Whereas elementary processes such as electron-positron annihilation and electron-nucleon scattering in EPOS4 are following standard procedures found in textbooks, the theoretical framework of both proton-proton and nucleus-nucleus scattering is quite unique, based on the (obvious!) fact that at very high energies, multiple (nucleonic or partonic) primary scatterings must happen in parallel, and not sequentially.

The EPOS4 approach brings together ancient knowledge about S-matrix theory (to deal with parallel scatterings) and modern concepts of perturbative QCD and saturation, going much beyond the usual factorization approach. The parallel scattering principle requires sophisticated Monte Carlo techniques, inspired by those used in statistical physics to investigate the Ising model.

Since 2 decades we know: Colliding heavy ions at relativistic energies behave like an expanding fluid. Huge transverse flow seems to be created, being in particular asymmetric (elliptical, triangular ...) which translates into flow harmonics v2, v3 etc. These are clear signatures of a "collective expansion".

We see as well "statistical particle production", a behavior being very different compared to "normal" particle production from string decay.

But similar collective or thermal features show up also at low energies, even for heavy flavor particles, and as well in small systems (pp). In the latter case, simulations indicate that we produce very short-lived "matter" with an energy density more than 1000 times bigger than the one in neutron stars.

More details (Slides)From very elementary considerations it is clear that multiple (nucleonic or partonic) primary scatterings must happen in parallel. This has very important consequences concerning the theoretical tools to be used for a realistic modeling of heavy ion collisions and proton-proton scattering.

For heavy ion collisions, treating collisons in parallel (as implemented in EPOS) is certainly mandatory at the LHC, but even at RHIC down to the BES energy range.

The reason is the fact that the nuclear reaction time, due to a gamma factor, becomes small compared to the formation time of particles.In case of proton-proton collisions, the discussion is a bit more involved, but also here large gamma factors require multiple parton scatterings to happen in parallel.

More details (Slides) (paper: arXiv)

A natural and intuitive way to implement and understand parallel scatterings is provided by S-matrix theory. It is easy to understand why and how even complicated parallel scattering scenarios (like muli-dijet production),

due to an enormous amount of cancellations, end up with simple expressions which amounts to single scattering

BUT only for inclusive cross sections (factorization) and NOT in general.

The challenge for EPOS: Use the full parallel scattering scenario, but in a smart way such that for inclusive cross section the cancellations actually work. This was finally achieved (→EPOS4), based on dynamical saturation scales.

More details (Paper) NEW!

More details (Slides)

A natural and intuitive way to implement and understand parallel scatterings is provided by S-matrix theory. It is easy to understand why and how even complicated parallel scattering scenarios (like muli-dijet production),

due to an enormous amount of cancellations, end up with simple expressions which amounts to single scattering

BUT only for inclusive cross sections (factorization) and NOT in general.

The challenge for EPOS: Use the full parallel scattering scenario, but in a smart way such that for inclusive cross section the cancellations actually work. This was finally achieved (→EPOS4), based on dynamical saturation scales.

More details (Paper) NEW!

More details (Slides)

Whereas the main purpose of EPOS4 is the realization of a consistent framework for parallel primary scatterings, several of the new elements, like the way saturation and the partonic spacelike cascade is implemented, affect heavy flavor results, like inclusive spectra of heavy flavor hadrons, or the multiplicity dependence of charmed mesons in proton-proton scattering,

where in the latter case, the strong non-linear increase is due to saturation and fluid effects.

More details (Papers)

where in the latter case, the strong non-linear increase is due to saturation and fluid effects.

More details (Papers)

The multiplicity dependence of multi-strange hadron yields in proton-proton and lead-lead collisions at several TeV allows to study the transition from very big to very small systems, in particular concerning collective effects.

We investigate this, employing new microcanonical hadronization procedures in the EPOS4 framework, as well as new methods allowing to transform energy-momentum flow through freeze-out surfaces into invariant mass elements.

We disentangle effects due to “canonical suppression” and “core-corona effects”, which both lead to a reduction of the yields at low multiplicity.

The average transverse momenta are affected by flow and saturation effects.

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We investigate this, employing new microcanonical hadronization procedures in the EPOS4 framework, as well as new methods allowing to transform energy-momentum flow through freeze-out surfaces into invariant mass elements.

We disentangle effects due to “canonical suppression” and “core-corona effects”, which both lead to a reduction of the yields at low multiplicity.

The average transverse momenta are affected by flow and saturation effects.

More details (Papers)

A very elementary discussion based on time scales shows that a parallel scattering formalism (as in EPOS4) should be employed for nucleus-nucleus (AA) collisions above 20-30 AGeV, whereas sequential scattering (cascade) is appropriate below 4 AGeV. Between these limits, partially parallel scattering is needed – not (yet) considered in EPOS4.

We simulate AA collisions from 5.02 TeV down to 4 GeV, in order to understand to what extent the model is compatible with experimental data, a necessary condition to allow conclusions about the disappearance of the fluid component at low energies.

This fluid contribution actually drops very strongly below 11AGeV. However, for more reliable statements, the partially parallel scattering needs to be implemented.

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We simulate AA collisions from 5.02 TeV down to 4 GeV, in order to understand to what extent the model is compatible with experimental data, a necessary condition to allow conclusions about the disappearance of the fluid component at low energies.

This fluid contribution actually drops very strongly below 11AGeV. However, for more reliable statements, the partially parallel scattering needs to be implemented.

More details (Papers)

The EPOS4 approach for high energy collisons amounts to primary (parallel) scatterings, followed by a core-corona separation, with a hydrodynamic evolution of the core part, the latter one being very time-consuming, even for small systems. We provide a “shortcut” in the sense that the hydrodynamical evolution is replaced by a parameterized fluid expansion (PFE), without changing anything else. A relatively simple parameterization allows to get results very close to the full simulation.

The purpose of such a PFE option is the possibility of being used for applications where the speed is crucial.

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The purpose of such a PFE option is the possibility of being used for applications where the speed is crucial.

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We continue our effort to see to what extent the model is compatible with experimental data in heavy ion collisions from 5.02 TeV down to 7.7 GeV. We try to understand in which way the role of the different components (primary interactions, hydro evolution, hadronic cascade) changes when we go down in energy up to the point where the plasma component disappears. Here, we focus on flow observables.

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We investigate here the system size dependence of flow harmonics, to better understand collectivity when going from big to small systems. For the moment we have PbPb results, pp will come soon. The model is not in particular tuned for flow results, it is a “general purpose” approach and the results shown here are part of a bigger project where we simulate “everything” (soft/hard probes, small/big systems, low/high energy) with the same model, same version (EPOS4.0.0).

Flow harmonics for different multiplicity classes: Flow harmonics versus pseudorapidity:

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Flow harmonics for different multiplicity classes: Flow harmonics versus pseudorapidity:

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The basic principle of treating (nucleonic or partonic) scatterings in parallel, based on S-matrix theory, has been used for two decades. But there is a major problem. For inclusive cross sections (but only for those!), important cancellations occur, leading to factorization (in pp) or binary scaling (in AA). In a parallel scattering scenario, these cancellations must come out (they cannot be imposed), which requires very high precision and good strategies -- and this is provided with EPOS4.

The treatment of parton ladders is completely redone, with unprecedented precision concerning the parton kinematics, in particular in case of heavy flavor partons being involved. Also, backward parton evolution in each of the parallel parton ladders considerably increases the precision of the generation of the "hard processes“. And this is crucial to assure all the above-mentioned cancellations.

Another crucial ingredient is the discovery that the "parallel objects“ are not simply parton ladders, but ladders with dynamical virtuality cutoffs, referred to as "saturation scales“, being fixed by some prescription that guarantees rigorously factorization and binary scaling at large transverse momenta.

As a consequence, we can compute within the EPOS framework parton distribution functions (EPOS PDFs) and use them to compute inclusive pp cross sections. The latter ones we may compare with calculations based on other known PDFs, or compared with the EPOS full Monte Carlo, as shown for pp at 13GeV in the plot below. We use a K-factor K=1 and a variable flavor number scheme.

We also use always -- for big and small systems -- microcanonical hadronization, using a new and very efficient algorithm, which allows decaying even big droplets, providing identical results compared to a grand canonical scenario. For small systems, hadrons like multi-strange baryons are suppressed. It should be noted that we do not do "particlization", but hadronization! At some given critical energy density (above the phase transition value), the plasma "decays" into (pre)hadrons, perfectly conserving energy, momentum, and flavor.