Recent STAR Results from Heavy-Ion and Polarized Proton Programs

Abstract. We present recent physics results from the STAR experiment at Relativistic Heavy Ion Collider (RHIC). The proceedings cover studies of azimuthal anisotropy in small and large systems, global and local hyperon polarization, correlation femtoscopy, antideuteron and J/ψ production from heavyion program as well as the measurements of longitudinal spin asymmetry from polarized proton program.


Introduction
The main goal of high-energy physics is to understand the properties of the strong interaction that can be described by the Quantum Chromodynamics (QCD). In order to measure the QCD matter, one can use ion-ion collisions. Variation of collision energy provides a unique opportunity to investigate the properties of the created medium on baryon chemical potential (µ B ) and temperature (T ). This medium is also known as Quark-Gluon Plasma (QGP). The Relativistic Heavy Ion Collider (RHIC) accelerates and collides nuclei from protons to uranium. Using different colliding species gives important information about the influence of the initial conditions, dynamical evolution and transport properties. RHIC is also the only accelarator of polarized proton beams. Studying the high-energy polorized p+p collisions is essential key in understanding of the spin structure of the proton in terms of gluon, quark and antiquark constitiuents. In these proceedings, we report recent results from heavy-ion and polorized proton-proton programs obtained in the Solenoidal Tracker At RHIC (STAR) experiment.

Azimuthal harmonics in small and large systems
The process of particle emission in the transverse plane is anisotropic. This anisotropy, known as anisotropic flow, can be measured via Fourier decomposition of the single-particle azimuthal angle (φ) with respect to the n th -order event plane (Ψ n ) [1]. The first three extracted flow coefficients v 1 , v 2 , and v 3 are called directed, elliptic, and triangular flow, respectively. The fluctuations-driven component of v 1 , named v f luc 1 is proportional to the dipole asymmetry of the collision system [2,3]. Azimuthal anisotropy is one the key observables because it carries information about the viscous hydrodynamic response to the initial spatial distribution in energy density due to fluctuations and geometry. Figure 1 shows the < N ch > dependence of the v f luc 1 (a), v 3 (b), and v 2 (c) flow coefficients [4]. The measurements have been performed for p+Au, d+Au, Cu+Cu, Cu+Au, and Au+Au collision at √ s NN = 200 GeV and U+U collisions at sqrts NN = 193 GeV. The inset in Fig. 1(a) compares the extracted values of K ≡ 1/(< N ch >< p 2 T >), that takes into account the long-range non-flow correlations induced by global momentum conservation, for each system.
For < N ch > ≥170, the v n values show a decrease with increasing values of < N ch >. This is consistent with the expected decrease of n for more central collision as compared to the midcentral ones. The decrease of v 2 for < N ch > ≤170 shows the dominant role of size-driven viscous attenuation of the flow harmonics for the give multiplicities. The system-dependent behaviour of v 2 shown in Fig. 1(c) can be attributed to the dependence of 2 on system size for a given value of < N ch >. Figure 2 shows the v 2 / 2 as a function of < N ch > −1/3 [4]. This confirms the system dependence of the 2 on system size. The v 2 / 2 as a function of < N ch > −1/3 for p+Au, d+Au, Cu+Cu, Cu+Au, Au+Au, and U+U collisions. (Inset) The respective ratios of the slopes extracted for each collision system separately relative to the slope extracted from a fit to the combined data sets.
The inset in Fig. 2 shows similarity between the slopes of the 2 -scaled v 2 for Cu+Cu, Cu+Au, Au+Au, and U+U collisions over the indicated multiplicity range. The eccentricityscaled results for p+Au and d+Au collisions also follow the data trend for these heavier collision species with larger systematic uncertainty.

Global hyperon polarization
The angular momentum carried by colliding nuclei can be transferred to the created system. Due to the spin-orbit coupling, this may lead to the global polarization of particle' spin along the direction of angular momentum of the system [5,6]. Experimentally, such a global polarization can be probed with hyperons via parity-violating weak decays, in which the daughter baryon is preferentially emitted in the direction of the hyperon's spin. In case of antihyperon, the daughter baryon tends to be emitted in the opposite direction to the parent spin.
Since the angular momentum of the system is perpendicular to a plane defined by the impact parameter vector and the beam direction (so-called reaction plane), the hypeon polarization can be measured via the azimuthal distribution of daughter baryons with respect to the reaction plane (Ψ 1 ) in the hyperon's rest frame (φ * p ): where α H is the hyperon decay constant, Res(Ψ 1 ) is the experimental resolution of the firstorder event plane. Figure 3 shows the global polarization of Λ andΛ hyperons as a function of collision energy ( √ s NN ) for 20-50% most central Au+Au collisions [7,8]. The global polarization results follow the same trend and seem to decrease with increasing collision energy.  The (3+1)D viscous hydrodynamic model vHLLE with the UrQMD initial state [9] agrees with the data over a wide range of collision energies, including √ s NN = 200 GeV within the current accuracy of the experimental measurements. Calculations from a Multi-Phase Transport (AMPT) model [10] predict slightly higher global polarization than those from the hydrodynamic model, but are also in good agreement with the data within uncertainties.

Polarization along the beam direction
Recently STAR has also reported the measurement of the hyperon polarization along the beam direction [11]: The beam direction component of the polarization, P z , arises from vorticity due to elliptic flow. It is expected that P z will be more sensitive to the later stages of the system evolution after the anisotropic flow is developed [2] as compared to global hyperon polarization which originates mostly from the initial velocity fields. The < cos(θ * p ) > was measured as a function of azimuthal angle of Λ (Λ) relative to Ψ 2 . The acceptance effects and inefficiencies were taken into account. Figure 4 shows < cos(θ * p ) > sub of Λ andΛ, obtained with event plane method, as a function of azimuthal angle relative to Ψ 2 for the 20%-60% centrality region. The lines in Fig. 4 represent the fit results using p 0 + 2p 1 sin(2φ − 2Ψ 2 ), where p 0 and p 1 are the fit parameters. The data are consistent with a sine structure for bothΛ and Λ. This is expected due to the elliptic flow.

Antideuteron production
The underlying mechanism for light (anti)nuclei production in relativistic heavy-ion collisions is not well understood. One of the possible approaches is through coalescence of (anti)nucleons. Since the binding energies of light nuclei are small (≈2.2 MeV for (anti)deuteron and ≈7.7 MeV for 3 He), the light nuclei cannot survive when the temperature is much higher than the binding energy. The typical kinetic freeze-out temperature for light hadrons is around 100 MeV, hence they may be formed by final-state coalescence, after nucleons are decoupled from the hot and dense system. In case of the coalescence picture, the invariant yield of light nuclei is related to the invariant yiled of nucleons as: where p p , p n , and p A are momenta of proton, neutron, and nucleus, respectively. Here p A = Ap p , assuming p p ≈ p n . The A and Z are the mass and charge number of the nucleus. The B A is a coalescence parameter and it reflects probability of nucleon coalescence. Figure 5 shows the excitation function of B 2 at p T /A= 0.65 GeV/c in 0%-10% most central Au+Au collisions [12].  The results are compared to those measured at AGS [13][14][15], SPS [16][17][18] and RHIC [19,20]. At energies below √ s NN = 20 GeV, the coalescence parameters B 2 decrease as a function of increasing collision energy, This implies that the size of the emitting source of nucleons increases with the collision energy. When √ s NN > 20 GeV, the rate of decrease seems to change and saturate up to 62.4 GeV. It might imply a change of the equation of state of the medium in those collisions. The B 2 from 200 GeV is found to be larger than the BES saturation values, which needs further studies. The B 2 values for antideuterons are systematically lower than those for deuterons, which implies that the overall size of the antibaryon-emitting source is larger than that of baryons.

Correlation femtoscopy
In 2015 STAR conducted a fixed-target (FXT) test run using gold ion collisions at √ s NN = 4.5 GeV to show that STAR is capable to run in a fixed-target configuration. One beam was circulated in the collider and lowered to directly graze the edge of a 1 mm thick (4% interaction probability) gold foil target. The target was placed at the edge of the TPC, about 211 cm away from the center of the detector to make use of the full tracking volume of the TPC. Approximately 1.3 million events were collected with a top ≈ 30% centrality trigger. Figure 6 (left) shows the measured femtoscopic radii as a function of transverse mass for 0-10% central Au+Au collisions in the fixed-target mode. Figure 6. (Left) Transverse mass dependence of R out , R side , and R long for pions measured for 0-10% Au+Au collisions in STAR (red stars), E895 (black triangles) [21], and E866 (green crosses) [22]. (Right) The R side vs. R long dependence for the E866, E895, STAR [23] and ALICE [24] experiments.
Only statistical uncertainties shown.
The STAR FXT results are compared with E895 [21] and E866 (E802) [22] and are consistent with the energy dependence trend of these other experiments within uncertainties. Figure 6 (right) shows the dependence of R side , which reflects the transverse size of the source, on R long that reflects the size in the longitudinal direction for several collision energies. As the collision energy increases in the FXT regime, compression reduces the source size and increases the baryon density, whereas the BES collider regime shows increasing longitudinal expansion.
The correlation femtoscopy technique was also used to study identical pion correlations in d+Au collisions at √ s NN = 200 GeV. Figure 7 shows the extracted ππ femtoscopic radii, The R inv decreases with pair tranverse momentum, k T = |p T,1 + p T,2 |, which is consistent with previuos measurement in p+p collisions at the same energy [25].

J/ψ suppression in Au+Au collisions
Among the various probes of the QGP, quarkonia play a special role as they are expected to dissociate in the medium when the Debye radius, inversely proportional to the medium temperature, becomes smaller than their size. Strong suppression of the J/ψ meson with respect to its yield in p+p collisions scaled by the number of binary nucleon-nucleon collisions has been observed at high transverse momenta (p T ) in central heavy-ion collisions at both RHIC and LHC energies. Recently, STAR has presented new measurement of J/ψ suppression at midrapidity in Au+Au collisions at √ s NN = 200 GeV through the dimuon decay channel [26] shown for p T >0.15 GeV/c in Fig. 8. The J/ψ R AA is seen to decrease from peripheral to central collisions, which is expected in the presence of the QGP. The results are compared to those obtained at √ s NN = 2.76 TeV [27].
The low-p T J/ψ's are more suppressed in central and midcentral collisions at RHIC than at the LHC, likely due to the smaller charm quark production cross section and thus smaller regeneration contribution at RHIC. Transport model calculations are consistent with the data at low p T . The calculation from Statistical Hadronization Model (SHM) is shown as the dashed line and also describes the data well in non-peripheral events [28].

W ± longitudinal spin asymmetry
The leptonic W + → e + ν and W − → e − ν decay channels provide sensitivity to the helicity distributions of the quarks, ∆u and ∆d, and antiquarks, ∆ū and ∆d, that is free of uncertainties associated with nonperturbative fragmentation. The primary observable is the longitudinal single-spin asymmetry A L = (σ + − σ − ) = (σ + + σ − ), where σ +(−) is the cross section when the helicity of the polarized proton beam is positive (negative). STAR reported new measurements of the single-spin asymmetries for decay positrons and electrons from W ± bosons produced in longitudinally polarized proton-proton collisions at √ s= 510 GeV [29]. The recorded data correspond to an integrated luminosity of about 250 pb − 1. The luminosity-weighted beam polarization was P= 0.56, with a relative scale uncertainty of 3.3% for the single-beam polarization and 6.4% for the product of the polarizations from both beams. The new W ± A L data are shown in Fig. 9 and consistent with the previously published results, but have statistical uncertainties that are 40%-50% smaller.  The results are compared with expectations based on the DSSV14 [30], NNPDF-pol1.1 [30] and BS15 [31] PDFs. The NNPDFpol1.1 analysis, unlike DSSV14 and BS15, includes the STAR 2011+2012 W ± data [32], which reduces in particular the uncertainties for W − expectations at negative η. The data confirm the existence of a sizable, positive ∆ū in the range 0.05< x <0.25 [32] and the existence of a flavor asymmetry in the polarized quark sea.

Summary
The recent results from the STAR experiment at RHIC has been overviewed. A comprehensive set of flow measurements for different colliding nuclei has been presented. The detailed comparisons of the measurements show the sensitivity of v n to the magnitude of the initialstate eccentricity, system size, and final-state interactions in the expanding matter. The Λ polarization along the beam directions with a quadrupole structure has been observed for the first time and needs futher theoretical input. The values of coalescence parameter, B 2 , for deuterons decrease as collision energy increases and seem to reach a minimum at about √ s NN = 20-40 GeV, indicating a change in the equation of state. B 2 values for antideuterons have been found to be less than those for deuterons at collision energies below 62.4 GeV. New STAR measurements of longitudinal single-spin asymmetry for W ± produced in polarized proton-proton collisions at √ s= 510 GeV have been shown. The A L data for W + and W − , combined with previously published STAR results, show a significant preference for ∆ū(x, Q 2 ) > ∆d(x, Q 2 ) in the fractional momentum range 0.05< x <0.25 at a scale of Q 2 = 10 (GeV/c) 2 .