Session GF: Bulk Matter and Correlations in Heavy-ion Collisions I

Baryon number, strangeness, and electric charge fluctuations in hydrodynamics at the LHC

At LHC energies it is possible to generate BSQ (baryon, strangeness, and electric) charge fluctuations from gluon splittings into quark anti-quark pairs, generated within the ICCING model. Here we propagate these conserved charges within an upgraded version of the hydrodynamic model, v-USPhydro, that conserves BSQ coupled to a 4-D equation of state {T,μB,μS,μQ} from Lattice Quantum Chromodynamics. We find that solely due to charge fluctuations that we expect large fluctuations in the chemical potentials {μB,μS,μQ} in local fluid cells  at freeze-out even at LHC energies.   

QCD equation of state at finite density with a critical point from an alternative expansion scheme

In Ref. [1], results for the QCD equation of state from the lattice Taylor expansion were combined with the 3D Ising model critical behavior, to build a family of equations of state which match first principle results and contain a critical point in the expected universality class for QCD. This family of equations of state was limited to baryon chemical potentials from 0  to 450MeV, due to the limitations of the Taylor expansion. In Ref.[2], an alternative expansion scheme was introduced, for extrapolating the lattice QCD equation of state to finite chemical potential. In this research, we combine these two approaches to obtain a family of equations of state in the range of baryon chemical potentials from  0 to  700 MeV and Temperature from  30 MeV to 800 MeV, that match the lattice QCD results at a small density and contain a 3D-Ising model critical point. With these new equations of state, we substantially extend the coverage of the QCD phase diagram. 

Our open-source code allows the user to choose the position and strength of the critical point. Our results provide input for hydrodynamical simulations at finite Temperature and unprecedentedly large baryon chemical potential and will help constrain the location of the critical point through a comparison with experimental data from the Second Beam Energy Scan at RHIC.

[1]  Paolo Parotto et al. “Lattice-QCD-based equation of state with a critical point”. In:arXiv preprintarXiv:1805.05249(2018)

[2]   S Borsányi et al. “Lattice QCD equation of state at finite chemical potential from an alternative expansion scheme”. In: Physical Review Letters126.23 (2021), p. 232001   

Description of the first order phase transition region of an equation of state for QCD with a critical point

The search for signatures of the possible critical point in the QCD phase diagram have been a major effort in the theory and experimental community in the last decades. Besides those features directly attributed to the critical point, evidence of its existence can also be found by searching for the first order phase transition line, i.e. evidence that it is no longer a crossover. In this equation of state, we map the full coexistence region of the first order phase transition from the 3D Ising model onto the QCD phase diagram. The scaling equation of state in the mean field approximation is mapped onto the phase diagram of strongly-interacting matter, based on the principle of universal behavior in the vicinity of a critical point. A thermodynamic description of the thermodynamically metastable and unstable states of matter is achieved beyond that of the Maxwell construction. This analytical approach then follows the true curves for the coexistence and spinodal lines in the phase diagram. We will discuss the features observed upon mapping the mean field Ising model onto the QCD phase diagram as well as the behavior of the pressure, density, and entropy describing the equation of state.   

Contribution of Hadron Families to the QCD Equation of State

Currently Lattice QCD simulations provide the best method of deriving the pressure of QCD as a function of the temperature. In the low-temperature regime, the thermodynamics can be understood in terms of a gas of non-interacting hadrons and resonances, but the contribution of the single hadronic species cannot be easily isolated. In this work we propose linear combinations of susceptibilities of conserved charges, that isolate the contribution of hadrons to the pressure of QCD according to their baryon number B, electric charge Q and strangeness S content. We build these partial pressures such that they vanish in the Stefan-Boltzmann limit. This generates a non-monotonic behavior which can be used to identify the melting temperature of each hadron family. We test the validity of these linear combinations in the Hadron Resonance Gas (HRG) model and compare them to available lattice QCD results.
*This material is based upon work supported by the National Science Foundation under grants no. PHY1654219, DGE-1746047, and by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, within the framework of the Beam Energy Scan Topical (BEST) Collaboration and Grant No. DE-SC0020633   

Equilibrium and Dynamical Properties of Hot and Dense Quark-Gluon matter from Holographic Black Holes.

By using gravity/gauge correspondence, we employ an Einstein-Maxwell-Dilaton model to compute the equilibrium and out-of-equilibrium properties of a hot and baryon rich strongly coupled quark-gluon plasma. The family of 5-dimensional holographic black holes, which are constrained to mimic the lattice QCD equation of state at zero density, is used to investigate the temperature and baryon chemical potential dependence of the equation of state [1]. We also obtained the baryon charge transport coefficients, the bulk and shear viscosities as well as the drag force and langevin diffusion coefficients associated with heavy quark jet propagation and the jet quenching parameter of light quarks in the baryon dense plasma, with a particular focus on the behavior of these observables on top of the critical end point and the line of first order phase transition predicted by the model [2].

[1] Grefa, J., Noronha, J., Noronha-Hostler, J., Portillo, I., Ratti, C., Rougemont, R. 10.1103/PhysRevD.104.034002

[2] Grefa, J.,Hippert, M., Noronha, J., Noronha-Hostler, J., Portillo, I., Ratti, C., Rougemont, R. arXiv:2203.00139 [nucl-th]   

Dynamical evolution of particle number fluctuations in hadronic transport

We study particle number fluctuations in infinite matter using hadronic transport simulations of a box with periodic boundary conditions. The study focuses on matter initialized at a series of thermodynamically and mechanically stable points in the phase diagram, and in particular on the influence of the critical point on the equilibrated values of the fluctuations. We compare fluctuations from hadronic transport simulations against the values calculated using the underlying density functional equation of state, and we show that the fluctuations obtained from simulations agree with the underlying theory qualitatively everywhere in the phase diagram, and quantitatively as long as the simulated matter is far enough from the critical point.   

Proton-Cumulant Analyses in an Energy Scan of the STAR Fixed-Target Program at √sNN= 3.2, 3.5, 3.9, 4.5, 5.2, 6.2, 7.2, and 7.7 GeV

Non-monotonic variations in higher-order cumulants of proton number distributions produced in heavy-ion collisions are expected to be an indicator of a critical point in the QCD phase diagram. Proton-fluctuation results from Au+Au collisions in Beam Energy Scan I (BES-I) demonstrated deviations from the non-critical baseline, starting at √s_NN = 27 GeV and continuing to the lowest BES-I energy of √s_NN = 7.7 GeV. The STAR Fixed-Target Program has extended the energy range available at the Relativistic Heavy-Ion Collider down to √s_NN = 3.0 GeV. Proton-cumulant results at 3.0 GeV have indicated a return to the expected baseline behavior. The remaining fixed-target analyses aim to identify whether critical behavior is observed in the region between 3.2 and 7.7 GeV. Au+Au data from the Fixed-Target Program from √s_NN = 3.2 GeV to 7.7 GeV are now available and proton-cumulant analyses are underway. A status report on the challenges, methods, and statistical significance of these analyses will be presented.   

Directed flow of $\phi$ mesons in Au+Au collisions at the second phase of beam energy scan (BES-II) program from STAR

    The \(\phi\) meson is composed of strange quarks (\(s\overline s\)) and has a small hadronic interaction cross-section, which reduces the influence of late stage rescattering in heavy-ion collisions.

    Thus the directed flow ($v_{1}$) of \(\phi\) mesons is sensitive to the early stages of the collisions and is an important observable for the study of QCD phase diagram at RHIC. In this talk, we will present measurements of directed flow of \(\phi\) mesons in Au+Au collisions at $\sqrt{s_{NN}}=3,\ 7.2,$ and $19.6$ GeV from the second phase of RHIC beam energy scan (BES-II) program. \(\phi\) mesons are reconstructed through the decay channel \(\phi\rightarrow K^{+}+ K^{-}\). We will compare our new results with the BES-I results.