Disappearance of partonic collectivity in $\sqrt{s_{NN}}$ = 3 GeV Au+Au collisions at RHIC

We report on the measurements of directed flow $v_1$ and elliptic flow $v_2$ for hadrons ($\pi^{\pm}$, $K^{\pm}$, $K_{S}^0$, $p$, $\phi$, $\Lambda$ and $\Xi^{-}$) from Au+Au collisions at $\sqrt{s_{NN}}$ = 3\,GeV and $v_{2}$ for ($\pi^{\pm}$, $K^{\pm}$, $p$ and $\overline{p}$) at 27 and 54.4\,GeV with the STAR experiment. While at the two higher energy midcentral collisions the number-of-constituent-quark (NCQ) scaling holds, at 3\,GeV the $v_{2}$ at midrapidity is negative for all hadrons and the NCQ scaling is absent. In addition, the $v_1$ slopes at midrapidity for almost all observed hadrons are found to be positive, implying dominant repulsive baryonic interactions. The features of negative $v_2$ and positive $v_1$ slope at 3\,GeV can be reproduced with a baryonic mean-field in transport model calculations. These results imply that the medium in such collisions is likely characterized by baryonic interactions.

We report on the measurements of directed flow v1 and elliptic flow v2 for hadrons (π ± , K ± , K 0 S , p, φ, Λ and Ξ − ) from Au+Au collisions at √ sNN = 3 GeV and v2 for (π ± , K ± , p and p) at 27 and 54.4 GeV with the STAR experiment. While at the two higher energy midcentral collisions the number-of-constituent-quark (NCQ) scaling holds, at 3 GeV the v2 at midrapidity is negative for all hadrons and the NCQ scaling is absent. In addition, the v1 slopes at midrapidity for almost all observed hadrons are found to be positive, implying dominant repulsive baryonic interactions. The features of negative v2 and positive v1 slope at 3 GeV can be reproduced with a baryonic mean-field in transport model calculations. These results imply that the medium in such collisions is likely characterized by baryonic interactions.

I. INTRODUCTION
Relativistic heavy-ion collisions at the Large Hadron Collider (LHC) and the Relativistic Heavy Ion Collider (RHIC), where the net-baryon density is low, are generally considered to have produced a new form of matter with partonic degrees of freedom, usually referred to as the strongly-coupled Quark Gluon Plasma (sQGP) [1][2][3][4][5]. However, it is necessary to identify changes in physical properties, e.g. in its equation of state (EOS), before ultimately claiming the discovery of the new form of matter. Since the discovery of the sQGP in 2005, the nature of the phase transition from hadronic matter to the QGP and of the Quantum Chromodynamics (QCD) phase diagram at finite net-baryon density have been the focus in the RHIC beam energy scan program. This is, after the discovery of the sQGP at vanishing net-baryon density, an important step toward understanding the phase structure of nuclear matter in the high baryon density region.
In order to extract underlying dynamic information, the particle differential distribution is often written in the form of a Fourier series [6][7][8], 2v n cos(n(φ − Ψ))) (1) where p T , y, φ and Ψ are, respectively, particle transverse momentum, rapidity, azimuthal angle of the particle and the event plane angle. Due to their sensitivity to the expansion dynamics of the produced matter, the first two Fourier expansion coefficients v 1 (directed flow) and v 2 (elliptic flow) are sensitive probes for studying the properties of the matter created in high-energy nuclear collisions [9][10][11]. At higher energies (nucleon-nucleon center-of-mass energy √ s NN > ∼ 27 GeV), where the transit time of the colliding nuclei (∼ 2R/γβ) is smaller than the typical production time of particles [12,13], flow harmonics are dominated by the collective expansion of initial partonic density distribution [14][15][16]. At lower energies, shadowing effect by the passing spectator nucleons becomes important [17][18][19][20][21][22]. At √ s NN < ∼ 4 GeV, nuclear mean-field effects will contribute to the observed azimuthal anisotropies [23][24][25][26]. Previous studies have shown that v 1 and v 2 are particularly sensitive to the incompressibility (κ) of the nuclear matter in the high baryon density region [27][28][29][30]. The constraints on κ by comparing experimental data with results from the theoretical transport model will certainly help us to understand nuclear EOS. In a systematic analysis of hadron spectra and anisotropic flow in Au+Au collisions at the energy range of √ s NN = 2 -4.5 GeV, the authors concluded that anisotropic flow is sensitive to the EOS and a realistic EOS with a transition to QGP is needed in order to understand * Deceased the experimental observations in the high baryon density region [31]. Large positive v 2 , especially for multistrange hadrons, along with the observation of its number-of-constituentquarks (NCQ) scaling are strong evidence for the formation of a hydrodynamically expanding QGP phase with partonic degrees of freedom [14][15][16]. Positive v 2 of light hadrons at midrapidity has been observed from the top RHIC energy down to 4.5 GeV [22]. On the other hand, at √ s NN ≥ 10 GeV, all midrapidity v 1 slopes are found to have negative values and approach to zero with increasing energy [19,20,32], where partonic collectivity is dominant. At lower collision energies the v 1 slope values for baryons become positive, while those for mesons remain negative [17,22,33,34]. For example, results of proton and light nuclei v 1 and v 2 from Au+Au collisions at √ s NN = 2.4 GeV were reported recently by the HADES experiment [35].

II. EXPERIMENT AND DATA ANALYSIS
In this paper we report systematic results of v 1 and v 2 for identified hadrons (π ± , K ± , K 0 S , p, φ, Λ, and Ξ − ) from 10-40% centrality Au+Au collisions at √ s NN = 3 GeV and v 2 of (π ± , K ± , p, andp) at √ s NN = 27 and 54.4 GeV from the STAR experiment. The data sets at 3, 27, and 54.4 GeV are 260, 560, and 600 × 10 6 events with minimum-bias trigger, respectively. The main detector of STAR is a cylindrical Time Projection Chamber (TPC) [36] 4 m in diameter and 4 m in length. The TPC resides in a solenoidal magnet providing a uniform magnetic field of 0.5 T along the longitudinal beam direction. The data at 3 GeV were taken, with beam energy of 3.85 GeV per nucleon, in 2018 in the fixed-target (FXT) mode. The target, with a thickness of 0.25 mm corresponding to a 1% interaction probability, is positioned inside the beam pipe near the edge of the TPC, at 200.7 cm from the TPC center along the beam axis. This gives an experimental acceptance coverage of −2 < η < 0 in pseudorapidity in the lab frame. The higher energy data were taken in the collider mode, where the beam bunch crossing was restricted to the TPC central region, yielding an acceptance of |η| < 1. The centrality of collisions is characterized by the number of charged tracks detected with the TPC within pseudorapidity |η| < 0.5 in collider mode collisions and −2 < η < 0 for FXT mode collisions. When two (or more) independent single collision events are superposed, it is called pile-up which often occurs in the fixed target mode. In order to remove the pile-up effect, events with multiplicity greater than 195 are excluded from the analysis at cm is required to eliminate possible beam interactions with the vacuum pipe of 4 cm radius at all three energies. In order to improve the track quality, momentum and ionization energy loss resolution from the TPC, the following track selections are applied: i) the number of hit points is larger than 15; ii) the ratio between the number of hit points and the maximum possible number of hit points is larger than 0.52; iii) the distance of closest approach (DCA) to the primary vertex is less than 3 cm [21]. The particle identification of charged pions with transverse momentum range 0.2 < p T < 1.6 GeV/c, charged kaons with 0.4 < p T < 1.6 GeV/c, and protons with 0.4 < p T < 2.0 GeV/c are based on ionization energy loss information measured with the TPC detector and time-offlight information measured with the Time-of-Flight (TOF) detector [37]. Reconstruction of K 0 S , Λ, and Ξ − is performed using the KF Particle Finder package based on the Kalman Filter method, initially developed for the CBM and ALICE experiments [38], and also used in STAR measurements [39]. In order to enhance the signal significance, the method utilizes the covariances of track parameters to determine and select on variables characterizing decay topology. The φ mesons are reconstructed through the decay channel, φ → K + + K − , where the combinatorial background is estimated using the mixed-event technique [21]. Figure 1 presents the density distributions in y and p T for π + , K + , p, φ, Λ, and Ξ − , measured with the TPC and TOF detectors in Au+Au collisions at √ s NN = 3 GeV. In the remainder of this paper, all notations are presented in the centerof-mass frame for both the collider and FXT datasets. The target is located at y = −1.05 and the positive sign of v 1 is defined by the forward positive rapidity region. The acceptance for all particles covers from midrapidity to target rapidity. The coverage of p T is from 0.2 to ∼ 2 GeV/c, depending on the rest mass of the particle. Before extracting the flow information one must determine the event plane angle on an event-by-event basis [40,41]. For the n th Fourier harmonic, the flow vector Q n = (Q nx , Q ny ) and the event plane angle Ψ n are event-by-event calculated by where sums go over all particles i used in the event plane calculation, φ i is the laboratory azimuthal angle, and the weight w i used here is p T for the i th particle. For the Au+Au collisions at √ s NN = 27 and 54.4 GeV, the second order event plane angle (Ψ 2 ) is reconstructed with tracks determined by the TPC and the event plane resolution is determined as , where A and B are independent subevents, from η ranges −1 < η < −0.05 and 0.05 < η < 1, respectively. The average .. runs over all events. At √ s NN = 3 GeV, the first order event plane angle (Ψ 1 ) is determined with the Event Plane Detector (EPD) covering the pseudorapidity region of −5.3 < η < −2.6 [42] in the lab frame. In this case, due to the strong v 1 signal and better resolution from Ψ 1 , a three-subevent method with both TPC and EPD is used to determine the first order event plane resolution for the v 1 measurements. The R 12 is converted R 11 for the measurements of v 2 [41]. The resulting event plane resolution as a function of the collision centrality, is shown in Fig. 2.
Using Ψ 1 to analyze v 2 is also used in the recent publication from HADES collaboration [35]. In all cases, standard acceptance corrections are carried out to ensure a uniform distribution of the event plane angle [41]. The final results are corrected for centrality bin width, event plane resolution, tracking efficiency and detector acceptance [19,21].
Systematic uncertainties are estimated point-by-point by varying track selection criteria, and the decay length of parent and daughter when using the KF Particle Finder package [38]. At √ s NN = 3 GeV, the leading systematic source is from particle misidentification by varying the ionization energy loss dE/dx, estimated to contribute 4.3% (1.5%) to π + (proton) v 1 slopes measurements. An additional, common systematic uncertainty from event plane resolution is estimated to be 1.4% and 3% for v 1 and v 2 , respectively. Assuming the sources are uncorrelated, the total systematic uncertainty is obtained by adding uncertainties mentioned above in quadrature.

III. RESULTS AND DISCUSSIONS
The rapidity dependence of the directed flow v 1 and elliptic flow v 2 of identified hadrons from Au+Au collisions at √ s NN = 3 GeV in 10-40% centrality is presented in Fig. 3. Due to the acceptance, the results from the rapidity region −1 < y < 0 are shown. The corresponding p T range for each hadron is shown in the figure. For comparison, calculations of transport theoretical model, JET AA Microscopic Transportation Model (JAM) [43] and Ultra-relativistic Quantum Molecular Dynamics (UrQMD) [24,25], are also given for the abundantly produced hadrons π + , K + , p, and Λ. The results from the cascade and baryonic mean-field modes of the JAM and UrQMD model are shown as colored bands. The same collision centrality and kinematic selection criteria as in the data are applied in the model calculations.
The values of the midrapidity slope, defined as dv 1 /dy| y=0 , are the largest for protons and Λs, see panel (a), and are close to zero for pions in panel (b). In panel (c), dv 1 /dy| y=0 are positive and have small charge dependence among kaons. The JAM and UrQMD mean-field calculation includes a Skyrme potential energy density function [29]. Comparing to the cascade mode, the repulsive interactions among baryons are enhanced via an additional mean-field option, resulting in a good agreement with experimental data. A similar conclusion can be drawn for the elliptic flow v 2 . As shown in the lower panels of Fig. 3, all of the measured midrapidity hadrons, (|y| ≤ 0.5) show negative values of v 2 implying an out-of-plane expansion in the collisions at 3 GeV, contrary to the in-plane expansion in high energy collisions [15,16]. Again, with the mean-field option with κ = 380 MeV, the JAM and UrQMD model calculations qualitatively reproduce the rapidity dependence of v 2 for baryons and pions. Nevertheless, we note that the UrQMD model overpredicts the strength of v 2 for strange baryon Λ and both JAM and UrQMD model fails to reproduce kaon v 2 , see Fig. 3. It is worth noting that, due to the strong influence of the Coulomb potential, the integrated v 2 of π − are all smaller than that of π + over the measured rapidity range.
In the above transport model calculations, no Coulomb force is included. Similar to the previous v 1 studies [19,20,44] from the STAR experiment, a polynomial fit of the form v 1 (y) = a + by + cy 3 was used to extract the strength of directed flow at midrapidity for π ± , K ± , K 0 S , p, and Λ, while the fit form v 1 (y) = by was used for φ and Ξ − due to the limited statistics. The fit range for all particles is −0.75 < y < 0. Hereafter, we refer to dv 1 /dy| y=0 as the slope obtained from the above fit. The cubic fit term, c, can reduce the sensitivity to the rapidity range. The constant term, a, accounts for the effects from event plane fluctuation and momentum conservation [45]. The constant term, a, is found to be < 0.005 for all particles except φ and Ξ − in the 10-40% centrality.
The elliptic flow scaled by the number of constituent quarks, v 2 /n q , for the copiously produced hadrons π ± (squares), K ± (crosses), p andp (circles) is shown as a function of the scaled transverse kinetic energy (m T − m 0 )/n q in Although the overall quark number scaling is evident, it has been observed that the best scaling is reached in the RHIC top energy √ s NN = 200 GeV collisions [15,50]. As the collision energy decreases, the scaling deteriorates. Particles and antiparticles are no longer consistent with the single-particle NCQ scaling [21] due to the mixture of the transported and produced quarks. More detailed discussions on the effects of transported quarks on collectivity can be found in Refs. [19,51]. As one of the important evidence for the QGP formation in high energy collisions at RHIC, the observed NCQ scaling originates from partonic collectivity [15,16,52]. For Au+Au collisions at 3 GeV, data points for π, K and p are represented by filled triangles, open triangles and filled stars, respectively in Fig. 4. It is apparent that all of the values of v 2 /n q are negative. Only proton results are shown, because of the lack of antiproton production at this energy. Contrary to the higher energy data shown, the quark scaling disappears in the observed elliptic flow for positively charged particles in such low energy collisions. The new results clearly indicate different properties for the matter produced. As shown in Fig. 3, the JAM and UrQMD model calculations with baryonic mean-field potential reproduce the observed negative values of v 2 for protons as well as Λs.
In other words, in the Au+Au collisions at 3 GeV, partonic interactions no longer dominate and baryonic scatterings take over. This observation is clear evidence that predominantly hadronic matter is created in such collisions.
Collision energy dependence of the directed and elliptic flow is summarized in Fig. 5, where panel (a) shows the slope of the p T -integrated directed flow at midrapidity, dv 1 /dy| y=0 , for π, K, p, Λ and multistrange hadrons φ and Ξ − from Au+Au collisions for the 10-40% centrality interval. Here K and π are the results of combination of K ± plus K 0 S and π ± , respectively. The p T -integrated v 2 at midrapidity of π, shown by a filled square is much more negative (∼ −0.2) implying stronger shadowing effect at lower center of mass energy. An additional reason for the significant decrease in v 2 is that the p T region of HADES results is relatively higher than STAR results. Due to partonic collectivity in Au+Au collisions at high energy [53], all observed v 1 slopes and v 2 at midrapidity are found to be negative and positive, respectively, while the observed trend in Fig. 5 for Au+Au collisions at 3 GeV is exactly the opposite. The early strong partonic expansion leads to the positive v 2 with NCQ scaling in high energy collisions while at 3 GeV, both weaker pressure gradient and the shadowing of the spectators result in the negative v 2 where the scaling is absent. Results from calculations using the hadronic transport model JAM and UrQMD, with the same centrality and kinematic cuts as used in the data analysis, are also shown as colored bands in the figure. By including the baryonic mean-field, the JAM and UrQMD model reproduced the trends for both dv 1 /dy| y=0 and v 2 for baryons including protons and Λ. The consistency of transport models (JAM and UrQMD) with baryonic mean-field for all measured baryons implies that the dominant degrees of freedom at collision energy of 3 GeV are the interacting baryons. The signatures for the transition from partonic dominant to hadronic and to baryonic dominant regions have also been discussed in Ref. [19,20,54,55] for the ratios of K + /π + and net-particle v 1 slopes, respectively.
Our new data clearly reveals that baryonic interactions dictate the collision dynamics in Au+Au collisions at 3 GeV. Collision energy dependence of (top panel) directed flow slope dv1/dy|y=0 for p, Λ, π(combined from π ± ), K(combined from K ± and K 0 S ), φ and Ξ − , and (bottom panel) elliptic flow v2 for p, π(combined from π ± ) in heavy-ion collisions [18,19,21,22,26]. Collision centrality for all data from RHIC is 10-40%, except for 4.5 GeV where 10-30% is for dv1/dy|y=0 and 0-30% is for v2. Note that the HADES [35] results of proton dv1/dy|y=0 and v2 from 20-30% scaled by a factor of 3 are from 1 < pT < 1.5 (GeV/c), which is in a higher pT region compared to our data (0.4 < pT < 2.0 (GeV/c)). Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The JAM and UrQMD results are shown as colored bands: golden, red and blue bands stand for JAM mean-field, UrQMD meanfield and UrQMD cascade mode, respectively. For clarity the x-axis value of the data points have been shifted.

IV. SUMMARY
In summary, we have reported on the p T and rapidity differential and integral measurements for directed flow v 1 and elliptic flow v 2 of identified hadrons π ± , K ± , K 0 S , φ, p, Λ and Ξ − from the 10-40% centrality Au+Au collisions at √ s NN = 3 GeV, and the high statistics measurements for v 2 of π ± , K ± , p and p at √ s NN = 27 and 54.4 GeV. The NCQ scaling of v 2 is observed for collision energies ≥ 7.7 GeV. Due to the formation of the QGP at center-of-mass collision energies larger than 10 GeV, one finds that each hadron's v 2 is positive while all slopes of v 1 are negative. For Au+Au collisions at 3 GeV, the NCQ scaling is absent and the opposite collective behavior is observed: the elliptic flow of all hadrons at midrapidity is negative; the slope of the directed flow of all hadrons, except π + , at midrapidity is positive. Furthermore, transport models JAM and UrQMD calculations with a baryonic meanfield qualitatively reproduced these results. These observations imply the vanishing of partonic collectivity and a new EOS, likely dominated by baryonic interactions in the high baryon density region.