he soup that is not too ho



Introduction
============

Studies of the properties of the strongly interacting matter are the goals of many experiments worldwide. The investigation of the so-called "hottest soup" - Quark-Gluon Plasma (QGP) - attracted nearly the full attention of heavy-ion physicists. Recently, the relatively colder and "denser" regions of the QCD phase diagram (shown in Fig. \[fig1\]a) gained the interest of the community, still having many unrevealed puzzles such as transitions between partonic and hadronic states or description of Neutron Stars (NS) and Neutron Star Mergers (NSM) Equation of State (EoS). This paper briefly summarizes the most vital experimental discoveries in that diagram region.

\[h!\] ![image](Figures/Fig1.png){width="90.00000%"}

Onset of QGP
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#### Nuclear modification factor:

The non-monotonic collision energy dependence of nuclear modification factor $R_{cp}$ is one of the possible signatures of the disappearance of the partonic degrees of freedom. It is described with the following equation: $$R_{CP} = \frac{\langle N^{per}_{bin}\rangle d^3N^{cen}_{AA}/d\eta d^2p_T}{\langle N^{cen}_{bin} \rangle d^3N^{per}_{AA}/d\eta d^2p_T}
    \label{R_cp}$$ The most peripheral AA collisions are expected to mimic the NN collisions and are used in the following studies due to the lack of data for proton-proton collisions at such a big range of collision energies. When the values of $R_{CP}$ are lower than unity, the matter expansion is suppressed. The opacity of the partonic deconfined medium explains it. On the other hand, the enhanced $R_{CP}$ is expected to be the effect of the domination of the hadronic interactions. The results obtained at STAR experiment @STAR:2017ieb are shown in the Fig. \[fig1\]b. The clear $\sqrt{s_{NN}}$ dependence is visible. The suppression of $R_{CP}$ is treated as a signature of the presence of the QGP phase for the higher energies.

#### Kink, horn, step:

In @Gazdzicki:1998vd authors suggested that according to the Statistical Model of the Early Stage (SMES), where a number of heavy flavors and whole entropy are the same before and after hadronization, measurements of entropy, strangeness, and temperature of the system in the function of Fermi energy are vital for the investigation of the onset of QGP. The changes in slopes of three quantities are explained as the activation of the partonic degrees of freedom, which is sketched in Fig. \[fig:kink\]. The NA61/SHINE collaboration used pions' production as a proxy for the entropy, charged kaons to pions ratio to stand for strangness to entropy, finally, and the temperature extracted from the inverse slope parameter of transverse mass spectra. Obtained results (see Fig. \[fig:kink\_exp\]) are in remarkable agreement with the theoretical predictions. The slope changes are present for the AA collisions, while, in the case of p+p, where the QGP phase is not expected, are negligible.

![image](Figures/kink.png){width="70.00000%"}

![image](Figures/kink_exp.png){width="90.00000%"}

First order phase transition
============================

#### Directed flow of protons:

$v_1$ is sensitive to the early stage of collision and compression of the medium. The $v_1$ slope in function of rapidity for all the hadrons does not change with the energy of the collision, except of protons @STAR:2014clz. A system undergoing a $1^{st}$ order phase transition characterized by the small pressure gradient due to mix phase formation causes the change of sign in the slope of $dv_1/dy$ for net baryons and/or due to softening of the EoS @Ohnishi:2017xjg. STAR performed the detailed measurements of $v_1$ for various collisions energies and the non-monotonic trends are visible (Fig. \[fig:cumulants\_exp\]a). It is treated as a signature of the first order phase transition and justified additionally by lack of agreement with the UrQMD simulations @Bleicher:1999xi, where the transition is not included.

![image](Figures/star_12.png){width="80.00000%"}

Critical Point
==============

#### Fluctuations of net-baryon distributions:

The non-monotonic behavior in the event-by-event fluctuations of globally conserved quantities is treated as one of the signatures of the presence of the Critical Point (CP) @Sombun:2017bxi [@Luo:2017faz]. The higher the cumulant order, the more sensitive it is to the correlation length. $4^{th}$ order is predicted predicted to have a non-monotonic energy dependence due to contribution from the CP. The observed in @STAR:2021fge $C_4/C_2$ suppression consistent with fluctuations driven by baryon number conservation indicates the domination of hadronic interaction - visible for lower $\sqrt{s_{NN}}$ in Fig. \[fig:cumulants\_exp\]b.

Neutron stars and neutron star mergers
======================================

#### Virtual photons:

Moving further on the phase diagram towards the higher baryon densities and lower temperatures, there is a region corresponding to NS ($T<10$ MeV, $\rho<10 \rho_0$[^1],) and NSM ($T<50$ MeV, $\rho<2-6 \rho_0$). The systems with similar properties ($T: 80-100$ MeV, $\rho<2-3 \rho_0$) can be created in the HADES experiment, what can serve as a reference for the astrophysical research of NS and NSM. The production of virtual photons, which are expected to be created during the whole evolution of the system's evolution can provide the information about the temperature of the system and consequently contribute to the process of EoS determination. In the Fig. \[fig:hades\]a, HADES used the reconstructed $e^+e^-$ mass distribution as a manifestation of virtual photons @HADES:2019auv. The obtained excess radiation (Fig. \[fig:hades\]b) shows nearly-exponential fall-off. The extracted temperature of the system's evolution is equal to $T = 71.8\pm 2.1$ MeV/$k_B$, while theoretical models predict the $T=50-80 $ MeV of the post-merger NS around the dense remnant core.

![image](Figures/hades_photons.png){width="70.00000%"}

Conclusions
===========

Many observables were investigated, providing an excellent reference for the theoretical studies of properties of the strongly interacting matter and its transitions. The impressive spectrum of data collected by STAR, NA61/SHINE, and HADES experiments is still under investigation, possibly leading to ground-breaking discoveries and establishing the EoS valid for the whole QCD phase diagram.

Acknowledgments
===============

I want to acknowledge the financial support of IDUB-POB-FWEiTE-3 project granted by Warsaw University of Technology under the program Excellence Initiative: Research University (ID-UB). This work is supported by the scholarship grant from the GET$\_$INvolved Programme of FAIR/GSI.

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[^1]: $\rho_0 \approx 0.16 fm^{-3}$ - density of normal matter

{'source': 'arXiv_out/2209'}