Flow and interferometry results from $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=4.5$ GeV

The beam energy scan (BES) program at the BNL Relativistic Heavy Ion Collider (RHIC) was extended to energies below $\sqrt{s_{NN}}=7.7$ GeV in 2015 by successful implementation of the fixed-target mode of operation in the STAR (Solenoidal Tracker At RHIC) experiment. In this mode, ions circulate in one ring of the collider and interact with a stationary target at the entrance of the STAR time projection chamber. The first results for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=4.5$ GeV are presented, demonstrating good performance of all the relevant detector subsystems in fixed-target mode. Results presented here include directed and elliptic flow of identified hadrons, and radii from pion femtoscopy. The latter, together with recent HADES results, reveal a long-sought peak structure that may be caused by the system evolving through a first-order phase transition from quark-gluon plasma to the hadronic phase. Directed and elliptic flow for pions are presented for the first time at this beam energy. Pion and proton elliptic flow show behavior which hints at constituent quark scaling, and demonstrate that a definitive conclusion will be achievable using the full statistics of the ongoing second phase of BES (BES-II). In particular, BES-II to date has recorded fixed-target data sets with two orders of magnitude more events at each of nine energies between $\sqrt{s_{NN}}=3.0$ and 7.7 GeV.

Figure 1

Photo of the gold target inserted inside the beam pipe. Inset: photo of the gold target on its aluminum support structure.

Figure 2

A schematic cross section of the STAR detector, showing the location of the target.

Figure 3

Reconstruction of a $\sqrt{s_{NN}}=4.5$ GeV $\mathrm{Au}+\mathrm{Au}$ event. TPC tracks are shown in red, projections to the vertex within the target are shown in yellow, and associated TOF hits are shown in blue.

Figure 4

The top panel shows the particle identification using $dE/dx$ in the TPC. The bottom panel shows particle identification using inverse velocity ($1/\beta$) measured by the TOF.

Figure 5

Centrality selection for STAR FXT $\sqrt{s_{NN}}=4.5$ GeV $\mathrm{Au}+\mathrm{Au}$ collisions. The centrality variable $N_{\mathrm{charged}}$ is the number of tracks that pass the basic track cuts. The black points are the data, the thin red curve is the combined Monte Carlo Glauber and negative binomial fit to the data, and the thick blue line is a Monte Carlo model of pile-up events [14]. Vertical lines indicate the minimum number of tracks required for an event to be in the corresponding centrality bin. Events with multiplicity greater than 240 are dominated by pile-up, and are excluded from all analyses.

Figure 6

Negative pion and proton relative yield versus rapidity and transverse momentum for STAR FXT $\sqrt{s_{NN}}=4.5$ GeV Au $+$ Au collisions. The black line indicates the location of midrapidity. The target (beam) rapidity in the center of mass frame is at $+1.52$ ($-1.52$).

Figure 7

Rapidity dependence of directed flow, $v_1\left(y\right)$, for protons with transverse momentum $0.4<p_{\text{T}}<2.0$ $\mathrm{GeV}/c$ from events with 10–25 % centrality. Two analysis methods, as discussed in the text, are compared. Plotted error bars are statistical only, and systematic errors are of comparable size. The curve is a cubic fit to the data.

Figure 8

Upper panel: Rapidity dependence of directed flow, $v_1\left(y\right)$, for negative pions with transverse momentum $p_{\text{T}}>0.2$ $\mathrm{GeV}/c$ and total momentum magnitude $\left|p\right|<1.6$ $\mathrm{GeV}/c$ from events within 10–30,% centrality. Here, the BBC-based event plane method is used. Plotted error bars are statistical only, and systematic errors are of comparable size. The solid curve is a cubic fit to the data. Lower panel: The same for positive pions.

Figure 9

The rapidity dependence of the directed flow for the $\mathrm{\Lambda }$ using the TPC event plane. Open symbols are the reflection of the solid symbols. The solid blue line is a cubic fit to the measured data. Plotted error bars are statistical only, while systematic errors are $\pm 0.7\times {10}^{-2}$.

Figure 10

The rapidity dependence of the directed flow for the $K_{\text{S}}^0$ using the TPC event plane. Open symbols are the reflection of the solid symbols. The solid blue line is a cubic fit to the measured data. Plotted error bars are statistical only, while systematic errors are $\pm 1.7\times {10}^{-2}$.

Figure 11

Beam energy dependence of the directed flow slope $d{v}_1/dy$ at midrapidity for baryons (upper plot) and mesons (lower plot) measured by STAR (this paper and Refs. [34, 37]) and by AGS experiment E895 [35, 42]. Some points are slightly offset horizontally.

Figure 12

$v_2$ of protons and pions from STAR FXT data analysis, and $v_2$ of protons from E895 experiment. Blue (red) stars represent STAR FXT proton (pion) data (0–30 % centrality), and black circles show E895 data (12–25 % centrality) [45].

Figure 13

$v_2$ scaled by the number of constituent quarks ($n_q$) for charged pions (red stars) and protons (blue stars) for 0–30 % central collisions. The values of $v_2$ scaled with $n_q$ for pions and protons are consistent with each other within errors. For comparison, points from E895 are also shown (black circles)

Figure 14

The excitation function $v_2$ for all charged particles or separately for protons and pions, measured by several experiments. The STAR FXT points for protons and for pions are near the region where a change in slope occurs. Data are shown from FOPI [48, 49], E895 [45], E877 [50], CERES [51], NA49 [52], PHENIX [53], PHOBOS [54], and from the STAR collider energies [46, 47, 55, 56, 57].

Figure 15

Projections of the correlation functions in the LCMS frame onto the $q_{\text{out}}$, $q_{\text{side}}$, and $q_{\text{long}}$ axes for ${\pi }^{-}{\pi }^{-}$ pairs from events in the 0–10 % centrality range. Pairs are created from tracks in the momentum range $0.1<p_{\text{T}}<0.3$ $\mathrm{GeV}/\mathit{c}$. For each projection $q_i$ shown, the other components of relative momentum are integrated over the range $|q_j|<35$ $\mathrm{MeV}/c$. The red curve shows the projections [58] of a three-dimensional fit to Eq. (4). Errors are statistical only.

Figure 16

Excitation function of $R_{\text{out}}$, $R_{\text{side}}$, and $R_{\text{long}}$ for four experiments: HADES [64], E895 [65], STAR, and E866 [66]. STAR points show both systematic (red boxes) and statistical errors (black lines) while errors for E895 and E866 are statistical only. HADES systematic errors are roughly the same size as the datapoints. The same momentum and centrality selections are applied as in Fig. 15.

Figure 17

Transverse mass dependence of $R_{\text{out}}$, $R_{\text{side}}$, and $R_{\text{long}}$ for three experiments: E895 [65], STAR, and E866 [66]. Pairs for the STAR points are created from negative pion tracks in the momentum range $0.15<p_{\text{T}}<0.8$ $\mathrm{GeV}/\mathit{c}$ from events in the 0–15 % centrality range. STAR points show both systematic (magenta boxes) and statistical errors (black lines) while errors for E895 and E866 are statistical only.

Figure 18

The centrality dependence of $R_{\text{out}}$, $R_{\text{side}}$, and $R_{\text{long}}$. Errors are statistical only. Here ${\pi }^{+}{\pi }^{+}$ and ${\pi }^{-}{\pi }^{-}$ pairs in the momentum range 0.15 $<p_{\text{T}}<$ 0.8 $\mathrm{GeV}/\mathit{c}$ are used.

Figure 19

$R_{\text{side}}$ vs. $R_{\text{long}}$, which measures the prolateness/oblateness of the pion emitting source when viewed from beside the beam. HADES [76], ALICE [77], and STAR [78] points include systematic errors; E895 [65] show statistical errors only. STAR fixed target data correspond to pion pairs with $〈k_T〉=0.22$ $\mathrm{GeV}/c$ from 0–5 % centrality events. The various centrality, $p_{\text{T}}$, and $k_{\text{T}}$ cuts used in the different experiments are discussed in the text. The grey curve indicates the evolution of the shape, as the collision energy is increased.

Figure 20

Top: The difference between the squared transverse femtoscopic radii are plotted as a function of the collision energy for central collisions. Bottom: The energy dependence of the ratio of the transverse radii. The centrality and $m_T$ values for the high-statistics datasets are HADES [76] (0–10 %, 349 $\mathrm{MeV}/c$); STAR fixed target (this work) (0–10 %, 303 $\mathrm{MeV}/c$); STAR collider [78] (0–10 %, 326 $\mathrm{MeV}/c$). The values for the earlier measurements are E895 [65] (0–11 %, 330 $\mathrm{MeV}/c$); E866 [66] (0–15 %, 295 $\mathrm{MeV}/c$). Only statistical errors are indicated, as changing the centrality [58] or transverse mass selection slightly will affect $R_{\mathrm{out}}$ and $R_{\mathrm{side}}$ similarly; see the text for a discussion of systematic effects, which can shift STAR datapoints, together, by $\sim 5\%$ ($\sim 20\%$) for $R_{\mathrm{out}}/R_{\mathrm{side}}$ ($R_{\mathrm{out}}^2-R_{\mathrm{side}}^2$).