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

Abstract

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. CONTENTS I. Introduction II. Lattice QCD results A. Phase diagram B. Equation of state at finite density C. Correlations and fluctuations of conserved charges III. Critical fluctuations and anomalous transport A. Fluctuation dynamics near the critical point 1. Introduction 2. Theoretical developments B. Chiral Magnetic Effect and related phenomena IV. EoS with 3D-Ising model critical point V. Initial Conditions A. Challenges of the Beam Energy Scan B. Pre-BEST status of 3D initial condition models C. Simple collision geometry based 3D initial condition D. Dynamical initial condition VI. Hydrodynamics A.

Freezing out critical fluctuations

“…All that said, we see it as of paramount importance to extend the application of this procedure to higher-order non-Gauusian cumulants, as they serve as stronger signals of the critical point [13,11]. While this will be the next immediate step to do, we also hope that the procedure we have developed and presented here can already be implemented within the full paradigm for the numerical simulation of beam energy scan at RHIC [9].…”

“…To convert these hints into definitive conclusions and thereby potentially discover the location of the critical point, one needs theoretical modeling that provides guidance as to what to expect in this case. Much work is being done by a number of groups to develop a description of the hydrodynamics with critical fluctuations near a critical point [8,9]. In addition to such a description, we need a freeze-out procedure to translate not only average hydrodynamic variables but also the critical fluctuations exhibited by the quark gluon plasma into the mean and fluctuations of hadron multiplicities that are subsequently observed.…”

“…As the hydrodynamic fields evolve, if relaxation rates are slow, as is the case for fluctuations near a critical point, these fluctuations can no longer be described by their equilibrium values slaved to hydrodynamic fields. There has been a considerable amount of work performed within both the stochastic and deterministic approaches to describe the evolution of fluctuations near the critical point [8,9]. In the deterministic approach, the correlation functions that describe the fluctuations, in essence, their moments, are considered as additional degrees of freedom with evolution equations of their own.…”

Phenomenological developments for event-by-event fluctuations of conserved charges

“…Fluctuations of (net-)proton number are one of the primary observables in RHIC-BES used to probe the QCD critical point on the phase diagram. Making quantitative predictions for the critical point signatures in heavy-ion collisions is challenging and currently much work is being done on that avenue within the framework of hydrodynamics with critical fluctuations [51][52][53]. The issue can also be approached from a different angle: the critical point signal, if it exists, should manifest itself in deviations from non-critical baseline expectations that do not incorporate any critical point effects.…”

Analytical structure of the equation of state at finite density: Resummation versus expansion in a low energy model

“…Uncovering the structure of the phase diagram of Quantum Chromodynamics at nonzero temperature and density has been the central goal for both the theoretical and the experimental nuclear physic community (see Ref. [1] for a review). Non-perturbative theoretical understanding of the QCD phase diagram is hampered by the so-called sign problem.…”