Helmholtz Graduate School for Hadron and Ion Research

The ALICE detector is ideally suited to study the production of anti- and hyper-matter due to its excellent particle identification capabilities. The measurement of the He¯4-nucleus in Pb–Pb collisons at sNN=2.76TeV is presented. We further show the performance for the reconstruction of the (anti-)hypertriton in the decay to He3+π− (He¯3+π+). In addition to this, two searches have been performed, one for the H-Dibaryon →Λpπ− and one for the Λn bound state (Λn¯→d¯π+). No signals are observed for these exotic states and upper limits have been determined.

Although CD8+ IL-2Rbeta (CD122)+ T cells with intermediate TCR reportedly develop extrathymically, their functions still remain largely unknown. In the present study, we characterized the function of CD8+ CD122+ T cells with intermediate TCR of C57BL/6 mice. The proportion of CD8+ CD122+ T cells in splenocytes gradually increased with age, whereas CD8+ IL-2Rbeta-negative or -low (CD122-) T cells conversely decreased. The IFN-gamma production from splenocytes stimulated with immobilized anti-CD3 Ab in vitro increased with age, whereas the IL-4 production decreased. When sorted CD8+ CD122+ T cells were stimulated in vitro by the anti-CD3 Ab, they promptly produced a much larger amount of IFN-gamma than did CD8+ CD122- T cells or CD4+ T cells, whereas only CD4+ T cells produced IL-4. The depletion of CD8+ CD122+ T cells from whole splenocytes greatly decreased the CD3-stimulated IFN-gamma production and increased the IL-4 production, whereas the addition of sorted CD8+ CD122+ T cells to CD8+ CD122+ T cell-depleted splenocytes restored the IFN-gamma production and partially decreased IL-4 production. It is of interest that CD8+ CD122+ T cells stimulated CD4+ T cells to produce IFN-gamma. The CD3-stimulated IFN-gamma production from each T cell subset was augmented by macrophages. Furthermore, CD3-stimulated CD8+ CD122+ T cells produced an even greater amount of IFN-gamma than did liver NK1.1+ T cells and also showed antitumor cytotoxicity. These results show that CD8+ CD122+ T cells may thus be an important source of early IFN-gamma production and are suggested to be involved in the immunological changes with aging.

We show how the measured particle ratios can be used to provide nontrivial information about the critical temperature of the QCD phase transition. This is obtained by including the effects of highly massive Hagedorn resonances on statistical models, which are used to describe hadronic yields. The inclusion of Hagedorn states creates a dependence of the thermal fits on the Hagedorn temperature, ${T}_{H}$, which is assumed to be equal to ${T}_{c}$, and leads to an overall improvement of thermal fits. We find that for $\mathrm{Au}+\mathrm{Au}$ collisions at the Relativistic Heavy Ion Collider at $\sqrt{{s}_{\mathit{NN}}}=200$ GeV the best square fit measure, ${\ensuremath{\chi}}^{2}$, occurs at ${T}_{c}~176$ MeV and produces a chemical freeze-out temperature of $172.6$ MeV and a baryon chemical potential of $39.7$ MeV.

Abstract 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 $${\sqrt{s}_\mathrm{NN}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> <mml:mi>NN</mml:mi> </mml:msub> </mml:math> = 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.

Abstract The deuteron coalescence parameter $$B_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> in proton+proton and nucleus+nucleus collisions in the energy range of $$\sqrt{s_{NN}}=$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msqrt> <mml:msub> <mml:mi>s</mml:mi> <mml:mrow> <mml:mi>NN</mml:mi> </mml:mrow> </mml:msub> </mml:msqrt> <mml:mo>=</mml:mo> </mml:mrow> </mml:math> 900–7000 GeV for proton + proton and $$\sqrt{s_{NN}}=$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msqrt> <mml:msub> <mml:mi>s</mml:mi> <mml:mrow> <mml:mi>NN</mml:mi> </mml:mrow> </mml:msub> </mml:msqrt> <mml:mo>=</mml:mo> </mml:mrow> </mml:math> 2–2760 GeV for nucleus + nucleus collisions is analyzed with the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) transport model, supplemented by an event-by-event phase space coalescence model for deuteron and anti-deuteron production. The results are compared to data by the E866, E877, PHENIX, STAR and ALICE experiments. The $$B_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> values are calculated from the final spectra of protons and deuterons. At lower energies, $$\sqrt{s_{NN}}\le 20$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msqrt> <mml:msub> <mml:mi>s</mml:mi> <mml:mrow> <mml:mi>NN</mml:mi> </mml:mrow> </mml:msub> </mml:msqrt> <mml:mo>≤</mml:mo> <mml:mn>20</mml:mn> </mml:mrow> </mml:math> GeV, $$B_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> drops drastically with increasing energy. The calculations confirm that this is due to the increasing freeze-out volume reflected in $$B_2\sim 1/V$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>B</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>∼</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mi>V</mml:mi> </mml:mrow> </mml:math> . At higher energies, $$\sqrt{s_{NN}}\ge 20$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msqrt> <mml:msub> <mml:mi>s</mml:mi> <mml:mrow> <mml:mi>NN</mml:mi> </mml:mrow> </mml:msub> </mml:msqrt> <mml:mo>≥</mml:mo> <mml:mn>20</mml:mn> </mml:mrow> </mml:math> GeV, $$B_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> saturates at a constant level. This qualitative change and the vanishing of the volume suppression is shown to be due to the development of strong radial flow with increasing energy. The flow leads to strong space-momentum correlations which counteract the volume effect.

This study examined the effects of rice bran oil (RBO) on mouse intestinal microbiota and urinary isoflavonoids. Dietary RBO affects intestinal cholesterol absorption. Intestinal microbiota seem to play an important role in isoflavone metabolism. We hypothesized that dietary RBO changes the metabolism of isoflavonoids and intestinal microbiota in mice. Male mice were randomly divided into two groups: those fed a 0.05% daidzein with 10% RBO diet (RO group) and those fed a 0.05% daidzein with 10% lard control diet (LO group) for 30 days. Urinary amounts of daidzein and dihydrodaidzein were significantly lower in the RO group than in the LO group. The ratio of equol/daidzein was significantly higher in the RO group (p < 0.01) than in the LO group. The amount of fecal bile acids was significantly greater in the RO group than in the LO group. The composition of cecal microbiota differed between the RO and LO groups. The occupation ratios of Lactobacillales were significantly higher in the RO group (p < 0.05). Significant positive correlation (r = 0.591) was observed between the occupation ratios of Lactobacillales and fecal bile acid content of two dietary groups. This study suggests that dietary rice bran oil has the potential to affect the metabolism of daidzein by altering the metabolic activity of intestinal microbiota.

Abstract We investigate hadronic particle spectra and flow characteristics of heavy-ion reactions in the FAIR/NICA energy range of 1 A GeV ≤ E lab ≤ 10 A GeV within a relativistic ideal hydrodynamic one-fluid approach. The particlization is realized by sampling the Cooper-Frye distribution for a grand canonical hadron gas on a hypersurface of constant energy density. Results of the hydrodynamic calculations for different underlying equations of state are presented and compared with experimental data and microscopic transport simulations. The sensitivity of the approach to physical model inputs concerning the initial state and the particlization is studied.

Abstract We present a comparison of directed and elliptic flow data by the FOPI collaboration in Au–Au, Xe–CsI, and Ni–Ni collisions at beam kinetic energies from 0.25 to 1.5 GeV per nucleon to simulations using the SMASH hadronic transport model. The Equation of State is parameterized as a function of nuclear density and momentum dependent potentials are newly introduced in SMASH. With a statistical analysis, we show that within the present status of the SMASH transport model, the collective flow data at lower energies is in the best agreement with a soft momentum dependent potential, while the elliptic flow at higher energies requires a harder momentum dependent equation of state.

A bstract The SU(3) spin model with chemical potential corresponds to a simplified version of QCD with static quarks in the strong coupling regime. It has been studied previously as a testing ground for new methods aiming to overcome the sign problem of lattice QCD. In this work we show that the equation of state and the phase structure of the model can be fully determined to reasonable accuracy by a linked cluster expansion. In particular, we compute the free energy to 14-th order in the nearest neighbour coupling. The resulting predictions for the equation of state and the location of the critical end points agree with numerical determinations to $$ \mathcal{O} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> </mml:math> (1%) and $$ \mathcal{O} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> </mml:math> (10%), respectively. While the accuracy for the critical couplings is still limited at the current series depth, the approach is equally applicable at zero and non-zero imaginary or real chemical potential, as well as to effective QCD Hamiltonians obtained by strong coupling and hopping expansions.

The invariant mass spectra of dileptons radiated from the fireballs formed in high-energy heavy-ion collisions have been successfully used to investigate the properties of hot and dense QCD matter. Using a realistic model for the in-medium electromagnetic spectral function, we predict polarization observables and compare them to experiment. This allows, for the first time, independent tests of the longitudinal and transverse components of the virtual photon's selfenergy. While the low- and high-mass regions exhibit the expected limits of transverse and unpolarized photons, respectively, baryon-driven medium effects in the ρ -meson mass region create a marked longitudinal polarization that transits into a largely unpolarized emission from the quark-gluon plasma, thus providing a sensitive test of microscopic emission processes in QCD matter. Applications to available data from the HADES and NA60 experiments at SIS and SPS energies, respectively, are consistent with our predictions and set the stage for quantitative polarization studies at FAIR and collider energies.

HADES is a running hadron and di-electron spectrometer installed at GSI, Germany. Currently, the HADES data and trigger system is being upgraded. The main aim is an increase in the event rate capabilities by a factor of up to 20 to reach 100 kHz in light systems and 20 kHz in heavy ion reactions. The datarate will be in the order of 400 MByte/s in peak. In this context, the complete readout system has been exchanged to use optical communication. In this contribution we present a general-purpose real-time network protocol that has been developed based on our requirements. These include strong timing constraints with latencies less than 5 μs for endpoint-to-endpoint communication including up to 10 intermediate hubs in a star-like network setup. In HADES, this network connects over 500 FPGAs distributed over the whole detector. Monitoring and slow control features as well as readout and trigger transportation were joined in a single network protocol. Hence, channel multiplexing with inherent arbitration by priority is implemented. Typically, switching from one channel to another takes less than 100 ns. For slow control and monitoring, a dedicated channel provides a data bus with a virtual address space spanning the whole network. The configuration is highly flexible and thus adaptable to different experimental setups and hardware. Therefore, the network can also be used in any other experiment of the upcoming FAIR facility.

We study the &amp;mu;-&amp;mu;45-T phase diagram of the 2+1-dimensional Gross-Neveu model, where &amp;mu; denotes the ordinary chemical potential, &amp;mu;45 the chiral chemical potential and T the temperature. We use the mean-field approximation and two different lattice regularizations with naive chiral fermions. An inhomogeneous phase at finite lattice spacing is found for one of the two regularizations. Our results suggest that there is no inhomogeneous phase in the continuum limit. We show that a chiral chemical potential is equivalent to an isospin chemical potential. Thus, all results presented in this work can also be interpreted in the context of isospin imbalance.

Rhodotorula mucilaginosa are saprophytic yeast, and opportunistic infections known as human rhodotorulosis are increasing in immunocompromised patients. In this study, we isolated R. mucilaginosa from pet dogs in Japan and determined the minimum inhibitory concentrations (MICs) of antifungal drugs on these isolates to investigate the drug susceptibility pattern. All 10 isolates according to the broth microdilution (BM) assay of the Clinical and Laboratory Standards Institute (CLSI) M27-A2 were resistance to azoles and genetically close to fluconazole (FLZ)-resistant human isolates of R. mucilaginosa. Due to resistance, it is expected that treatment will be difficult if they infect humans.

In recent years Hagedorn states have been used to explain the physics close to the critical temperature within a hadron gas. Because of their large decay widths these massive resonances lower η/s to near the AdS/CFT limit within the hadron gas phase. A comparison of the Hagedorn model to recent lattice results is made and it is found that for both T c = 176 MeV and T c = 196 MeV, the hadrons can reach chemical equilibrium almost immediately, well before the chemical freeze-out temperatures found in thermal fits for a hadron gas without Hagedorn states. In this paper we also observe the effects of Hagedorn States on the K +/π+ horn seen at AGS, SPS, and RHIC.

Abstract Hadron production ( $$\pi ^\pm $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>±</mml:mo> </mml:msup> </mml:math> , proton, $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> , $$K_S^0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>K</mml:mi> <mml:mi>S</mml:mi> <mml:mn>0</mml:mn> </mml:msubsup> </mml:math> , $$K^\pm $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>K</mml:mi> <mml:mo>±</mml:mo> </mml:msup> </mml:math> ) in $$\pi ^- + \textrm{C}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>-</mml:mo> </mml:msup> <mml:mo>+</mml:mo> <mml:mtext>C</mml:mtext> </mml:mrow> </mml:math> and $$\pi ^- + \textrm{W}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>-</mml:mo> </mml:msup> <mml:mo>+</mml:mo> <mml:mtext>W</mml:mtext> </mml:mrow> </mml:math> collisions is investigated at an incident pion beam momentum of $$1.7~\textrm{GeV}/c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>1.7</mml:mn> <mml:mspace/> <mml:mtext>GeV</mml:mtext> <mml:mo>/</mml:mo> <mml:mi>c</mml:mi> </mml:mrow> </mml:math> . This comprehensive set of data measured with HADES at SIS18/GSI significantly extends the existing world data on hadron production in pion induced reactions and provides a new reference for models that are commonly used for the interpretation of heavy-ion collisions. The measured inclusive differential production cross-sections are compared with state-of-the-art transport model (GiBUU, SMASH) calculations. The (semi-) exclusive channel $$\pi ^- + A \rightarrow \Lambda + K_S^0 +X$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>-</mml:mo> </mml:msup> <mml:mo>+</mml:mo> <mml:mi>A</mml:mi> <mml:mo>→</mml:mo> <mml:mi>Λ</mml:mi> <mml:mo>+</mml:mo> <mml:msubsup> <mml:mi>K</mml:mi> <mml:mi>S</mml:mi> <mml:mn>0</mml:mn> </mml:msubsup> <mml:mo>+</mml:mo> <mml:mi>X</mml:mi> </mml:mrow> </mml:math> , in which the kinematics of the strange hadrons are correlated, is also investigated and compared to a model calculation. Agreement and remaining tensions between data and the current version of the considered transport models are discussed.

Dark photons, the hypothetical gauge bosons associated with an additional <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>U</a:mi> <a:msup> <a:mrow> <a:mo>(</a:mo> <a:mn>1</a:mn> <a:mo>)</a:mo> </a:mrow> <a:mo>′</a:mo> </a:msup> </a:mrow> </a:math> symmetry, can couple to standard model particles through a small kinetic mixing parameter <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>ɛ</b:mi> </b:math> with the ordinary photon. This mechanism provides a portal between the dark sector and visible matter. In this study, we present a procedure to derive theoretical upper bounds on the kinetic mixing parameter <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:msup> <c:mi>ɛ</c:mi> <c:mn>2</c:mn> </c:msup> <c:mrow> <c:mo>(</c:mo> <c:msub> <c:mi>M</c:mi> <c:mi>U</c:mi> </c:msub> <c:mo>)</c:mo> </c:mrow> </c:mrow> </c:math> by analyzing dilepton spectra from heavy-ion collisions across a broad energy range, from SIS to LHC energies. Our analysis is based on the microscopic parton-hadron-string dynamics (PHSD) transport approach, which successfully reproduces the measured dilepton spectra in <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi>p</d:mi> <d:mo>+</d:mo> <d:mi>p</d:mi> </d:mrow> <d:mo>,</d:mo> <d:mo> </d:mo> <d:mrow> <d:mi>p</d:mi> <d:mo>+</d:mo> <d:mi>A</d:mi> </d:mrow> </d:math> , and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mi>A</e:mi> <e:mo>+</e:mo> <e:mi>A</e:mi> </e:mrow> </e:math> collisions across the same energy range. Besides the dilepton channels resulting from interactions and decays of standard model particles (such as mesons and baryons), the PHSD has been extended to include the decay of hypothetical dark photons into dileptons, <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:mi>U</f:mi> <f:mo>→</f:mo> <f:msup> <f:mi>e</f:mi> <f:mo>+</f:mo> </f:msup> <f:msup> <f:mi>e</f:mi> <f:mo>−</f:mo> </f:msup> </f:mrow> </f:math> . The production of these dark photons occurs via Dalitz decays of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:msup> <g:mi>π</g:mi> <g:mn>0</g:mn> </g:msup> <g:mo>,</g:mo> <g:mo> </g:mo> <g:mi>η</g:mi> <g:mo>,</g:mo> <g:mo> </g:mo> <g:mi>ω</g:mi> <g:mo>,</g:mo> <g:mo> </g:mo> <g:msup> <g:mi>η</g:mi> <g:mo>′</g:mo> </g:msup> </g:math> , and <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mi mathvariant="normal">Δ</h:mi> </h:math> resonances; direct decays of <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mi>ρ</j:mi> <j:mo>,</j:mo> <j:mo> </j:mo> <j:mi>ω</j:mi> </j:math> , and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:mi>ϕ</k:mi> </k:math> ; the kaon mode <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:mrow> <l:msup> <l:mi>K</l:mi> <l:mo>+</l:mo> </l:msup> <l:mo>→</l:mo> <l:msup> <l:mi>π</l:mi> <l:mo>+</l:mo> </l:msup> <l:mi>U</l:mi> </l:mrow> </l:math> ; and thermal <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>q</m:mi> <m:mover accent="true"> <m:mi>q</m:mi> <m:mo>¯</m:mo> </m:mover> </m:mrow> </m:math> annihilation in the quark-gluon plasma. Our results show that high-precision measurements of dilepton spectra in heavy-ion collisions provide a sensitive and competitive probe of dark photons in the MeV to multi-GeV mass range. Furthermore, we quantify the experimental accuracy required to constrain the remaining viable parameter space of kinetic mixing in dark photon scenarios.

Abstract The effective mass of heavy quark in QGP is related to the heavy quark potential at a large distance. In this study we test different heavy quark potentials, namely, the screened potential such as the free energy and the internal energy of the heavy quark pair in QGP, and the unscreened potential, which was recently proposed by the HotQCD Collaboration, through the thermal production of charm quarks in heavy-ion collisions at the LHC. We find that the free energy potential overestimates charm production in heavy-ion collisions at the LHC, while the unscreened potential produces results closest to the experimental data from the ALICE Collaboration among the three potentials.

Correction: Eur. Phys. J. Spec. Top. https://doi.org/10.1140/epjs/s11734-025-01958-5<br/><br/>The Image Sources and Credits information section was missing from this article and should have read ‘The FCC Project formally acknowledges and credits all organisations and contributors whose data and imagery form part of the basemaps used in this work. These include © Esri, Airbus DS, FAO, FEMA, GSA, NASA, NGA, NOAA, USGS, CGIAR, NCEAS, Rijkswaterstaat, SITG – State of Geneva (CH), swisstopo, Facebook, Garmin, Geoland, Geodatastyrelsen, Google, Intermap, Maxar, Microsoft, N Robinson, NLS, NMA, OS, Planet, TomTom, as well as © OpenStreetMap contributors, Esri Community Maps contributors, and the GIS User Community.<br/><br/>Every effort has been made to correctly acknowledge all data providers and rights holders. Any omission is unintentional, and the FCC Project remains available to review and amend credits upon request from legitimate data owners.’<br/><br/>The original article has been corrected.

Abstract Heavy-ion collision experiments offer a unique opportunity to explore the early stages of the Universe by creating matter under extreme conditions of high temperature and baryon density. The properties of such matter are governed by the equation-of-state (EoS), which remains a central focus of investigation from both experimental and theoretical perspectives. Flow harmonics are among the most sensitive observables for probing the EoS, as they strongly reflect the underlying interactions and degrees-of-freedom of the system. In this article, we review the current status of our understanding of the EoS based on microscopic transport models, emphasizing comparisons with experimental data in the few-GeV energy range. We focus on the constraints of the EoS from nucleon, light cluster and hypernuclei observables such as the directed $$v_1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>v</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> and elliptic $$v_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>v</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> flow harmonics.

The Low's theorem is applied to the soft gluon emission from heavy quark scattering in quark-gluon plasma (QGP). The QGP is described by the dynamical quasi-particle model (DQPM) which reproduces the EoS from lQCD at finite temperature and chemical potential. We show that if the emitted gluon is soft and of long wavelength, the scattering amplitude can be factorized into the scattering part and the emission part and the Slavnov-Taylor identities are satisfied in the leading order. Imposing a proper upper limit on the emitted gluon energy, we obtain the scattering cross sections of charm quark as well as the transport coefficients (momentum drag and diffusion) in the QGP with and without gluon emission.