Exploiting Intrinsic Triangular Geometry in Relativistic ${}^3\mathrm{He}+\mathrm{Au}$ Collisions to Disentangle Medium Properties

Recent results in $d+\mathrm{Au}$ and $p+\mathrm{Pb}$ collisions at RHIC and the LHC provide evidence for collective expansion and flow of the created medium. We propose a control set of experiments to directly compare particle emission patterns from $p+\mathrm{Pb}$, $d+\mathrm{Au}$, and ${}^3\mathrm{He}+\mathrm{Au}$ or $t+\mathrm{Au}$ collisions at the same $\sqrt{s_{NN}}$ . Using a Monte Carlo Glauber simulation we find that a ${}^3\mathrm{He}$ or triton projectile, with a realistic wave function description, induces a significant intrinsic triangular shape to the initial medium. If the system lives long enough, this survives into a significant third-order flow moment $v_3$ even with viscous damping. By comparing systems with one, two, and three initial hot spots, one could disentangle the effects from the initial spatial distribution of the deposited energy and viscous damping. These are key tools for answering the question of how small a droplet of matter is necessary to form a quark-gluon plasma described by nearly inviscid hydrodynamics.

Figure 1

Monte Carlo Glauber simulation results for the spatial anisotropies ${ϵ}_2$ [panel (a)] and ${ϵ}_3$ [panel (b)] in $p+\mathrm{Pb}$, $d+\mathrm{Au}$, ${}^3\mathrm{He}+\mathrm{Au}$, and $t+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$ as a function of impact parameter. The points are calculated with a Gaussian smearing with $\sigma =0.4\mathrm{fm}$ for the energy distribution from each participating nucleon. The lines are the results for central events with a larger Gaussian smearing with $\sigma =0.7\mathrm{fm}$.

Figure 2

An example time evolution of a ${}^3\mathrm{He}+\mathrm{Au}$ event from the initial state to the final state. The color scale indicates the local temperature and the arrows are proportional to the velocity of the fluid cell from which the arrow originates.

Figure 3

$v_n/{ϵ}_n$ versus ${ϵ}_n$ with the flow coefficient for pions evaluated at $p_T=1.0\mathrm{GeV}/c$ from $p+\mathrm{Pb}$, $d+\mathrm{Au}$, and ${}^3\mathrm{He}+\mathrm{Au}$ central ($b<2\mathrm{fm}$) events. The results are with input parameters $\eta /s=1/4\pi$ and initial Gaussian smearing $\sigma =0.4\mathrm{fm}$, and freeze-out temperatures of $T_F=150\mathrm{MeV}$ (left) and $T_F=170\mathrm{MeV}$ (right), respectively.

Figure 4

Pion momentum anisotropies $v_2$ and $v_3$ as a function of transverse momentum from individual $p+\mathrm{Pb}$, $d+\mathrm{Au}$, and ${}^3\mathrm{He}+\mathrm{Au}$ central ($b<2\mathrm{fm}$) events (full lines) Dashed lines are the event-averaged values. The inset shows the ratio of ${}^3\mathrm{He}+\mathrm{Au}$ to $d+\mathrm{Au}$ for $v_3$ and ${ϵ}_3$.

Figure 5

(a) Pion and proton $v_2$ versus $p_T$ for $d+\mathrm{Au}$ and ${}^3\mathrm{He}+\mathrm{Au}$ central ($b<2\mathrm{fm}$) events at RHIC energies using hydrodynamics for $\eta /s=1/(4\pi )$ in comparison to data for 0%–5% central $d+\mathrm{Au}$ data from PHENIX [24]. (b) Pion $v_3$ versus $p_T$ for ${}^3\mathrm{He}+\mathrm{Au}$ central ($b<2\mathrm{fm}$) events at RHIC energies using viscous hydrodynamics for $\eta /s=0.2,1,2$ over $4\pi$ as well as the result of a different smearing parameter, $\sigma$. (c) Pion $v_3$ versus $p_T$ for $p+\mathrm{Pb}$ and ${}^3\mathrm{He}+\mathrm{Au}$ central ($b<2\mathrm{fm}$) events at LHC energies using viscous hydrodynamics for $\eta /s=1/(4\pi )$ in comparison to data for 0.5%–2.5% central $p+\mathrm{Pb}$ data from CMS [25].