heavy-ion reactions at low beam energies is examined within a hadronic transport approach. In this article the production of electron-positron pairs from a new approach named SMASH (Simulating Many Accelerated Strongly-interacting Hadrons) is introduced. The dilepton emission is consistently taken into account below the hadronic threshold. 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 medium effects is investigated with a coarse-graining approach based on the same hadronic evolution. The effect of explicit in-medium modifications to the vector meson spectral functions is important for dilepton invariant mass spectra in ArKCl and larger systems, even though the transport approach with vacuum properties reveals similar features due the coupling to baryonic resonance and the intrinsically included collisional broadening. This article provides a comprehensive comparison of our calculations with published dielectron results from the HADES collaboration. In addition, the emission of dileptons is predicted in gold-gold and pion-beam experiments for which results are expected soon.Comment: 21 pages, 25 figures, replaced with accepted version, revised text for publication (Secs. I, III.A.2, III.B, III.C.1, III.D.2