Measurements of second-harmonic Fourier coefficients from azimuthal anisotropies in $p+p,$ $p+\mathrm{Au},$ $d+\mathrm{Au},$ and ${}^3\mathrm{He}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200 \mathrm{GeV}$

Recently, the PHENIX Collaboration has published second- and third-harmonic Fourier coefficients $v_2$ and $v_3$ for midrapidity $(\left|\eta \right|<0.35)$ charged hadrons in 0%–5% central $p+\mathrm{Au}$, $d+\mathrm{Au}$, and ${}^3\mathrm{He}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV, utilizing three sets of two-particle correlations for two detector combinations with different pseudorapidity acceptance [Acharya et al., Phys. Rev. C 105, 024901 (2022)]. This paper extends these measurements of $v_2$ to all centralities in $p+\mathrm{Au}$, $d+\mathrm{Au}$, and ${}^3\mathrm{He}+\mathrm{Au}$ collisions, as well as $p+p$ collisions, as a function of transverse momentum ($p_T$) and event multiplicity. The kinematic dependence of $v_2$ is quantified as the ratio $R$ of $v_2$ between the two detector combinations as a function of event multiplicity for $0.5<p_T<1$ and $2<p_T<2.5\mathrm{GeV}/c$. A multiphase-transport (AMPT) model can reproduce the observed $v_2$ in most-central to midcentral $d+\mathrm{Au}$ and ${}^3\mathrm{He}+\mathrm{Au}$ collisions. However, the AMPT model systematically overestimates the measurements in $p+p$, $p+\mathrm{Au}$, and peripheral $d+\mathrm{Au}$ and ${}^3\mathrm{He}+\mathrm{Au}$ collisions, indicating a higher nonflow contribution in the AMPT model than in the experimental data. The AMPT model fails to describe the observed $R$ for $0.5<p_T<1\mathrm{GeV}/c$, but there is qualitative agreement with the measurements for $2<p_T<2.5\mathrm{GeV}/c$.

Figure 1

Correlation functions $C\left(\mathrm{\Delta }\varphi \right)$ in 5%–10% centrality $p+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV measured using (a) CNT-FVTXS, (b) CNT-FVTXN, (c) CNT-BBCS, (d) FVTXS-FVTXN, and (e) BBCS-FVTXS detector combinations. The short-dashed (black) curve shows the Fourier fit to correlation functions. The dotted (green), dash-dotted (red), dashed-double-dotted (blue), and long-dashed (magenta) curves indicate $c_1$, $c_2$, $c_3$, and $c_4$ components, respectively.

Figure 2

Correlation functions $C\left(\mathrm{\Delta }\varphi \right)$ in 5%–10% centrality $d+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV measured using (a) CNT-FVTXS, (b) CNT-FVTXN, (c) CNT-BBCS, (d) FVTXS-FVTXN, and (e) BBCS-FVTXS detector combinations. The short-dashed (black) curve shows the Fourier fit to correlation functions. The dotted (green), dash-dotted (red), dashed-double-dotted (blue), and long-dashed (magenta) curves indicate $c_1$, $c_2$, $c_3$, and $c_4$ components, respectively.

Figure 3

Correlation functions $C\left(\mathrm{\Delta }\varphi \right)$ in 5%–10% centrality ${}^3\mathrm{He}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV measured using (a) CNT-FVTXS, (b) CNT-FVTXN, (c) CNT-BBCS, (d) FVTXS-FVTXN, and (e) BBCS-FVTXS detector combinations. The short-dashed (black) curve shows the Fourier fit to correlation functions. The dotted (green), dash-dotted (red), dashed-double-dotted (blue), and long-dashed (magenta) curves indicate $c_1$, $c_2$, $c_3$, and $c_4$ components, respectively.

Figure 4

Second-harmonic azimuthal anisotropy $v_2\{3\times 2\mathrm{PC}\}$ in (a) 0%–5% [24], (b) 5%–10%, (c) 10%–20%, (d) 20%–40%, (e) 40%–60%, and (f) 60%–88% centrality $p+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV with the FVTXS-CNT-FVTXN (BF) and BBCS-FVTXS-CNT (BB) detector combinations as a function of $p_T$. The solid (black) squares are shifted for visibility. The bands around the (black) squares and (black) circles show the systematic uncertainties. The bands around the dashed (red) and dotted (blue) curves show statistical uncertainties in the AMPT calculations with the $3\times 2\mathrm{PC}$ method. The solid (green) curves show $v_2$ in AMPT using the parton participant plane.

Figure 5

Second-harmonic azimuthal anisotropy $v_2\{3\times 2\mathrm{PC}\}$ in (a) 0%–5% [24], (b) 5%–10%, (c) 10%–20%, (d) 20%–40%, (e) 40%–60%, and (f) 60%–88% centrality $d+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV with the FVTXS-CNT-FVTXN (BF) and BBCS-FVTXS-CNT (BB) detector combinations as a function of $p_T$. The solid (black) squares are shifted for visibility. The bands around the (black) squares and (black) circles show the systematic uncertainties. The bands around the dashed (red) and dotted (blue) curves show statistical uncertainties in the AMPT calculations with the $3\times 2\mathrm{PC}$ method. The solid (green) curves show $v_2$ in AMPT using the parton participant plane.

Figure 6

Second-harmonic azimuthal anisotropy $v_2\{3\times 2\mathrm{PC}\}$ in (a) 0%–5% [24], (b) 5%–10%, (c) 10%–20%, (d) 20%–40%, (e) 40%–60%, and (f) 60%–88% centrality ${}^3\mathrm{He}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV with the FVTXS-CNT-FVTXN (BF) and BBCS-FVTXS-CNT (BB) detector combinations as a function of $p_T$. The solid (black) squares are shifted for visibility. The bands around the (black) squares and (black) circles show the systematic uncertainties. The bands around the dashed (red) and dotted (blue) curves show statistical uncertainties in the AMPT calculations with the $3\times 2\mathrm{PC}$ method. The solid (green) curves show $v_2$ in AMPT using the parton participant plane.

Figure 7

Second-harmonic azimuthal anisotropy $v_2$ with the $3\times 2\mathrm{PC}$ method in (open symbols) 60%–84% central $p+\mathrm{Au}$ collisions and (solid symbols) MB $p+p$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV with the FVTXS-CNT-FVTXN (BF) and BBCS-FVTXS-CNT (BB) detector combinations as a function of $p_T$. The open (black) squares and (black) circles are shifted for visibility. The solid bands around the (black) circles and (black) squares show experimental systematic uncertainties. The bands around the dashed (red) and dotted (blue) curves show statistical uncertainties in the AMPT calculations with the $3\times 2\mathrm{PC}$ method in $p+p$ collisions. The solid (green) curve shows $v_2$ in AMPT using the parton participant plane in $p+p$ collisions.

Figure 8

Second-harmonic azimuthal anisotropy $v_2\{3\times 2\mathrm{PC}\}$ as a function of centrality in (a), (b) $p+\mathrm{Au}$, (c), (d) $d+\mathrm{Au}$, and (e), (f) ${}^3\mathrm{He}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV with the FVTXS-CNT-FVTXN (BF) and BBCS-FVTXS-CNT (BB) detector combinations. The bands around the (black) circles and (black) squares show experimental systematic uncertainties. The bands around the dashed (red) and dotted (blue) curves show statistical uncertainties in the AMPT calculations with the $3\times 2\mathrm{PC}$ method. The solid (green) curves show $v_2$ in AMPT using the parton participant plane.

Figure 9

Second-harmonic azimuthal anisotropy $v_2\{3\times 2\mathrm{PC}\}$ as a function of charged-particle multiplicity $\frac{d{N}_{\mathrm{ch}}}{d\eta }$ at midrapidity in $p+p$, $p+\mathrm{Au}$, $d+\mathrm{Au}$, and ${}^3\mathrm{He}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}$ = 200 GeV with (a), (c) the BBCS-FVTXS-CNT (BB) and (b), (d) FVTXS-CNT-FVTXN (BF) detector combinations. The bands around the data points show experimental systematic uncertainties and the bands around the curves show statistical uncertainties in the AMPT calculations. Note that AMPT results for $p+p$ collisions in panels (c) and (d) are outside of the plot range due to their large values.

Figure 10

The ratio $R$ of $v_2\left\{\mathrm{BF}\right\}$ to $v_2\left\{\mathrm{BB}\right\}$ as a function of charged-particle multiplicity $\frac{d{N}_{\mathrm{ch}}}{d\eta }$ at midrapidity in (squares) $p+\mathrm{Au}$, (diamonds) $d+\mathrm{Au}$, (crosses) ${}^3\mathrm{He}+\mathrm{Au}$, and (circles) $p+p$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV. The bands around the data points show experimental systematic uncertainties and the bands around the curves show statistical uncertainties in the AMPT calculations.