A combined constraint on the QCD equation of state, at high densities, from connecting neutron star observations to data from heavy ion reactions is presented. We use the Chiral Mean Field Model which can describe neutron star and iso-spin symmetric matter and allows the consistent calculation of the density and momentum dependent potentials of baryons which are then implemented in the UrQMD transport model. In contrast to previous studies, the same equation of state constrained from neutron star properties is also able to describe experimental observables in heavy ion reactions at the HADES experiment. Unlike many other approaches our results are not constraint to densities up to nuclear saturation or perturbative results which allows a continuous description of the equation of state over a large range in baryon density.

Germany

Jan Steinheimer

Manjunath Omana Kuttan

Tom Reichert

Japan

Yasushi Nara

Marcus Bleicher

Simultaneous description of high density QCD matter in heavy ion collisions and neutron star observations

<p>The energy and centrality dependence of the kaon resonance ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mo>(</mo><msup><mi>K</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup><mo>+</mo><msup><mover accent="true"><mi>K</mi><mo>¯</mo></mover><mrow><mo>*</mo><mn>0</mn></mrow></msup><mo>)</mo></mrow><mo>/</mo><mrow><mo>(</mo><msup><mi>K</mi><mo>+</mo></msup><mo>+</mo><msup><mi>K</mi><mo>−</mo></msup><mo>)</mo></mrow></mrow></math> is explored in the RHIC-BES and CBM-FAIR energy regime. To this aim, the ultrarelativistic quantum molecular dynamics model is employed to simulate reconstructable <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>K</mi><mo>*</mo></msup></math> resonances in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Au</mi><mo>+</mo><mi>Au</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mo>+</mo><mi>p</mi></mrow></math> collisions from <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>3</mn><mo>–</mo><mn>39</mn></mrow></math> GeV. We obtain a good description of the resonance yields and mean transverse momenta over the whole investigated energy range. The decrease of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>K</mi><mo>*</mo></msup><mo>/</mo><mi>K</mi></mrow></math> ratio with increasing centrality is in line with the available experimental data. We also observe the experimenatlly measured increase in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>〈</mo><msub><mi>p</mi><mtext>T</mtext></msub><mo>〉</mo></mrow></math> with increasing centrality which is interpreted as a lower reconstruction probability of low-<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>p</mi><mtext>T</mtext></msub><mspace width="4pt"></mspace><msup><mi>K</mi><mo>*</mo></msup></mrow></math> due to the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mtext>T</mtext></msub></math> dependent absorption of the decay daughter hadrons. We conclude that the observed suppression of reconstructable <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>K</mi><mo>*</mo></msup></math> resonances provides a strong sign of an extended hadronic rescattering stage at all investigated energies. Its duration increases from peripheral to central reactions as expected. Following a method, suggested by the STAR experiment, a lower bound on the duration of the hadronic stage is extracted using the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>K</mi><mo>*</mo></msup><mo>/</mo><mi>K</mi></mrow></math> ratios at chemical and kinetic freeze-out. The resulting lifetimes are in good agreement with the experimental data, but shorter than the actual lifetime of the hadronic phase in the transport simulations.</p>

Amine Chabane

Lisa Engel

Resonance suppression during the hadronic stage from the FAIR to the intermediate RHIC energy regime

<p>The UrQMD model with a density dependent equation of state, including a first-order phase transition, is used to study the time dependence of baryon number and proton number susceptibilities up to third order in heavy ion reactions of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>E</mi><mi>lab</mi></msub><mo>=</mo><mn>2</mn><mo>–</mo><mn>3</mn><mspace width="0.16em"></mspace><mi>A</mi><mspace width="0.16em"></mspace><mi>GeV</mi></mrow></math>. A significant deviation from the Gaussian fluctuations of the baryon number fluctuation in coordinate space is observed. The proton number fluctuations are always suppressed as they constitute only a small fraction of the total baryon number during the dense phase of the collision. It is found that the only measurable, but small, signal would be an enhancement of the third order (or higher) proton cumulant in a finite rapidity window <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Δ</mi><mi>y</mi></mrow></math> that is larger than one unit of rapidity. In addition, it is found that the coordinate fluctuations will lead to an enhancement of cluster production due to the correlations in coordinate space. However, this enhancement is small and mainly occurs during the dense part of the collision before the system actually freezes out.</p>

Thailand

Thiranat Bumnedpan

Christoph Herold

Ayut Limphirat

Time evolution of light nuclei cumulants and ratios with a first-order phase transition in the UrQMD transport model

We present realistic estimates for the duration of the hadronic stage in central Au+Au reactions in the RHIC-BES energy regime. To this aim, we employ a full set of coupled rate equations to describe the time evolution of the system from chemical to kinetic freeze-out. Combined with the recently measured data by the STAR collaboration on <math altimg='si1.svg'><msup><mrow><mi>K</mi></mrow><mrow><mo>&#8270;</mo></mrow></msup><mo stretchy='false'>/</mo><mi>K</mi></math> ratios, we show that the previous estimates substantially underestimated the duration of this stage due to the omission of the regeneration of hadron resonances. We provide an improved relation between the <math altimg='si1.svg'><msup><mrow><mi>K</mi></mrow><mrow><mo>&#8270;</mo></mrow></msup><mo stretchy='false'>/</mo><mi>K</mi></math> ratio at chemical and kinetic freeze-out and the life time of the hadronic phase. The calculated improved life times are now in line with estimates from other methods and are relevant for the NA61 and STAR collaborations and for upcoming experiments at the FAIR facility.

Tim Neidig

Apiwit Kittiratpattana

Carsten Greiner

Determining the duration of the hadronic stage at RHIC-BES energies via resonance suppression using a full set of rate equations

We calculate the contribution of the decay products of excited nuclear cluster states to the event-by-event fluctuations of protons in the energy range from <math altimg='si1.svg'><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi><mi>N</mi></mrow></msub></mrow></msqrt><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>2</mn><mo linebreak='goodbreak' linebreakstyle='after'>&#8722;</mo><mn>5</mn></math> GeV within the statistical model. We find that the inclusion of the excited nuclear clusters yields corrections to all cumulant ratios, ranging from 1% for ratio of second to first-order cumulant to 100% for the sixth to second order cumulant towards the lowest inspected energy. As expected the contribution of excited cluster states is most important at low energies <math altimg='si2.svg'><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi><mi>N</mi></mrow></msub></mrow></msqrt><mo linebreak='goodbreak' linebreakstyle='after'>&lt;</mo><mn>3.5</mn></math> GeV and becomes negligible at higher collision energies. Especially in light of the expected ultra-high precision data from CBM at FAIR, this new contribution is important to allow for a quantitative comparison with (potentially later available) lattice QCD or effective model results.

Czechia

Slovakia

Boris Tomášik

Excited cluster states: A new source for proton number fluctuations in the high baryon density regime

It is shown that the hadronic phase in ultra-relativistic heavy ion collisions can be used to understand the properties of the $$f_0(980)$$ resonance. In particular it is shown that the centrality dependence of the $$f_0(980)/\pi $$ and $$f_0(980)/\phi $$ ratios depends strongly on the $$f_0(980)\rightarrow {\overline{K}}+K$$ branching ratio and whether the $$f_0(980)$$ is produced as a $$\left| {\overline{q}}q \right\rangle $$ or $$\left| {\overline{s}}s \right\rangle $$ state. These conclusions are drawn from calculations within the partial chemical equilibrium of the HRG model within Thermal-FIST as well as with the fully non-equilibrium hybrid-transport approach UrQMD. Our findings show how the hadronic phase in heavy ion collisions can be used for studies of exotic hadron properties otherwise possible only in dedicated experiments such as PANDA.

United States

Volodymyr Vovchenko

The structure of the $$f_0(980)$$ from system size dependent hadronic resonance ratios in p + p, p + Pb, and Pb + Pb collisions at the LHC

We study the temporal evolution of quantum mechanical fermionic particles exhibiting one bound state within a one-dimensional attractive square-well potential in a heat bath of bosonic particles. For this open quantum system we formulate the non-equilibrium Kadanoff-Baym equations for the system particles by taking the interactions to be elastic 2-2 scatterings with the heat-bath particles. The corresponding spatially inhomogeneous integro-differential equations for the one-particle Greens's function are solved numerically. We demonstrate how the system particles equilibrate and thermalize with the heat bath and how the off-diagonal elements of the density matrix, expressed in the one-particle energy eigenbasis, decohere, so that only the diagonal entries, i.e. the occupation numbers, survive. In addition, the time evolution of the (retarded) Green's function also determines the spectral properties of the various one-particle quantum states.

Jan Rais

Hendrik van Hees

Open quantum systems with Kadanoff-Baym equations

The centrality determination and the estimated fluctuations of number of participant nucleons  $$N_{part}$$  <math> <msub> <mi>N</mi> <mrow> <mi>part</mi> </mrow> </msub> </math>   in Au–Au collisions at 1.23 AGeV beam kinetic energy suffers from severe model dependencies. Comparing the Glauber Monte Carlo (MC) and UrQMD transport models, it is shown that  $$N_{part}$$  <math> <msub> <mi>N</mi> <mrow> <mi>part</mi> </mrow> </msub> </math>   is a strongly model dependant quantity. In addition, for any given centrality class, Glauber MC and UrQMD predicts drastically different  $$N_{part}$$  <math> <msub> <mi>N</mi> <mrow> <mi>part</mi> </mrow> </msub> </math>   distributions. The impact parameter b and the number of charged particles  $$N_{ch}$$  <math> <msub> <mi>N</mi> <mrow> <mi>ch</mi> </mrow> </msub> </math>   on the other hand are much more correlated and give an almost model independent centrality estimator. It is suggested that the total baryon number balance, from integrated rapidity distributions, can be used instead of  $$N_{part}$$  <math> <msub> <mi>N</mi> <mrow> <mi>part</mi> </mrow> </msub> </math>   in experiments. Preliminary HADES data show significant differences to both, UrQMD simulations and STAR data in this respect.

Kai Zhou

Horst Stoecker

Model dependence of the number of participant nucleons and observable consequences in heavy-ion collisions

We investigate the development of the directed, <math><msub><mrow><mi>v</mi></mrow><mrow><mn>1</mn></mrow></msub></math>, and elliptic flow, <math><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub></math>, in heavy ion collisions in mid-central Au+Au reactions at <math><msub><mrow><mi>E</mi></mrow><mrow><mi>lab</mi></mrow></msub><mo>=</mo><mn>1.23</mn><mi>A</mi></math> GeV. We demonstrate that the elliptic flow of hot and dense matter is initially positive (<math><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>&gt;</mo><mn>0</mn></math>) due to the early pressure gradient. This positive <math><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub></math> transfers its momentum to the spectators, which leads to the creation of the directed flow <math><msub><mrow><mi>v</mi></mrow><mrow><mn>1</mn></mrow></msub></math>. In turn, the spectator shadowing of the in-plane expansion leads to a preferred decoupling of hadrons in the out-of-plane direction and results in a negative <math><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub></math> for the observable final state hadrons. We propose a measurement of <math><msub><mrow><mi>v</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>−</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub></math> flow correlations and of the elliptic flow of dileptons as methods to pin down this evolution pattern. The elliptic flow of the dileptons allows then to determine the early-state EoS more precisely, because it avoids the strong modifications of the momentum distribution due to shadowing seen in the protons. This opens the unique opportunity for the HADES and CBM collaborations to measure the Equation-of-State directly at 2-3 times nuclear saturation density.

Ukraine

Oleh Savchuk

China

Pengcheng Li

Mark Gorenstein

Decoding the flow evolution in Au+Au reactions at 1.23 GeV using hadron flow correlations and dileptons

The pion-to-proton ratio is identified as a potential signal for a non-equilibrium first-order chiral phase transition in heavy-ion collisions, as the pion multiplicity is directly related to entropy production. To showcase this effect, a non-equilibrium Bjorken expansion starting from realistic initial conditions along a Taub adiabat is used to simulate the entropy production. Different dynamical criteria to determine the final entropy-per-baryon number are investigated and matched to a hadron resonance gas model along the chemical freeze out curve to obtain the final pion and proton numbers. We detect a strong enhancement of their multiplicity ratio at the energies where the system experiences a strong phase transition as compared to a smooth crossover which shows almost no enhancement.

Enhanced pion-to-proton ratio at the onset of the QCD phase transition