Quadrupole Anisotropy in Dihadron Azimuthal Correlations in Central $d\mathbf{+}\mathrm{Au}$ Collisions at $\sqrt{s_{NN}}\mathbf{=}200\mathrm{GeV}$

The PHENIX collaboration at the Relativistic Heavy Ion Collider (RHIC) reports measurements of azimuthal dihadron correlations near midrapidity in $d+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$. These measurements complement recent analyses by experiments at the Large Hadron Collider (LHC) involving central $p+\mathrm{Pb}$ collisions at $\sqrt{s_{NN}}=5.02\mathrm{TeV}$, which have indicated strong anisotropic long-range correlations in angular distributions of hadron pairs. The origin of these anisotropies is currently unknown. Various competing explanations include parton saturation and hydrodynamic flow. We observe qualitatively similar, but larger, anisotropies in $d+\mathrm{Au}$ collisions at RHIC compared to those seen in $p+\mathrm{Pb}$ collisions at the LHC. The larger extracted $v_2$ values in $d+\mathrm{Au}$ are consistent with expectations from hydrodynamic calculations owing to the larger expected initial-state eccentricity compared with that from $p+\mathrm{Pb}$ collisions. When both are divided by an estimate of the initial-state eccentricity the scaled anisotropies follow a common trend with multiplicity that may extend to heavy ion data at RHIC and the LHC, where the anisotropies are widely thought to arise from hydrodynamic flow.

Figure 1

Azimuthal conditional yields, $Y(\Delta \varphi )$, for (open [black] squares) 0%–5% most central and (open [black] circles) peripheral (50%–88% least central) collisions with a minimum $\Delta \eta$ separation of 0.48 units. Difference $\Delta Y(\Delta \varphi )$ (filled [blue] circles), which is ([blue] curve) fit to $a_0+2a_2\cos (2\Delta \varphi )$, where $a_0$ and $a_2$ are computed directly from the data. (shaded [blue] band) Statistical uncertainty on $a_2$. The bottom left (right) panel shows the same quantity for same-sign (opposite-sign) pairs.

Figure 2

The $n$th-order pair anisotropy, $c_n$, of the central collision excess as a function of associated particle $p_T^a$. $c_2$ (filled [red] circles) and $c_3$ (filled [green] squares) are for $0.5<p_T^t<0.75\mathrm{GeV}/c$, $0.48<|\Delta \eta |<0.7$. $c_2$ as extracted from $d+\mathrm{Au}$ HIJING events using the same procedure as in the data is also shown (open circles). $c_3$ as expected for our $p_T$ selections from Ref. [31] is shown as a dashed line.

Figure 3

Charged hadron second-order anisotropy, $v_2$, as a function of transverse momentum for (filled [blue] circles) PHENIX and (open [black] squares) ATLAS [9]. Also shown are hydrodynamic calculations from Bozek [14, 31] (dotted [blue] curve) and Bzdak et al. [32, 39] for impact-parameter glasma initial conditions (solid curve) and the MC-Glauber model initial conditions (dashed curve).

Figure 4

The eccentricity-scaled anisotropy, $v_2/{\epsilon }_2$, vs charged-particle multiplicity ($d{N}_{\mathrm{ch}}/d\eta$) for $d+A$ and $p+\mathrm{Pb}$ collisions [8, 9]. Also shown are $\mathrm{Au}+\mathrm{Au}$ data at $\sqrt{s_{NN}}=200\mathrm{GeV}$ [34, 35, 36] and $\mathrm{Pb}+\mathrm{Pb}$ data at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$ [37, 38]. The $v_2$ are for similar $p_T$ selections. The colored curves are for different nucleon representations in the ${\epsilon }_2$ calculation in the MC-Glauber model. The errors shown are statistical only and only shown on the $d+\mathrm{Au}$ point with the pointlike centers ${\epsilon }_2$ for clarity. Owing to the lack of available multiplicity data in $p+\mathrm{Pb}$ and $d+\mathrm{Au}$ collisions, the $d{N}_{\mathrm{ch}}/d\eta$ values for those systems are calculated from HIJING [27]. All $d{N}_{\mathrm{ch}}/d\eta$ values are in the center of mass system.