Elliptic and triangular flow anisotropy in deuteron-gold collisions at $\sqrt{s_{NN}}=200$ GeV at RHIC and in proton-lead collisions at $\sqrt{s_{NN}}=5.02$ TeV at the LHC

We study elliptic and triangular flow in the collisions of deuteron-gold nuclei at $\sqrt{s_{NN}}=200$ GeV at RHIC and of proton-lead nuclei at $\sqrt{s_{NN}}=5.02$ TeV at the LHC, utilizing (3+1)-dimensional ideal hydrodynamics for the dynamic evolution of the fireball and a Monte Carlo Glauber based energy deposition model for simulating the fluctuating initial conditions. Sizable values of elliptic and triangular flow are obtained for both colliding systems, and the results are consistent with PHENIX, ALICE, ATLAS, and CMS measurements. For these studied centralities, we find that the elliptic flow in proton-lead collisions is smaller than deuteron-gold collisions, while the triangular flows are comparable in both colliding systems. Our results indicate that the observed collective anisotropic flow in deuteron-gold and proton-lead collisions may be obtained from relativistic hydrodynamic evolution of the fireball with initial-state fluctuations.

Figure 1

The initial eccentricities ${\epsilon }_2$ and ${\epsilon }_3$ as a function of $N_{\mathrm{mult}}$, for d-Au collisions at $\sqrt{s_{NN}}=200$ GeV and for p-Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV.

Figure 2

The probability distribution of particle number $P\left(N_{}\right)$ and the centrality as a function of $N_{\mathrm{mult}}$, for d-Au collisions at $\sqrt{s_{NN}}=200$ GeV and p-Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV.

Figure 3

Elliptic and triangular flow as a function of $p_T$ for d-Au collisions at $\sqrt{s_{NN}}=200$ GeV at RHIC for 0–5 % and 0–20 % centralities.

Figure 4

Elliptic and triangular flow as a function $p_T$ for p-Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV at the LHC for 0–1 %, 0–2 %, 0–5 %, and 0–20 % centralities.

Figure 5

The initial eccentricities ${\epsilon }_2$ and ${\epsilon }_3$ as a function of $N_{\mathrm{part}}$ for d-Au collisions at $\sqrt{s_{NN}}=200$ GeV, and for p-Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV.

Figure 6

The initial eccentricities ${\epsilon }_2$ and ${\epsilon }_3$ as a function $E_T$ for d-Au collisions at $\sqrt{s_{NN}}=200$ GeV, and for p-Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV.

Figure 7

$v_2$ and $v_3$ as a function of $p_T$ for d-Au collisions at $\sqrt{s_{NN}}=200$ GeV at RHIC for 0–5 % centrality, using different centrality determination methods.

Figure 8

$v_2$ and $v_3$ as a function $p_T$ for p-Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV at the LHC for 0–5 % centrality, using different centrality determination methods.