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We investigate the long-standing question of the effect of proton-antiproton annihilation on the (anti-)proton yield, while respecting detailed balance for the five-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 is used to account for the regeneration of (anti-)protons via 5π→p¯p. We investigate Au+Au and Pb+Pb collisions from √sNN=17.3GeV−5.02 TeV in a viscous hybrid approach. Our results show that back-reactions happen for a fraction of 15%–20% of all annihilations, independent of the beam energy or centrality of the system. The inclusion of the back-reaction results in the regeneration of half of the (anti-)proton yield lost to annihilations at midrapidity. We also find that, concerning the multiplicities, treating the back-reaction as a chain of two-body reactions is equivalent to a single 5-to-2 reaction.

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.

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.

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. Here, a newly developed hadronic transport approach, SMASH (Simulating Many Accelerated Strongly-interacting Hadrons) is introduced. The overall bulk dynamics in low energy heavy ion collisions is shown including the excitation function of elliptic flow employing several equations of state. The implications of this new approach for dilepton production are discussed and preliminary results for afterburner calculations at the highest RHIC energy are presented and compared to previous UrQMD results. A detailed understanding of a hadron gas with vacuum properties is required to establish the baseline for the exploration of the transition to the quark-gluon plasma in heavy ion collisions at high net baryon densities.

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.