Open accessJournal Article

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

04 Mar 2021-Physical Review C (American Physical Society)-Vol. 103, Iss: 3, pp 034901
Abstract: 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.

Topics: , Baryon (50%)
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Open accessJournal Article
01 Aug 2021-Physical Review C
Abstract: 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

9 Citations

Open accessJournal Article
Abstract: 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.

Topics: Lattice QCD (59%), , Equation of state (56%) ... read more

6 Citations

Open accessJournal Article
Maximilian Attems1, Maximilian Attems2Institutions (2)
Abstract: A smoking gun signature for a first-order phase transition with negative speed of sound squared $${c}_s^2$$ is the occurrence of a spinodal instability. In the gauge/gravity duality it corresponds to a Gregory-Laflamme type instability, which can be numerically simulated as the evolution of unstable planar black branes. Making use of holography its dynamics is studied far from and near a critical point with the following results. Near a critical point the interface between cold and hot stable phases, given by its width and surface tension, is found to feature a wider phase separation and a smaller surface tension. Far away from a critical point the formation time of the spinodal instability is reduced. Across softer and harder phase transitions, it is demonstrated that mergers of equilibrated peaks and unstable plateaux lead to the preferred final single phase separated solution. Finally, a new atypical setup with dissipation of a peak into a plateau is discovered. In order to distinguish the inhomogeneous states I propose a new criterium based on the maximum of the transverse pressure at the interface which encodes phase-mixed peaks versus fully phase separated plateaux.

Topics: , Spinodal (59%), Instability (55%) ... read more

2 Citations

Open accessJournal Article
Abstract: 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.

Topics: , QCD matter (50%)

2 Citations

Open accessJournal Article
Abstract: 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.

Topics: , Strangeness (60%),

1 Citations

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Matthias Troyer1, Uwe-Jens Wiese2Institutions (2)
Abstract: Quantum Monte Carlo simulations, while being efficient for bosons, suffer from the "negative sign problem" when applied to fermions--causing an exponential increase of the computing time with the number of particles. A polynomial time solution to the sign problem is highly desired since it would provide an unbiased and numerically exact method to simulate correlated quantum systems. Here we show that such a solution is almost certainly unattainable by proving that the sign problem is nondeterministic polynomial (NP) hard, implying that a generic solution of the sign problem would also solve all problems in the complexity class NP in polynomial time.

Topics: , Quantum Monte Carlo (62%), NP (60%) ... read more

779 Citations

Open accessJournal Article
Abstract: Several approaches to QCD with two {ital massless} quarks at finite temperature T and baryon chemical potential {mu} suggest the existence of a tricritical point on the boundary of the phase with spontaneously broken chiral symmetry. In QCD with {ital massive} quarks there is then a critical point at the end of a first order transition line. We discuss possible experimental signatures of this point, which provide information about its location and properties. We propose a combination of event-by-event observables, including suppressed fluctuations in T and {mu} and, simultaneously, enhanced fluctuations in the multiplicity of soft pions. {copyright} {ital 1998} {ital The American Physical Society }

Topics: Tricritical point (58%), ,  ... read more

759 Citations

Open accessJournal Article
10 Nov 1999-Physical Review D
Abstract: The event-by-event fluctuations of suitably chosen observables in heavy ion collisions at CERN SPS, BNL RHIC, and CERN LHC can tell us about the thermodynamic properties of the hadronic system at freeze-out. By studying these fluctuations as a function of varying control parameters, it is possible to learn much about the phase diagram of QCD. As a timely example, we stress the methods by which present experiments at the CERN SPS can locate the second-order critical end point of the first-order transition between quark-gluon plasma and hadron matter. Those event-by-event signatures which are characteristic of freeze-out in the vicinity of the critical point will exhibit nonmonotonic dependence on control parameters. We focus on observables constructed from the multiplicity and transverse momenta of charged pions. We first consider how the event-by-event fluctuations of such observables are affected by Bose-Einstein correlations, by resonances which decay after freeze-out, and by fluctuations in the transverse flow velocity. We compare our thermodynamic predictions for such noncritical event-by-event fluctuations with NA49 data, finding broad agreement. We then focus on effects due to thermal contact between the observed pions and a heat bath with a given (possibly singular) specific heat, due to the direct coupling between themore » critical fluctuations of the sigma field and the observed pions. We also discuss the effect of the pions produced in the decay of sigma particles just above threshold after freeze-out on the inclusive pion spectrum and on multiplicity fluctuations. We estimate the size of these nonmonotonic effects, which appear near the critical point, including restrictions imposed by finite size and finite time, and conclude that they should be easily observable. (c) 1999 The American Physical Society.« less

Topics: , Quark–gluon plasma (54%), Pion (52%) ... read more

608 Citations

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