Author(s): Abdallah, MS; Adam, J; Adamczyk, L; Adams, JR; Adkins, JK; Agakishiev, G; Aggarwal, I; Aggarwal, MM; Ahammed, Z; Alekseev, I; Anderson, DM; Aparin, A; Aschenauer, EC; Ashraf, MU; Atetalla, FG; Attri, A; Averichev, GS; Bairathi, V; Baker, W; Ball Cap, JG; Barish, K; Behera, A; Bellwied, R; Bhagat, P; Bhasin, A; Bielcik, J; Bielcikova, J; Bordyuzhin, IG; Brandenburg, JD; Brandin, AV; Bunzarov, I; Butterworth, J; Cai, XZ; Caines, H; Calderon De La Barca Sanchez, M; Cebra, D; Chakaberia, I; Chaloupka, P; Chan, BK; Chang, FH; Chang, Z; Chankova-Bunzarova, N; Chatterjee, A; Chattopadhyay, S; Chen, D; Chen, J; Chen, JH; Chen, X; Chen, Z; Cheng, J; Chevalier, M; Choudhury, S; Christie, W; Chu, X; Crawford, HJ; Csanad, M; Daugherity, M; Dedovich, TG; Deppner, IM; Derevschikov, AA; Dhamija, A; Di Carlo, L; Didenko, L; Dong, X; Drachenberg, JL; Dunlop, JC; Elsey, N; Engelage, J; Eppley, G; Esumi, S; Evdokimov, O; Ewigleben, A; Eyser, O; Fatemi, R; Fawzi, FM; Fazio, S; Federic, P; Fedorisin, J; Feng, CJ; Feng, Y; Filip, P; Finch, E; Fisyak, Y; Francisco, A; Fu, C | Abstract: We report a systematic measurement of cumulants, Cn, for net-proton, proton, and antiproton multiplicity distributions, and correlation functions, κn, for proton and antiproton multiplicity distributions up to the fourth order in Au+Au collisions at sNN=7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4, and 200 GeV. The Cn and κn are presented as a function of collision energy, centrality and kinematic acceptance in rapidity, y, and transverse momentum, pT. The data were taken during the first phase of the Beam Energy Scan (BES) program (2010-2017) at the BNL Relativistic Heavy Ion Collider (RHIC) facility. The measurements are carried out at midrapidity (|y|l 0.5) and transverse momentum 0.4

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Cumulants and correlation functions of net-proton, proton, and antiproton multiplicity distributions in Au+Au collisions at energies available at the BNL Relativistic Heavy Ion Collider

The BEST framework for the search for the QCD critical point and the chiral magnetic effect

The Beam Energy Scan Theory (BEST) Collaboration was formed with the goal of providing a theoretical framework for analyzing data from the Beam Energy Scan (BES) program at the relativistic heavy ion collider (RHIC) at Brookhaven National Laboratory. The physics goal of the BES program is the search for a conjectured QCD critical point as well as for manifestations of the chiral magnetic effect. We describe progress that has been made over the previous five years. This includes studies of the equation of state and equilibrium susceptibilities, the development of suitable initial state models, progress in constructing a hydrodynamic framework that includes fluctuations and anomalous transport effects, as well as the development of freezeout prescriptions and hadronic transport models. Finally, we address the challenge of integrating these components into a complete analysis framework. This document describes the collective effort of the BEST Collaboration and its collaborators around the world. 

The search for the QCD critical point in heavy-ion collision experiments requires dynamical simulations of the bulk evolution of QCD matter as well as of fluctuations. We consider two essential ingredients of such a simulation: a generic extension of hydrodynamics by a parametrically slow mode or modes (``$\mathrm{Hydro}+$'') and a description of fluctuations out of equilibrium. By combining the two ingredients, we are able to describe the bulk evolution and the fluctuations within the same framework. Critical slowing-down means that equilibration of fluctuations could be as slow as hydrodynamic evolution, and thus fluctuations could significantly deviate from equilibrium near the critical point. We generalize hydrodynamics to partial-equilibrium conditions where the state of the system is characterized by the off-equilibrium magnitude of fluctuations in addition to the usual hydrodynamic variables---conserved densities. We find that the key element of the new formalism---the extended entropy taking into account the off-equilibrium fluctuations---is remarkably similar to the 2PI action in the quantum field theory. We show how the new $\mathrm{Hydro}+$ formalism reproduces two major effects of critical fluctuations on the bulk evolution: the strong frequency dependence of the anomalously large bulk viscosity as well as the stiffening of the equation of state with an increasing frequency or wave number. While the agreement with known results confirms its validity, the fact that $\mathrm{Hydro}+$ achieves this within a local and deterministic framework gives it significant advantages for dynamical simulations.

Hydrodynamics with parametric slowing down and fluctuations near the critical point

We present a strangeness-neutral equation of state for QCD that exhibits critical behavior and matches lattice QCD results for the Taylor-expanded thermodynamic variables up to fourth order in $$\mu _B/T$$
 . It is compatible with the SMASH hadronic transport approach and has a range of temperatures and baryonic chemical potentials relevant for phase II of the Beam Energy Scan at RHIC. We provide an updated version of the software BES-EoS, which produces an equation of state for QCD that includes a critical point in the 3D Ising model universality class. This new version also includes isentropic trajectories and the critical contribution to the correlation length. Since heavy-ion collisions have zero global net-strangeness density and a fixed ratio of electric charge to baryon number, the BES-EoS is more suitable to describe this system. Comparison with the previous version of the EoS is thoroughly discussed.

Strangeness-neutral equation of state for QCD with a critical point

In the context of the ongoing search for the QCD critical point at the Relativistic Heavy-Ion Collider, we study the equation of state near the critical point in the temperature and baryon chemical potential plane. We use the parametric representation introduced in earlier literature, which maps the universal three-dimensional Ising equation of state onto the QCD phase diagram using several non-universal parameters. We focus on the quartic cumulant of the baryon number, or baryon number susceptibility ${\ensuremath{\chi}}_{4}^{B}$, which can be accessed experimentally via net-proton fluctuation kurtosis measurements. It was originally predicted, through universality arguments based on the leading singular contribution, that ${\ensuremath{\chi}}_{4}^{B}$ and net-proton kurtosis should show a specific nonmonotonic behavior due to the critical point. In particular, when following the freeze-out curve on the phase diagram by decreasing beam energy, the kurtosis is expected to dip, and then peak, when the beam energy scan passes close to the critical point. We study the effects of the nonuniversal and thus far unknown parameters of the Ising-to-QCD mapping on the behavior of ${\ensuremath{\chi}}_{4}^{B}$. We find that, while the peak remains a solid feature, the presence of the critical point does not necessarily cause a dip in ${\ensuremath{\chi}}_{4}^{B}$ on the freeze-out line below the transition temperature. The critical point contribution to the dip appears only for a narrow set of mapping parameters, when subleading singular terms are sufficiently suppressed.

A. R. Nava Acuna

Papers

Quartic cumulant of baryon number in the presence of a QCD critical point

Strangeness-neutral equation of state for QCD with a critical point