Soft Physics at RHIC

Recent soft physics results from collisions of ultra-relativistic nuclei at Relativistic Heavy Ion Collider (RHIC) operating at Brookhaven National Laboratory (BNL) are reviewed. Topics discussed cover the Beam Energy Scan program with some emphasis on anisotropic particle flow.


Introduction
At sufficiently high temperature T or baryon chemical potential µ B QCD predicts a phase transition from hadrons to the plasma of its fundamental constituents -quarks and gluons. Search for and understanding of the nature of this transition has been a long-standing challenge to high-energy nuclear and particle physics community. In 2005, just five years after start up of RHIC, first convincing arguments on the existence of de-confined partonic matter were published [1]. Exciting discoveries made by four experiments BRAHMS, PHOBOS, PHENIX and STAR on perfect quark-gluon liquid [1], constituent number scaling of particle flow [2,3], jet quenching [4] and heavy-quark suppression [5] were recently complemented by the first detection of anti-strange nucleus [6] and by the observation of the heaviest anti-nucleus - 4 He [7]. The medium produced in collisions of ultra-relativistic nuclei at RHIC, having a highly non-trivial properties of strongly interacting quark-gluon plasma (sQGP), is definitely worth to study over much broader energy range. A central goal now is to map out as much as possible of the QCD phase diagram in T , µ B plane trying to understand various ways in which the hadron-to-QGP transition may occur.
While the soft physics results from the high energy frontier, the Large Hadron Collider (LHC) at CERN, are covered by P. Kuijer's contribution to this workshop [8], the low energy frontier of RHIC is presented in this talk. For the topics not included or not sufficiently covered in depth in this minireview I refer interested reader to consult PHENIX and STAR contributions in recently published proceedings of the Quark Matter 2011 conference [9].

Beam Energy Scan Program
During eleven years of its operation the RHIC machine has delivered a variety of nuclear beams (Au, Cu, d feature of the phase diagram in a T , µ B plane, where the nature of the transition changes from a discontinuous (first-order) transition to an analytic crossover. Latter, according to lattice calculations, occurs when µ B ≈ 0 and drives the de-confining phase transition at the top RHIC energy and above. Statistical hadronization model fit to mid-rapidity particle ratios (π − /π + , K − /K + ,p/p, K − /π − and p/π − ) from 5% most central Au+Au collisions was used by STAR to extract the chemical freeze-out (vanishing inelastic collisions) conditions [10]. Fig.1 shows that the BES program has extended the µ B range at the RHIC from around 20MeV to about 400 MeV. π − , K − andp yields were fit with a blast wave model to extract the kinetic freeze-out (vanishing elastic collisions) conditions [10]. The kinetic freeze-out temperature (T kin ) is observed to slightly decrease whereas the collective radial flow velocity β increases with decreasing √ s NN . The large µ B values at midrapidity indicate the formation of high net-baryon density matter, which is expected to reach a maximum value around 8 GeV [11].

Anisotropic flow
Study of the conversion of coordinate space anisotropies into momentum space anisotropies plays a central role in ongoing efforts to characterize the transport properties of sQGP. The azimuthal anisotropic flow strength is usually parametrized via Fourier coefficients v n ≡ cos n(φ − Ψ n ) , where φ is the azimuthal angle of the particle, Ψ n is the azimuthal angle of the initial-state spatial plane of symmetry (the reaction plane) and n is the order of the harmonic. The event planes from the higher moments at various rapidities are defined with various reaction plane detectors (e.g. Reaction Plane and Muon Piston Calorimeter detectors at |η| =1.0-2.8 and |η|=3.1-3.7, respectively, in PHENIX).
The big surprise at RHIC came from the measurement of the v 2 coefficient, integrated elliptic flow, which brings information on the pressure and stiffness of the equation of state during the earliest collision stages. It was found that v 2 increases by 70% from the top SPS energy √ s NN =17.2 GeV to the top RHIC energy √ s NN =200 GeV [1]. The large value of v 2 observed at RHIC and recently also at LHC [8], [12] is one of the cornerstones of the perfect liquid bulk matter dynamics. Moreover, the differential v 2 (p T ), characterizing in detail the hydrodynamic response to the initial geometry, seems to be unchanged between the top RHIC energy and LHC energy of √ s NN =2.76 TeV [8,12]. Hence, both at RHIC and at the LHC created matter behaves as the strongly coupled nearly perfect fluid. The latest results on v 2 (p T ) shown on the left panel of Fig.2 allow us to conclude that the interval over which the elliptic flow saturates now extends almost two orders of magnitude: from 2.76 TeV to 39 GeV. Since v 2 (p T ) at the top SPS energy is much below the saturation curve it would be interesting to see what happens at already collected √ s NN =27 and 19.6 GeV BES energies.
At midrapidity smooth distribution of the matter in the overlapping region of two equal-mass incoming nuclei implies vanishing of all odd harmonic. The central panel of Fig.1 shows that, due to fluctuations in the initial matter distribution, this assumption is ill-founded. Moreover, for 39 GeV ≤ √ s NN ≤ 200 GeV the data on v 3 (p T ) seems to saturate and so the 'lumpiness' of initial geometry over this energy interval remains the same. Excitation function of v 4 (p T ), which could provide additional constraints on initial geometries and transport coefficients, plotted on the right panel of Fig.1, shows the similar saturation. It is noteworthy that the initial state fluctuations also show up in two-particle correlation function ∆η and ∆φ for particles with 2 < p T < 5 GeV/c from 1% most central Au+Au collisions [14].

Elliptic flow of identified particles
Interestingly, the flow patterns are also reflected in the constituent quark number (ncq) scaling of particle identified data. Plotting v 2 /ncq versus (m T − m 0 )/ncq for various particle species, where ncq is the number of constituent quarks of a hadron with mass m 0 and m T − m 0 is its transverse kinetic energy, one finds the data to collapse onto a single universal curve. Suggested by parton coalescence and recombination models [3], the universal scaling of light flavor mesons and baryons [2], including multi-strange baryons and φ-meson [3] first observed at the top RHIC energy is now considered as an evidence of partonic collectivity of nuclear matter. For hadrons containing the heavy quarks the situation is less clear. Contrary to substantial elliptic flow of mesons containing the heavy quarks found recently by PHENIX [17] the latest STAR measurements of J/ψ [15] are consistent with v 2 ≈ 0 disfavoring thus the coalescence scenario of J/ψ production from thermalized charm quarks. Recent PHENIX measurements [13] of elliptic flow of π ± , K ± , p andp from Au+Au collisions confirm that at √ s NN = 62 and 39 GeV the ncq-scaling still holds, with some deviations in the (m T − m 0 )/ncq range of 0.2 − 0.5 GeV/c 2 especially for (anti)protons and more prominent for 39 GeV. This observation is confirmed and further extended by the new STAR measurements of the elliptic flow of particles at √ s NN = 39, 11.5 and 7.7 GeV [11]. Differences are observed in the v 2 of particles and antiparticles, which increase as √ s NN decreases suggesting that the ncq-scaling for all particle species (including nuclei) as observed at top RHIC energies [3] is no longer valid at these lower energies. Fig.3 shows the STAR data on elliptic flow of various particles produced in 0-80% central Au+Au collisions at √ s NN =7.7, 11.5 and 39 GeV [16]. Most of the particle species follow the ncq-scaling, except for the φ-mesons, which have v 2 at 11.5 GeV systematically lower than the other hadrons. This may provide an evidence for a change in the degrees of freedom around √ s NN ≈ 10 GeV. If in addition, a hierarchy of the violation of the ncq-scaling could be established when going from p to Λ, Ξ and Ω it could provide further insights into the relative importance of hadronic and partonic phase in the early stage of the reaction.

Summary
Recent soft physics results from RHIC have substantially extended our knowledge of hot and dense de-confined QCD matter. The BES program covering a large part of the conjectured QCD phase diagram revealed significant differences in particle and anti-particle v 2 coming from the high net-baryon density at midrapidity. Small v 2 of φ-meson indicates that hadronic interactions start to dominate over partonic interactions around 11.5 GeV. Saturation of differential elliptic flow v 2 (p T ) from √ s NN = 2.76 TeV down to √ s NN = 39 GeV extends substantially the region where the sQGP can be created and studied under controlled laboratory conditions. A non-negligible contribution to azimuthal anisotropy of produced particles comes from the fluctuations in the initial matter distribution of colliding nuclei.