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

The beam energy scan (BES) program at RHIC was undertaken to study the nature of the Quantum Chromodynamics (QCD) phase diagram in the plane of temperature versus baryon chemical potential, which is explored by varying the collision energy when heavy nuclei interact Rischke (2004); Stephanov (2005); Fukushima and Sasaki (2013); Brambilla et al. (2014). The phase diagram region of current interest, at relatively high baryon chemical potential, is not accessible so far by first-principle lattice QCD calculations Bazavov et al. (2020). There is thus a wide-ranging international effort to investigate it experimentally Galatyuk (2019).

The BES-II program covers collision energies at and below $\sqrt{s_{\rm NN}}=19.6$ GeV and has the goals of investigating the turn-off of the quark-gluon plasma (QGP) signatures already reported at higher beam energies, and of searching for evidence for a possible first-order phase transition and a critical point Aggarwal et al. (2010); STA (2014). The lowest beam energy which is accessible at RHIC with adequate luminosity in the collider mode of operation is $\sqrt{s_{\rm NN}}=7.7$ GeV. Therefore a fixed-target (FXT) program has been developed to broaden the reach of BES-II and allow the STAR experiment Ackermann et al. (2003) to access energies below $\sqrt{s_{\rm NN}}=7.7$ GeV. In this paper, results are presented from a first run using a single RHIC beam at the normal injection energy ($E_{\rm total}$ = 9.8 GeV/nucleon, $E_{\rm kinetic}$ = 8.9 GeV/nucleon) incident on a gold target inside STAR beam-pipe, providing Au+Au collisions at $\sqrt{s_{\rm NN}}=4.5$ GeV. In reporting a small subsample of data at a single beam energy, we address a subset of the BES-II goals; moreover, the current results have broad implications by virtue of being the first demonstration of STAR’s capability to use FXT mode to extend studies lower in beam energy than previously possible.

Similar Au+Au collision energies were studied during the fixed-target heavy-ion program at the Alternating Gradient Synchrotron (AGS) in the 1990s Rai et al. (1999), covering the range 2.7 to 4.9 GeV in $\sqrt{s_{\rm NN}}$. The present measurements of heavy-ion collisions at 4.5 GeV with STAR in FXT mode extend the systematics of the world data on a number of observables at these energies. Note that the AGS/E895 measurements are the only available data for a heavy system (Au+Au) near $\sqrt{s_{\rm NN}}=4.5$ GeV. The CERN energy scan by the NA49 experiment with Pb+Pb collisions reported data at higher energies, namely at $\sqrt{s_{\rm NN}}=6.4$ GeV and above.

For the results reported in this paper, RHIC provided a single beam of gold ions with a kinetic energy of 8.9 GeV per nucleon in the laboratory frame. The beam was incident on a gold target of thickness 1.93 g/cm² (1 mm), corresponding to a 4% interaction probability (determined using the inelastic Au+Au cross section). The target was installed inside the vacuum pipe, below its center and 211 cm (see Fig. 1) to the west of the center of the STAR detector (see Fig. 2). RHIC was setup up circulating six bunches with a total beam intensity of $3.4\times 10^{9}$ ions, and filled bunches passed the target at a rate of 500 kHz. The beam was then carefully lowered 1.8 cm (note that the radius of the beam pipe in the interior of the detector was 2.0 cm) such that its halo was grazing the top edge of the target. An average of 0.2 gold ions were incident on the target with each passing beam bunch. The target thickness was such that 4% of the incident gold ions experienced an inelastic hadronic collision. The trigger rate of 1 kHz was influenced by the bunch rate, the number of incident ions per bunch, the interaction probability, and the trigger bias (discussed later). The number of filled bunches was selected to ensure that tracks from out-of-time collisions would not be associated with triggered events in the gold target. The amount of circulating beam allowed to be incident on the target was adjusted to fill the STAR data acquisition bandwidth, while minimizing radiation on the inner silicon detectors (which were not used for this test run). The store was held for one hour, and there was no perceptible loss of beam intensity over that period. The one-hour duration was determined by the time allocated to the proof-of-principle test run. The detector systems used for this test run were the Time Projection Chamber (TPC) Anderson et al. (2003), the time-of-flight (TOF) Llope (2012), and the Beam-Beam Counter (BBC) Judd et al. (2018). In this fixed-target configuration, the TPC covered a range of polar angles specified by $0.1<\eta_{\rm lab}<2$, the TOF covered the range $0.1<\eta_{\rm lab}<1.5$, and the BBC, which was only used for triggering, covered the range $3.3<\eta_{\rm lab}<5.0$. This FXT configuration provided tracking and particle identification from target rapidity to midrapidity. Details of the pion and proton acceptance in rapidity and transverse momentum are shown in the next section.

Central Au+Au events were recorded by requiring a coincidence between the downstream trigger detector, an arrangement of scintillator tiles called the Beam-Beam Counter (BBC) Judd et al. (2018), and a high multiplicity signal in the time-of-flight (TOF) barrel Llope (2012). The TOF multiplicity requirement was 130 or more for the bulk of the data to ensure that the trigger would not fire on collisions between beam halo and the aluminum beam pipe or target support structure. Previous studies of collisions between the beam halo and the beam pipe had recorded central Au+Al events with TOF multiplicities as high as 120 tracks. Analysis of the data from this test run indicates that the background was negligible, and that finding has allowed the FXT physics runs performed in 2018, 2019 and 2020 to use minimum-bias triggers. From this brief test run, about 1.3 million events with centrality 0-30% were recorded.

As a first indicator of the performance of the STAR detector in fixed-target mode, a reconstructed event is shown in Fig. 3. In some ways, the performance for mid-rapidity tracks in FXT mode exceeds the performance in collider mode. The mid-rapidity tracks are five meters long as opposed to two meters, which improves the TPC $dE/dx$ resolution from 6.8% to 4.6%. Furthermore, TOF $K/\pi$ separation is maintained up to 2.5 GeV/$c$ instead of up to 1.6 GeV/$c$ (see Fig. 4). The lower particle multiplicities in the FXT events compared to those in higher-energy collider mode collisions result in larger tracking efficiencies. In other ways, the performance for FXT is more challenging. The rapidity boost of the center-of-mass means that a larger fraction of the mid-rapidity particles require TOF hits for particle identification, and the $\eta$ acceptance limits raise the low-$p_{T}$ cut-offs for kaons and protons.

The event selection cut requires the primary vertex to be within 1 cm of the target; 96.6% of events pass this cut. Accepted tracks are required to have a distance of closest approach to the primary vertex of less than 3 cm (roughly six times the tracking resolution) and to include greater than half of the possible TPC hits to avoid double-counting of split tracks.

The distribution of charged particle multiplicities is shown in Fig. 5. Also shown in Fig. 5 are the centrality selection criteria. The centrality class and the average number of participating nucleons, labeled $\langle N_{\rm part}\rangle$ (minimum bias) in Table 1, were estimated using a Monte Carlo Glauber model Ray and Daugherity (2008) assuming a negative binomial distribution for charged particle production. The Glauber model has been employed by STAR for centrality binning at collider energies from 200 to 7.7 GeV, and by the HADES collaboration for fixed-target Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 2.4 GeV Adamczewski-Musch et al. (2018). Comparison of the Glauber Monte Carlo and the data indicates that the trigger efficiency approaches unity for the most central collisions, and therefore we take this as an assumption and estimate the trigger efficiencies for less central collisions from the ratio of the number of recorded events over 267,000 (the average number of events for the two most central bins). For the 0-5%, 5-10%, 10-15%, 15-20%, 20-25% and 25-30% bins, the efficiencies are 100%, 100%, 97%, 76%, 47% and 26%, respectively. Overall, the trigger selects events corresponding to 22.5% of the minimum-bias distribution. The estimated $\langle N_{\rm part}\rangle$ for each bin is then determined by taking a weighted average of $N_{\rm part}$, with weights equal to the number of recorded events for a given $N_{\rm charged}$, calculated as a function of $N_{\rm charged}$ from the Glauber model Miller et al. (2007). The uncertainty on the estimated $\langle N_{\rm part}\rangle$ values arises primarily from the central trigger which did not constrain the Glauber fits at low multiplicity. Also shown in Fig. 5 is the estimated contribution of events which were the result of the pile-up of a triggered event along with a second minimum-bias collision in the target from the same bunch. Our estimate of the overall pile-up rate for all triggers is 0.8%, which is consistent with there being a 20% probability of having a gold ion incident on the target with each passing beam bunch. This pile-up probability is cross-checked and confirmed by measuring the number of vertices reconstructed from collisions one filled bunch after the triggered collision. Due to the momentum resolution of the tracks and the projection distance back to the target (0.5 to 3.0 meters), the average distance of closest approach of a primary track to its vertex of origin is several millimeters. Thus, tracks from two separate collisions within the target would be reconstructed as emerging from a single vertex.

The location of the target along the beam axis was chosen to be $z=211$ cm (where $z=0$ corresponds to the center of the detector) in order to maximize the acceptance of the STAR Time Projection Chamber (TPC) Anderson et al. (2003) for fixed-target events. Protons and pions were selected from all charged tracks within a 2$\sigma$ band centered on the Bichsel prediction for $dE/dx$ Bichsel (2006). The acceptance effects are illustrated in Fig. 6 by the distribution of the measured $p_{T}$ and rapidity, $y$, for protons and pions. For both the pions and protons, the right-hand edge is the $\eta_{\rm lab}$ = 0.1 acceptance limit, while the left-hand edge illustrates the $\eta_{\rm lab}$ = 2 acceptance limit. The magnetic field of the solenoid defines the low $p_{T}$ limit of 100 MeV/$c$. The detector does not impose a high $p_{T}$ limit; the high $p_{T}$ fall-off exhibited in Fig. 6 is due the exponential production. For pions, there is good acceptance from midrapidity ($y=0$) to beam rapidity ($y=1.52$), while for protons, the $\eta_{\rm lab}=2$ acceptance limit imposes a varying low $p_{T}$ limit. Geometric acceptances for charged kaons would fall between those of pions and protons, but, as seen in Fig. 4, particle identification using $dE/dx$ would be limited to $p_{\rm total}<600$ MeV/$c$, precluding analysis of midrapidity charged kaons. In this paper, the rapidity of a particle is always given in the collision center-of-momentum frame, not the laboratory frame.

Characteristics of the QGP, including the nature of the transition between QGP and hadronic matter Steinheimer et al. (2014); Konchakovski et al. (2014); Ivanov and Soldatov (2015); Nara et al. (2017); Singha et al. (2016); Nara et al. (2018, 2020), can be explored via measurements of azimuthal anisotropy with respect to the collision reaction plane. The reaction plane is defined by the beam axis and the vector connecting the centers of the two colliding nuclei. This anisotropy is characterized by a series of Fourier coefficients Ollitrault (1992); Voloshin and Zhang (1996); Poskanzer and Voloshin (1998); Bilandzic et al. (2011):

where the angle brackets indicate an average over all events and particles of interest, $\phi$ denotes the azimuthal angle of each particle, $\Psi_{\text{R}}$ is the azimuthal angle of the reaction plane, and $n$ denotes the harmonic number. The sign of $v_{1}$ is positive for particles near the projectile rapidity, which is the same convention as used in fixed-target relativistic heavy-ion experiments at higher and lower beam energies. The present study explores the first two harmonics: directed flow ($v_{1}$) in the current section, and elliptic flow ($v_{2}$) in Section V.

The second term in the Fourier decomposition of the azimuthal distribution, an elliptic flow $v_{2}$, of identified particles (protons and pions) measured in Au+Au collisions at $\sqrt{s_{\text{NN}}}$ = 4.5 GeV, is discussed in this section. Elliptic flow of protons is compared with the earlier AGS data, while elliptic flow of pions has not been measured at this beam energy before. The appearance of number of constituent quark (NCQ) scaling, i.e. the collapse of quark-number-scaled flow strengths for mesons and baryons onto a single curve, is considered to be evidence of QGP formation Adams et al. (2004a); Tian et al. (2009). Further and more detailed exploration of the energy region where NCQ scaling is not present is very interesting, as it might provide characterisation of relevant observables at the lower energies, where creation of QGP is in question. Protons, which have been analyzed at a similar energy by the E895 experiment at the AGS Pinkenburg et al. (1999), are compared to the previously published results from this experiment, while pions could only be compared to the results at higher energies. (Note that the results for protons at higher energies are published Adamczyk et al. (2013, 2016)). Both positively and negatively charged pions are investigated separately in this analysis and it is found that they show the same behavior within uncertainties. Therefore, in the final plots positive and negative pions are presented together to improve the statistical significance of the result.

In this analysis of elliptic flow, two methods are used: (1) the event plane method using TPC information Ollitrault (1992); Voloshin and Zhang (1996); Poskanzer and Voloshin (1998) and (2) the two-particle cumulants method Bilandzic et al. (2011). The event plane resolution is about 20$\%$. Resonance decays generate unrelated correlations of particles in the final state. Such correlations are a non-flow contribution and they bias the elliptic flow measurement. Since particles from resonance decays are correlated both in $\eta$ and $\phi$, we can reduce the non-flow contribution caused by resonances by measuring elliptic flow using particles which are not correlated in $\eta$. The implementation of this idea is different in each method. For the event plane method, we divide each event into two sub-events. For the cumulant method, we require a 0.1 gap in $\eta$ between all considered pairs. Both methods give results which are consistent within their uncertainties.

Figure 12 shows the elliptic flow $v_{2}$ as a function of transverse kinetic energy $m_{\text{T}}-m$ for pions and protons obtained with the event plane method, where $m$ is mass and $\mbox{$m_{\text{T}}$}=\sqrt{m^{2}+p_{\text{T}}^{2}}$ is transverse mass. It is compared to E895 results Pinkenburg et al. (1999) obtained using the same method. We analyze the 0-30% most central events. For pions and protons, we require $|y|<0.5$. In this analysis, we use tracks with $0.2<\mbox{$p_{\text{T}}$}<2.0$ GeV/c, but due to STAR acceptance in FXT mode at $\sqrt{s_{\text{NN}}}$ = 4.5 GeV, we could analyze only protons with higher values of $p_{\text{T}}$, namely $\mbox{$p_{\text{T}}$}>0.4$  GeV/c (see Fig. 6). The proton results are consistent with E895 results Pinkenburg et al. (1999).

To test the NCQ scaling, we divide $v_{2}$ and $m_{\text{T}}-m$ (Fig. 12) by the number of constituent quarks (3 for protons and 2 for pions). The results are presented in Fig. 13. The observed scaling with the number of constituent quarks at 4.5 GeV is similar to what is observed for Au+Au at higher collision energies Adamczyk et al. (2013, 2016). The system created for Au+Au at $\sqrt{s_{\text{NN}}}$ = 4.5 GeV has, perhaps surprisingly, larger collectivity than expected, and there is no significant difference in identified particle elliptic flow behavior when compared to higher energies. The results in Figure 13 are in possible conflict with expectations. Constituent-quark scaling ($\tfrac{1}{3}v_{2}^{p}\left(m_{T}/3\right)=\tfrac{1}{2}v_{2}^{\pi}\left(m_{T}/2\right)$ at intermediate $m_{T}$) at these energies would suggest partonic collectivity – quark gluon plasma creation – in Au+Au collisions at energies as low as $\sqrt{s_{NN}}=4.5$ GeV. Higher statistical precision is needed to test the NCQ scaling hypothesis decisively, and this is forthcoming in the second phase of the beam energy scan.

Figure 14 shows the beam energy dependence of $v_{2}$ measurements, integrated over $p_{\text{T}}$. The current results are consistent with the trends established by the previously published data.

Two-particle correlations at low relative momentum can be used to extract information on the space-time structure of the particle-emitting source. Femtoscopy– the technique of constructing and analyzing these correlations– has been performed in heavy-ion experiments over a broad range of energies Lisa et al. (2005). In addition to providing a stringent test of the space-time structure of the final-state emission distribution predicted by specific dynamical models Lisa et al. (2005), the energy dependence of femtoscopic scales may reveal fundamental insights into the QGP equation of state. As we discuss below, the low-energy results presented here help reveal a structure predicted Rischke and Gyulassy (1996); Pratt (1986) to probe the latent heat of the deconfinement transition.

In this first set of results from fixed-target running at the STAR experiment, we report that the directed flow ($v_{1}$) of protons and $\Lambda$ baryons is in line with existing systematics at higher and lower energy. This is important, as the directed flow of baryons shows a sign change and a minimum just above the present beam energy, while the directed flow of net baryons shows a double sign change Adamczyk et al. (2014a); Adamczyk et al. (2018). This is one of the most intriguing experimental results from the BES-I program, as well as one of the most difficult for models to explain Steinheimer et al. (2014); Konchakovski et al. (2014); Ivanov and Soldatov (2015); Nara et al. (2017); Singha et al. (2016); Nara et al. (2018, 2020).

We have also presented the first measurements of azimuthal anisotropy of charged pions and neutral kaons at these energies. Both show directed flow ($v_{1}$) signals in the direction opposite to that of the baryons, continuing trends observed at higher energies. The difference between $\pi^{+}$ and $\pi^{-}$ flow becomes stronger as the collision energy is reduced, perhaps signaling isospin or Coulomb dynamics. Interestingly, within the relatively large statistical uncertainties, the data are consistent with constituent quark scaling of elliptic flow, an effect proposed at much higher energies to arise from quark coalescence in the QGP phase.

Femtoscopic radii with charged pions are consistent with earlier measurements of energy, transverse mass, and centrality systematics. Collisions at $\sqrt{s_{\rm NN}}=4.5$ GeV are in the transition region between dynamics dominated by stopping (producing an oblate source) and boost-invariant dynamics (prolate source).

More importantly, these new measurements with much-improved statistics, 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 the QGP to the hadronic phase. Previous results were insufficiently precise to detect this effect. This is the promise of an experimental program that revisits heavy ion collisions in this energy range: improving the quantitative precision of measurements, with well-understood systematics consistent over a broad energy range, may produce qualitatively new opportunities. Now that the predicted Rischke and Gyulassy (1996) $R_{\rm out}/R_{\rm side}$ energy systematic has been revealed, it deserves theoretical attention from hydro and transport modelers. The magnitude and width of the structure may allow an estimate of the latent heat of the QCD deconfinement transition.

Overall, while these measurements are important and of interest on their own, they also pave the way for the FXT energy scan with nominally one hundred times more events at each of 9 beam energy points. The FXT energy scan is an integral part of the BES-II program at RHIC which began in early 2019. It extends the reach of the STAR experiment across an important energy regime of high baryon chemical potential, ranging from 420 to 720 MeV Cleymans et al. (2006), corresponding to collision energies from $\sqrt{s_{\text{NN}}}=7.7$ GeV down to 3.0 GeV.

We acknowledge valuable discussions with Yasushi Nara and Horst Stöcker. We thank the RHIC Operations Group and RCF at BNL, the NERSC Center at LBNL, and the Open Science Grid consortium for providing resources and support. This work was supported in part by the Office of Nuclear Physics within the U.S. DOE Office of Science, the U.S. National Science Foundation, the Ministry of Education and Science of the Russian Federation, National Natural Science Foundation of China, Chinese Academy of Science, the Ministry of Science and Technology of China and the Chinese Ministry of Education, the Higher Education Sprout Project by Ministry of Education at NCKU, the National Research Foundation of Korea, Czech Science Foundation and Ministry of Education, Youth and Sports of the Czech Republic, Hungarian National Research, Development and Innovation Office, New National Excellency Programme of the Hungarian Ministry of Human Capacities, Department of Atomic Energy and Department of Science and Technology of the Government of India, the National Science Centre of Poland, the Ministry of Science, Education and Sports of the Republic of Croatia, RosAtom of Russia and German Bundesministerium fur Bildung, Wissenschaft, Forschung and Technologie (BMBF), Helmholtz Association, Ministry of Education, Culture, Sports, Science, and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS).