Azimuthal anisotropy relative to the participant plane from a multiphase transport model in central $p+\mathrm{Au}$, $d+\mathrm{Au}$, and ${}^3\mathrm{He}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200$ GeV

Recent data from $p+p$ and $p+\mathrm{Pb}$ collisions at the Large Hadron Collider (LHC), and $d+\mathrm{Au}$ and ${}^3\mathrm{He}+\mathrm{Au}$ collisions at the Relativistic Heavy Ion Collider (RHIC) reveal patterns that—when observed in the collision of heavy nuclei—are commonly interpreted as indicators of a locally equilibrated system in collective motion. The comparison of these data sets, including the forthcoming results from $p+\mathrm{Au}$ and $p+\mathrm{Al}$ collisions at RHIC, will help to elucidate the geometric dependence of such patterns. It has recently been shown that a multiphase transport model (AMPT) can describe some of these features in LHC data with a parton-parton scattering cross section comparable to that required to describe $A+A$ data. In this paper, we extend these studies by incorporating a full wave-function description of the ${}^3\mathrm{He}$ nucleus to calculate elliptical and triangular anisotropy moments $v_2$ and $v_3$ for $p+\mathrm{Au}$, $d+\mathrm{Au}$, and ${}^3\mathrm{He}+\mathrm{Au}$ collisions at the RHIC top energy of 200 GeV. We find reasonable agreement with the measured $v_2$ in $d+\mathrm{Au}$ and ${}^3\mathrm{He}+\mathrm{Au}$ and $v_3$ in ${}^3\mathrm{He}+\mathrm{Au}$ for transverse momentum $\left(p_T\right)\lesssim 1\mathrm{GeV}/c$, but underestimate these measurements for higher values of $p_T$. We predict a pattern of coefficients $(v_2,v_3)$ for $p+\mathrm{Au}$, dominated by differences in the number of induced local hot spots (i.e., one, two, or three) arising from intrinsic geometry. Additionally, we examine how this substantial azimuthal anisotropy accrues during each individual evolutionary phase of the collision in the AMPT model. The possibility of a simultaneous description of RHIC- and LHC-energy data, the suite of different geometries, and high multiplicity $p+p$ data is an exciting possibility for understanding the underlying physics in these systems.

Figure 1

(a) Two-particle correlation for charged particles within $0.90<p_T<1.04\mathrm{GeV}/c$ for $p+p$ and ${}^3\mathrm{He}+\mathrm{Au}$ events at $\sqrt{s_{{}_{NN}}}=200$ GeV. (b) Contributions to the correlation function arising from jet fragmentation are removed by subtracting away the per-trigger yield from $p+p$ events. The resulting correlation function is shown in yellow.

Figure 2

AMPT calculation results for the azimuthal anisotropy moments $v_2$ and $v_3$ for central $d+\mathrm{Au}$ at $\sqrt{s_{{}_{NN}}}=200$ GeV, compared with experimental results from the PHENIX experiment.

Figure 3

AMPT calculation results for the azimuthal anisotropy moments $v_2$ and $v_3$ for central $p+\mathrm{Au}$ at $\sqrt{s_{{}_{NN}}}=200$ GeV.

Figure 4

AMPT calculation results for the azimuthal anisotropy moments $v_2$ and $v_3$ for central ${}^3\mathrm{He}+\mathrm{Au}$ at $\sqrt{s_{{}_{NN}}}=200$ GeV, compared with experimental results from the PHENIX experiment.

Figure 5

(a) Ratio of elliptic and (b) triangular anisotropy moments as a function of $p_T$ in $p+\mathrm{Au}$ and ${}^3\mathrm{He}+\mathrm{Au}$ compared with a baseline in $d+\mathrm{Au}$. Dashed lines are the ratios of $\varepsilon$ values from the initial geometry.

Figure 6

Effects on $v_n$ of enabling and disabling the parton-scattering phase and the hadronic cascade in AMPT for (a), (b) ${}^3\mathrm{He}+\mathrm{Au}$, and (c), (d) $p+\mathrm{Au}$.

Figure 7

Elliptic and triangular anisotropy moments in (a) ${}^3\mathrm{He}+\mathrm{Au}$ and (b) $p+\mathrm{Au}$ collisions following partonic scattering using partons immediately prior to hadronization and hadrons immediately after hadronization via coalescence.