Hadronic Transport Approach Research Articles

SMASH as an event generator for heavy-ion collisions

In this article we present an overview of the SMASH hadronic transport approach that is applied for non-equilibrium dynamics of hadrons in heavy-ion collisions. We will give an overview about the ingredients of the approach and the applications for the dynamical description of heavy-ion collisions and for calculations of fundamental properties of the hadron gas. The main emphasis of the article will be the infrastructure for sustainable software development that we have developed over the last 10 years including extensive unit tests and continuous integration. We will also provide one section about the performance of the code and how it can be analyzed and improved in the future.

Global angular momentum generation in heavy-ion reactions within a hadronic transport approach

Global angular momentum generation in heavy-ion reactions within a hadronic transport approach

Collisional Broadening within a Hadronic Transport Approach

We explore the emergence of the collisional broadening of hadrons under the influence of different media using the hadronic transport approach SMASH (Simulating Many Accelerated Strongly interacting Hadrons), which employs vacuum properties and contains no a priori information about in-medium effects. In this context, we define collisional broadening as a decrease in the lifetime of hadrons, and it arises from an interplay between the cross-sections for inelastic processes and the available phase space. We quantify this effect for various hadron species, in both a thermal gas in equilibrium and in nuclear collisions. Furthermore, we distinguish the individual contribution of each process and verify the medium response to different vacuum assumptions; we see that the decay width that depends on the resonance mass leads to a larger broadening than a mass-independent scenario.

Impact of hadronic interactions and conservation laws on cumulants of conserved charges in a dynamical model

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 the BNL Relativistic Heavy Ion Collider (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 are 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 calculations which are often performed in a grand canonical ensemble.

Temperature and net baryochemical potential dependence of η/s in a hybrid approach

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.

The applicability of hydrodynamics in heavy ion collisions at sqrt{s_mathrm{NN}} = 2.4–7.7 GeV

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}_mathrm{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.

Role of proton-antiproton regeneration in the late stages of heavy-ion collisions

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 $5\ensuremath{\pi}\ensuremath{\rightarrow}\mathrm{p}\overline{\mathrm{p}}$. We investigate $\mathrm{Au}+\mathrm{Au}$ and $\mathrm{Pb}+\mathrm{Pb}$ collisions from $\sqrt{{s}_{NN}}=17.3\phantom{\rule{4pt}{0ex}}\mathrm{GeV}\ensuremath{-}5.02$ 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.

Harmonic flow correlations in Au+Au reactions at 1.23 AGeV: a new testing ground for the equation-of-state and expansion geometry

Correlations between the harmonic flow coefficients v_1, v_2, v_3 and v_4 of nucleons in semi-peripheral Au+Au collisions at a beam energy of 1.23 AGeV are investigated within the hadronic transport approach ultra-relativistic quantum molecular dynamics (UrQMD). In contrast to ultra-relativistic collision energies (where the flow coefficients are evaluated with respect to the respective event plane), we predict strong correlations between the flow harmonics with respect to the reaction plane. Based on an event-by-event selection of the midrapidity final state elliptic flow of nucleons we show that as a function of rapidity, (I) the sign of the triangular flow changes, (II) that the shape of v_4 changes from convex to concave, and (III) that v_3propto v_1v_2 and v_4propto v_2^2 for all different event classes, indicating strong correlations between all investigated harmonic flow coefficients.

Collective flow at SIS energies within a hadronic transport approach: Influence of light nuclei formation and equation of state

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 behavior. 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 $\text{Au}+\text{Au}$ collisions at ${E}_{\mathrm{lab}}=1.23A$ 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 behavior. This study establishes the current understanding of collective behavior 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.

Deuteron production in relativistic heavy ion collisions via stochastic multiparticle reactions

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.

Strangeness-neutral equation of state for QCD with a critical point

We present a strangeness-neutral equation of state for QCD that exhibits critical behavior and matches lattice QCD results for the Taylor-expanded thermodynamic variables up to fourth order in $$\mu _B/T$$ . It is compatible with the SMASH hadronic transport approach and has a range of temperatures and baryonic chemical potentials relevant for phase II of the Beam Energy Scan at RHIC. We provide an updated version of the software BES-EoS, which produces an equation of state for QCD that includes a critical point in the 3D Ising model universality class. This new version also includes isentropic trajectories and the critical contribution to the correlation length. Since heavy-ion collisions have zero global net-strangeness density and a fixed ratio of electric charge to baryon number, the BES-EoS is more suitable to describe this system. Comparison with the previous version of the EoS is thoroughly discussed.

Particle production in AgAg collisions at EKin=1.58A 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 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.

Constraining resonance properties through kaon production in pion–nucleus collisions at low energies

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 kin = 1.7 GeV (Adamczewski-Musch et al 2019 Phys. Rev. Lett. 123 022002). 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.

A Non-Equilibrium Approach to Photon Emission from the Late Stages of Relativistic Heavy-Ion Collisions

Cross sections for photon production in hadronic scattering processes have been calculated according to an effective chiral field theory. For π + ρ → π + γ and π + π → ρ + γ 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 ω mesons are found to contribute significantly to the total photon production. Finally, the impact of considering the finite width of the ρ 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.

Influence of the neutron-skin effect on nuclear isobar collisions at energies available at the BNL Relativistic Heavy Ion Collider

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.

Particle production via strings and baryon stopping within a hadronic transport approach

The stopping of baryons in heavy ion collisions at beam momenta of plab = 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-requisite 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 xF 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.

Jet quenching in the hadron gas: An exploratory study

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.

Strangeness production via resonances in heavy-ion collisions at energies available at the GSI Schwerionensynchrotron

Production of strange hadrons in elementary and heavy-ion reactions is studied with the hadronic transport approach SMASH (Simulating Many Accelerated Strongly-interacting Hadrons). 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 ($E_\text{kin} = 1-2A\,\text{GeV}$) 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.

Benchmarking a nonequilibrium approach to photon emission in relativistic heavy-ion collisions

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.

SMASH – A new hadronic transport approach

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.