Measurement of Long-Range Angular Correlation and Quadrupole Anisotropy of Pions and (Anti)Protons in Central $d+\mathrm{Au}$ Collisions at $\sqrt{s_{NN}}=200$ GeV

We present azimuthal angular correlations between charged hadrons and energy deposited in calorimeter towers in central $d+\mathrm{Au}$ and minimum bias $p+p$ collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$. The charged hadron is measured at midrapidity $|\eta |<0.35$, and the energy is measured at large rapidity ($-3.7<\eta <-3.1$, Au-going direction). An enhanced near-side angular correlation across $|\mathrm{\Delta }\eta |>2.75$ is observed in $d+\mathrm{Au}$ collisions. Using the event plane method applied to the Au-going energy distribution, we extract the anisotropy strength $v_2$ for inclusive charged hadrons at midrapidity up to $p_T=4.5\mathrm{GeV}/c$. We also present the measurement of $v_2$ for identified ${\pi }^{\pm }$ and (anti)protons in central $d+\mathrm{Au}$ collisions, and observe a mass-ordering pattern similar to that seen in heavy-ion collisions. These results are compared with viscous hydrodynamic calculations and measurements from $p+\mathrm{Pb}$ at $\sqrt{s_{NN}}=5.02\mathrm{TeV}$. The magnitude of the mass ordering in $d+\mathrm{Au}$ is found to be smaller than that in $p+\mathrm{Pb}$ collisions, which may indicate smaller radial flow in lower energy $d+\mathrm{Au}$ collisions.

Figure 1

The azimuthal correlation functions $C(\mathrm{\Delta }\varphi ,p_T)$, as defined in Eq. (2), for track-tower pairs with different track $p_T$ selections in (a)–(c) 0%–5% central $d+\mathrm{Au}$ collisions and (d)–(f) minimum bias $p+p$ collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$. From top to bottom, the track $p_T$ bins are (a), (d) 0.2–1.0, (b), (e) 1.0–2.0, and (c), (f) $2.0–4.0\mathrm{GeV}/c$. The pairs are formed between charged tracks measured in the PHENIX central arms at $|\eta |<0.35$ and towers in the MPC-S calorimeter ($-3.7<\eta <-3.1$, Au going). A near-side peak is observed in the central $d+\mathrm{Au}$ collisions which is not seen in minimum bias $p+p$ collisions. Each correlation function is fit with a four-term Fourier cosine expansion; the individual components $n=1$ to $n=4$ are drawn on each panel, together with the fit function sum.

Figure 2

(a) $c_2(p_T)$ for track-tower pairs from 0%–5% $d+\mathrm{Au}$ collisions and $c_2(p_T)$ for pairs in minimum bias $p+p$ collisions times the dilution factor $(\mathrm{\Sigma }{E_T}^{p+p}/\mathrm{\Sigma }{E_T}^{d+\mathrm{Au}})$. Panel (b) shows their ratio, indicating that the contribution to the $c_2$ amplitude in $d+\mathrm{Au}$ from elementary processes present in $p+p$ is small, only a few percent at low $p_T$ and rising to only 10% by 4.5 GeV/$c$. Both statistical (bar) and systematic (band) uncertainties are shown.

Figure 3

Measured $v_2(EP)$ for midrapidity charged tracks in 0%–5% central $d+\mathrm{Au}$ at $\sqrt{s_{NN}}=200\mathrm{GeV}$ using the event plane method in (a). Also shown are $v_2$ measured in central $p+\mathrm{Pb}$ collisions at $\sqrt{s_{NN}}=5.02\mathrm{TeV}$ [2, 3, 6] and our prior measurements with two particle correlations [$v_2(2p)$] for $d+\mathrm{Au}$ collisions [16]. A polynomial fit to the current measurement and the ratios of experimental values to the fit are shown in (b).

Figure 4

Measured $v_2(p_T)$ for identified pions and (anti)protons, each charged combined, in 0%–5% central $d+\mathrm{Au}$ collisions at RHIC. In (a) the data are compared with the calculation from a viscous hydrodynamic model [31, 32, 33], and in (b) the $v_2$ data for pions and protons in 0%–20% central $p+\mathrm{Pb}$ collisions at LHC are shown for comparison [12], they are measured from pair correlations with a peripheral event yield subtraction.