Search

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.

Background: Simulations by transport codes are indispensable for extracting valuable physical information from heavy-ion collisions. Pion observables such as the π-/π+ yield ratio are expected to be sensitive to the symmetry energy at high densities. Purpose: To evaluate, understand, and reduce the uncertainties in transport-code results originating from different approximations in handling the production of Δ resonances and pions. Methods: We compare ten transport codes under controlled conditions for a system confined in a box, with periodic boundary conditions, and initialized with nucleons at saturation density and at a temperature of 60 MeV. The reactions NN↔NΔ and Δ↔Nπ are implemented, but the Pauli blocking and the mean-field potential are deactivated in the present comparison. Thus, these are cascade calculations including pions and Δ resonances. Results are compared to those from the two reference cases of a chemically equilibrated ideal gas mixture and of the rate equation. Results: For the numbers of Δ and π, deviations from the reference values are observed in many codes, and they depend significantly on the size of the time step. These deviations are tied to different ways in ordering the sequence of reactions, such as collisions and decays, that take place in the same time step. Better agreements with the reference values are seen in the reaction rates and the number ratios among the isospin species of Δ and π. Both the reaction rates and the number ratios are, however, affected by the correlations between particle positions, which are absent in the Boltzmann equation, but are induced by the way particle scatterings are treated in many of the transport calculations. The uncertainty in the transport-code predictions of the π-/π+ ratio, after letting the existing Δ resonances decay, is found to be within a few percent for the system initialized at n/p=1.5. Conclusions: The uncertainty in the final π-/π+ ratio in this simplified case of particles in a box is sufficiently small so that it does not strongly impact constraining the high-density symmetry energy from heavy-ion collisions. Most of the sources of uncertainties have been understood, and individual codes may be further improved in future applications. This investigation will be extended in the future to heavy-ion collisions to ensure the problems identified here remain under control.

The deuteron yield in Pb+Pb collisions at sNN=2.76TeV is consistent with thermal production at a freeze out temperature of T=155MeV. The existence of deuterons with binding energy of 2.2 MeV at this temperature was described as "snowballs in hell" [P. Braun-Münzinger, B. Dönigus, and N. Löher, CERN Courier, August 2015]. We provide a microscopic explanation of this phenomenon, utilizing relativistic hydrodynamics and switching to a hadronic afterburner at the above-mentioned temperature of T=155MeV. The measured deuteron pT spectra and coalescence parameter B2(pT) are reproduced without free parameters, only by implementing experimentally known cross sections of deuteron reactions with hadrons, most importantly πd↔πnp.

The deuteron binding energy is only 2.2 MeV. At the same time, its yield inPb+Pb collisions at $\sqrt{s_{NN}} = $2.76 TeV corresponds to a thermal yieldat the temperature around 155 MeV, which is too hot to keep deuterons bound.This puzzle is not completely resolved yet. In general, the mechanism of lightnuclei production in ultra-high energy heavy ion collisions remains underdebate. In a previous work [1] we suggest a microscopic explanation of thedeuteron production in central ultra-relativistic Pb+Pb collisions, the mainmechanism being $\pi pn \leftrightarrow \pi d$ reactions in the hadronic phaseof the collision. We use a state-of-the-art hybrid approach, combiningrelativistic hydrodynamics for the hot and dense stage and hadronic transportfor a later, more dilute stage. Deuteron rescattering in the hadronic stage isimplemented explicitly, using its experimentally measured vacuumcross-sections. In these proceedings we extend our previous work to non-centralcollisions, keeping exactly the same methodology and parameters. We find thatour approach leads to a good description of the measured deuteron transversemomentum spectra at centralities up to 40%, and underestimates the amount ofdeuterons at low transverse momentum at higher centralities. Nevertheless, thecoalescence parameter $B_2$, measured by ALICE collaboration, is reproducedwell in our approach even for peripheral collisions.

The deuteron binding energy is only 2.2 MeV. At the same time, its yield inPb+Pb collisions at $\sqrt{s_{NN}} = $2.76 TeV corresponds to a thermal yieldat the temperature around 155 MeV, which is too hot to keep deuterons bound.This puzzle is not completely resolved yet. In general, the mechanism of lightnuclei production in ultra-high energy heavy ion collisions remains underdebate. In a previous work [1] we suggest a microscopic explanation of thedeuteron production in central ultra-relativistic Pb+Pb collisions, the mainmechanism being $\pi pn \leftrightarrow \pi d$ reactions in the hadronic phaseof the collision. We use a state-of-the-art hybrid approach, combiningrelativistic hydrodynamics for the hot and dense stage and hadronic transportfor a later, more dilute stage. Deuteron rescattering in the hadronic stage isimplemented explicitly, using its experimentally measured vacuumcross-sections. In these proceedings we extend our previous work to non-centralcollisions, keeping exactly the same methodology and parameters. We find thatour approach leads to a good description of the measured deuteron transversemomentum spectra at centralities up to 40%, and underestimates the amount ofdeuterons at low transverse momentum at higher centralities. Nevertheless, thecoalescence parameter $B_2$, measured by ALICE collaboration, is reproducedwell in our approach even for peripheral collisions.