EPOSir+PHSDe in Heavy-Ion Collisions

• The paper demonstrates that final-state observables, such as rapidity distributions and elliptic flow, are more strongly influenced by dynamical evolution than by the initial conditions.
• It employs a rope-based reorganization to convert EPOS-derived prehadrons for compatibility with PHSD transport, effectively mitigating the overproduction of hadrons.
• Systematic comparisons show that while EPOSir+PHSDe inherits EPOS-like initial fluctuations, the subsequent PHSD evolution results in softer spectra and reduced anisotropy.

Searching arXiv for the EPOSir+PHSDe paper and closely related heavy-ion modeling work. arXiv.search {"query":"ti:\"Disentangling Initial-State and Evolution Effects in Heavy-Ion Collisions Using EPOS and PHSD\" OR (Jafarpour et al., 5 Sep 2025)","max_results":5,"sort_by":"submittedDate","sort_order":"descending"} Searching for related EPOS/PHSD arXiv papers to situate the hybrid method in context. arXiv.search {"query":"EPOS PHSD heavy-ion collisions initial conditions hydrodynamics transport","max_results":10,"sort_by":"relevance","sort_order":"descending"} EPOSir+PHSDe is a hybrid calculation designed to disentangle the relative importance of initial conditions and subsequent dynamical evolution in relativistic heavy-ion collisions. It combines the EPOS4 initial stage, denoted EPOSi, with the PHSD microscopic transport evolution, denoted PHSDe, by taking EPOS-derived prehadrons as input to PHSD after an intermediate rope-based reorganization of the dense core. In this construction, EPOS and PHSD are not treated merely as alternative event generators; they become components of a controlled comparison in which one can contrast identical initial conditions with different evolution, or different initial conditions with similar evolution. For Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV, the central conclusion is that final-state rapidity distributions, transverse-momentum spectra, and elliptic flow are influenced more strongly by the dynamical evolution than by the detailed initial state (Jafarpour et al., 5 Sep 2025).

1. Conceptual definition and comparative role

EPOSir+PHSDe was introduced as a “control experiment” for separating two ingredients that are usually entangled within a single collision model: the initial stage and the evolution stage. The hybrid uses EPOS initial conditions—more precisely, the EPOS4 initial stage EPOSi with its multiple-parallel-scattering S-matrix picture—but evolves them with PHSD transport rather than with EPOS hydrodynamics. Because EPOSi cannot be inserted directly into PHSD without modification, the authors first add the EPOS rope procedure, producing EPOSir (“EPOSi + ropes”), and then extrapolate the resulting prehadrons into the PHSD coordinate system for transport evolution (Jafarpour et al., 5 Sep 2025).

The comparative logic of the construction is explicit. EPOS versus EPOSir+PHSDe isolates the effect of different evolution under the same initial conditions. EPOSir+PHSDe versus PHSD isolates the effect of different initial conditions under similar transport evolution. This makes EPOSir+PHSDe neither a simple variant of EPOS nor a simple initialization option inside PHSD. Its purpose is methodological: it is built to expose which stage of the calculation most strongly controls the final observables.

A plausible implication is that EPOSir+PHSDe should be understood less as a new autonomous theory of heavy-ion dynamics than as an instrument for model discrimination. In that sense, its significance lies in comparative inference rather than in replacing either parent framework.

2. Parent frameworks and the hybrid architecture

The parent models differ fundamentally in both early-time modeling and late-time dynamics. EPOS starts from instantaneous parallel scatterings in an S-matrix formalism. Elementary interactions are modeled as Pomerons, interpreted as parton ladders, with dynamical saturation and strong initial density fluctuations. EPOS then performs a core-corona separation; the core is assumed to rapidly equilibrate and undergo relativistic viscous hydrodynamics, followed by microcanonical hadronization and a hadronic cascade with UrQMD. PHSD, by contrast, begins from independent primary nucleon-nucleon collisions described by a LUND string model with FRITIOF/PYTHIA and evolves the system through fully microscopic off-shell transport based on Kadanoff–Baym equations, using the DQPM description of the QGP (Jafarpour et al., 5 Sep 2025).

The resulting hybrid keeps the EPOS-style fluctuating initialization while discarding the EPOS hydrodynamic evolution in favor of PHSD transport. Its architecture can be summarized compactly:

Approach	Initial state	Evolution
EPOS	Instantaneous parallel scatterings in an S-matrix framework; Pomerons; core-corona separation	Viscous hydrodynamics, microcanonical hadronization, UrQMD
PHSD	Independent primary $NN$ scatterings via LUND string model with FRITIOF/PYTHIA	Fully microscopic transport with off-shell partons and hadrons
EPOSir+PHSDe	EPOSi plus ropes, converted into PHSD-compatible prehadrons	PHSD transport

Within this three-way comparison, the characteristic outcomes differ in a systematic way. EPOS builds strong radial and elliptic flow, especially at intermediate $p_T$. PHSD yields good low-$p_T$ behavior but tends toward softer spectra and reduced flow at intermediate and high $p_T$. EPOSir+PHSDe inherits EPOS-like initial fluctuations, yet its final observables lie much closer to PHSD than to EPOS, which is the central physical message of the study.

3. Construction of EPOSir and transfer into PHSD

The initialization problem is central to the hybrid. In EPOSi, primary scatterings occur instantaneously at $t=0$, and cut Pomerons generate flux tubes or string objects that break into string segments, i.e. prehadrons. EPOS then applies a core-corona separation through an energy-loss estimate along the segment trajectory,

$$P_{t}^{new} = P_{t} - f_{Eloss} \int_{\gamma} \rho\, dL,$$

where $\gamma$ is the trajectory, $P_t$ is the string-segment transverse momentum, $f_{Eloss}$ is a constant, and $NN$0 is the local string density. Segments with $NN$1 escape and become corona; segments with $NN$2 are trapped and assigned to the core (Jafarpour et al., 5 Sep 2025).

For EPOSir, the core is reorganized into ropes, namely connected high-density regions of fused strings. These ropes are broken into clusters slice-by-slice in space-time rapidity $NN$3, which the paper explicitly defines as

$NN$4

The rope slices are then microcanonically decayed into hadrons, referred to in the paper as rope core prehadrons.

This rope procedure is not an aesthetic modification; it solves a concrete consistency problem. Passing EPOSi directly into PHSD was found to overproduce hadrons severely: the paper states that direct EPOSi+PHSDe gives roughly twice as many hadrons as experiment. The reason given is that hydrodynamic EPOS normally converts a substantial part of the initial energy into collective flow and work, thereby reducing multiplicity. The rope construction compensates by converting part of the initial mass production into kinetic energy or flow already at the initialization stage.

To insert EPOS-derived prehadrons into PHSD, the positions are extrapolated back to the PHSD start time according to

$NN$5

where $NN$6 and $NN$7 are the position and velocity at production time $NN$8. Corona prehadrons are inserted directly in this way. For rope-core prehadrons, the decay products are placed at the positions of their parent string segments so that the intended energy-density profile is preserved on the PHSD initial grid.

Once initialized, PHSD applies its local critical-energy-density criterion,

$NN$9

If the local energy density exceeds $p_T$0, core prehadrons melt into partons; if it does not, they remain hadronic. For $p_T$1 GeV, the paper reports that almost all prehadrons melt within the first few PHSD time steps, with the partonic phase beginning around $p_T$2 fm/$p_T$3.

4. Evolution diagnostics and momentum eccentricity

To quantify how pressure gradients develop during the collision, the study uses the momentum eccentricity $p_T$4,

$p_T$5

with $p_T$6, $p_T$7, and $p_T$8 the cell energy density (Jafarpour et al., 5 Sep 2025).

In EPOS, the energy-momentum tensor is written as

$p_T$9

and the local energy density is extracted from the local rest frame through $p_T$0. In PHSD and EPOSir+PHSDe, the paper instead employs a cell-based estimate

$p_T$1

with $p_T$2 fm and $p_T$3 fm, and in the center-of-mass frame

$p_T$4

The time evolution of $p_T$5 provides one of the clearest discriminants among the models. EPOS exhibits a strong and continuous increase of momentum eccentricity, together with large event-by-event fluctuations; the average rises monotonically. EPOS with $p_T$6 shows a similar but somewhat reduced growth. PHSD saturates much earlier, around $p_T$7 fm/$p_T$8, and fluctuates less. EPOSir+PHSDe begins with stronger initial fluctuations inherited from EPOS, but the PHSD transport stage dominates the subsequent evolution and drives $p_T$9 toward a saturation value close to PHSD.

This comparison directly supports the article’s central inference: the initial geometry and its fluctuations are not irrelevant, but the mechanism by which the system evolves that geometry into momentum-space anisotropy is more decisive for the final pressure anisotropy.

5. Final-state observables in Au+Au collisions at $p_T$0 GeV

The analysis focuses on rapidity, transverse-momentum spectra, and flow harmonics $p_T$1. For charged-particle pseudorapidity distributions $p_T$2, PHSD reproduces BRAHMS data very well across centrality classes and matches the shape. EPOS also reproduces the data reasonably well, although its $p_T$3 distribution is generally narrower. EPOSir+PHSDe yields slightly more particles near midrapidity and agrees well with semi-peripheral data. For identified-hadron rapidity densities, all three models slightly overpredict pions and kaons, the light-meson distributions are somewhat broader than the data, proton and antiproton trends are qualitatively correct, EPOSir+PHSDe gives the net-proton rapidity distribution closest to BRAHMS when averaged over the weak-decay uncertainty, and PHSD tends to be somewhat higher than the others in forward rapidity (Jafarpour et al., 5 Sep 2025).

For transverse mass and transverse momentum spectra, the systematic pattern is again comparative rather than absolute. All three models reproduce pion and kaon spectra well, especially at low $p_T$4. EPOS best reproduces the STAR $p_T$5 spectra for protons and antiprotons. At intermediate and high $p_T$6, EPOS describes the data best, whereas PHSD and EPOSir+PHSDe become increasingly softer and undershoot the data. The paper attributes this to the strong early hydrodynamic flow in EPOS, generated by the core-corona separation and early equilibration, which hardens the spectra, especially for heavier particles. PHSD’s microscopic transport and hadronization lead instead to softer spectra. Crucially, EPOSir+PHSDe remains much closer to PHSD than to EPOS despite starting from EPOS-like initial conditions.

The elliptic flow analysis uses the standard Fourier decomposition

$p_T$7

with

$p_T$8

For $p_T$9 of pions, kaons, and protons, EPOS gives the best overall description of the PHENIX data over the full $t=0$0 range. PHSD reproduces proton $t=0$1 reasonably well and kaons up to about $t=0$2 GeV/$t=0$3, while pions begin to deviate above $t=0$4 GeV/$t=0$5. EPOSir+PHSDe lies closer to PHSD and is slightly lower for pions and kaons and for high-$t=0$6 protons. For $t=0$7 of charged hadrons, EPOS and PHSD both describe the PHOBOS data reasonably well at midrapidity, EPOSir+PHSDe is slightly lower, and EPOS produces a wider and more non-Gaussian profile.

A particularly explicit conclusion emerges from these comparisons: EPOS and EPOSir+PHSDe start from similar initial conditions but diverge because their dynamics differ, whereas EPOSir+PHSDe and PHSD start from different initial conditions but end up similar because their evolution is similar.

6. Interpretation, model implications, and common misconceptions

The principal conclusion of the study is that final-state bulk observables and elliptic flow are controlled more strongly by the dynamical evolution than by the detailed initial conditions. This statement is not based on a single observable; it is supported by the paired comparisons that the hybrid was designed to enable. When the initial state is held approximately fixed and the evolution is changed, the final spectra and flow change substantially. When the evolution is held similar and the initial state is changed, the final observables remain comparatively close (Jafarpour et al., 5 Sep 2025).

One common misconception is that sufficiently detailed initial-state fluctuations alone determine the final anisotropic flow pattern. The EPOSir+PHSDe comparison argues against that simplification. The hybrid inherits stronger initial fluctuations from EPOS, yet the later PHSD transport drives the system toward PHSD-like observables. This suggests that initial-state information is filtered through the specific transport or hydrodynamic response of the medium rather than being mapped directly into the final hadron distributions.

A second misconception would be to interpret EPOSir+PHSDe as a straightforward fusion of the “best parts” of EPOS and PHSD. The paper instead presents it as a deliberately constructed hybrid whose value lies in diagnosis. Its rope-based initialization is introduced because a direct insertion of EPOSi into PHSD badly overproduces multiplicity, and its final-state similarity to PHSD is therefore part of the physical result, not merely a technical accident.

The paper also clarifies the role of the core-corona split and viscosity inside EPOS. For spectra and $t=0$8, the core carries the strong collective flow, while the corona contributes little anisotropy; the corona-only $t=0$9 is near zero. Adding core and corona reduces the pure-core signal, and hadronic rescattering further modifies the final observables, typically increasing $$P_{t}^{new} = P_{t} - f_{Eloss} \int_{\gamma} \rho\, dL,$$0 somewhat. The comparison between $$P_{t}^{new} = P_{t} - f_{Eloss} \int_{\gamma} \rho\, dL,$$1 and $$P_{t}^{new} = P_{t} - f_{Eloss} \int_{\gamma} \rho\, dL,$$2 in EPOS shows only modest differences: larger viscosity makes spectra slightly harder and pseudorapidity densities slightly higher, while leaving the qualitative behavior unchanged.

Taken together, these results place EPOSir+PHSDe within the broader methodological problem of heavy-ion phenomenology: identifying which aspects of a successful event description stem from initialization and which stem from the response dynamics. Within the limits of the Au+Au, $$P_{t}^{new} = P_{t} - f_{Eloss} \int_{\gamma} \rho\, dL,$$3 GeV study, the paper’s answer is unambiguous. The initial state matters, especially for the amplitude and fluctuations of anisotropic geometry, but the dominant control over the final hadron spectra and elliptic flow comes from the subsequent dynamical evolution.