Transverse single-spin asymmetry of charged hadrons at forward and backward rapidity in polarized $p+p$, $p+\mathrm{Al}$, and $p+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$

Reported here are transverse single-spin asymmetries ($A_N$) in the production of charged hadrons as a function of transverse momentum ($p_T$) and Feynman-$x$ ($x_F$) in polarized $p^{\uparrow }+p$, $p^{\uparrow }+\mathrm{Al}$, and $p^{\uparrow }+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$. The measurements have been performed at forward and backward rapidity ($1.4<|\eta |<2.4$) over the range of $1.5\mathrm{GeV}/c<p_T<7.0\mathrm{GeV}/c$ and $0.04<|x_F|<0.2$. A nonzero asymmetry is observed for positively charged hadrons at forward rapidity ($x_F>0$) in $p^{\uparrow }+p$ collisions, whereas the $p^{\uparrow }+\mathrm{Al}$ and $p^{\uparrow }+\mathrm{Au}$ results show smaller asymmetries. This finding provides new opportunities to investigate the origin of transverse single-spin asymmetries and a tool to study nuclear effects in $p+A$ collisions.

Figure 1

Side view of the PHENIX detector in 2015.

Figure 2

Estimation of $K/\pi$ ratios at the collision vertex (Generation) and $K/\pi$ ratios for reconstructed muon arm tracks in in the geant4 simulation (Reconstruction) for $p+p$ collisions. The variations from the different physics list in the geant4 simulation are shown as the bands on the reconstructed $K/\pi$ ratios. According to the simulation, the reconstructed particle composition is modified compared to the generated one due to interaction with the detector material.

Figure 3

Estimation of $K/\pi$ ratios at the collision vertex (Generation) and $K/\pi$ ratios for reconstructed muon arm tracks in in the geant4 simulation (Reconstruction) for $p+A$ collisions. The variations from the different physics lists in the geant4 simulation are shown as the bands on the reconstructed $K/\pi$ ratios. According to the simulation, the reconstructed particle composition is modified compared to the generated one due to interaction with the detector material.

Figure 4

The distribution of generated $x_F$ for reconstructed $x_F$ bins from geant4 simulation in $p+p$ collisions.

Figure 5

$A_N$ of charged hadrons from $p^{\uparrow }+p$ collisions as a function of $p_T$ in the (a) backward ($x_F<0$,) and (b) forward ($x_F>0$) regions. Vertical bars (boxes) represent statistical (systematic) uncertainties. Points are shifted by $p_T=+0.2\mathrm{GeV}/c$ for negatively charged hadrons. A scale uncertainty from the polarization (3%) is not included.

Figure 6

$A_N$ of charged hadrons from $p^{\uparrow }+p$ collisions as a function of $x_F$, where $x_F>0$ is along the direction of the polarized proton. Vertical bars (boxes) represent statistical (systematic) uncertainties. Points are shifted by $x_F=+0.003$ for negatively charged hadrons. Dotted bands represent twist-3 model calculations [28] by varying the $K/\pi$ ratio by $\pm 30\%$ of the central value. A scale uncertainty from the polarization (3%) is not included.

Figure 7

$A_N$ of negatively charged hadrons from $p^{\uparrow }+p$, $p^{\uparrow }+\mathrm{Al}$, and $p^{\uparrow }+\mathrm{Au}$ collisions as a function of $p_T$ in the (a) backward ($x_F<0$) and (b) forward ($x_F>0$) regions. Vertical bars (boxes) represent statistical (systematic) uncertainties. Points are shifted by $p_T=+0.02$ $(+0.04)\mathrm{GeV}/c$ for $p^{\uparrow }+\mathrm{Al}$ ($p^{\uparrow }+\mathrm{Au}$) results. A scale uncertainty from the polarization (3%) is not included.

Figure 8

$A_N$ of positively charged hadrons from $p^{\uparrow }+p$, $p^{\uparrow }+\mathrm{Al}$, and $p^{\uparrow }+\mathrm{Au}$ collisions as a function of $p_T$ in the (a) backward ($x_F<0$) and (b) forward ($x_F>0$) regions. Vertical bars (boxes) represent statistical (systematic) uncertainties. Points are shifted by $p_T=+0.02$ $(+0.04)\mathrm{GeV}/c$ for $p^{\uparrow }+\mathrm{Al}$ ($p^{\uparrow }+\mathrm{Au}$) results. A scale uncertainty from the polarization (3%) is not included.

Figure 9

$A_N$ of (a) negatively charged hadrons and (b) positively charged hadrons from $p^{\uparrow }+p$, $p^{\uparrow }+\mathrm{Al}$, and $p^{\uparrow }+\mathrm{Au}$ collisions as a function of $x_F$, where $x_F>0$ is along the direction of the polarized proton. Vertical bars (boxes) represent statistical (systematic) uncertainties. Points are shifted by $x_F=-0.01,-0.005,+0.005,+0.01(-0.005,-0.003,+0.003,+0.005)$ at $-0.2<x_F<-0.05,-0.05<x_F<0.04,0.04<x_F<0.05,0.05<x_F<0.2$, respectively for $p^{\uparrow }+\mathrm{Au}$ ($p^{\uparrow }+\mathrm{Al}$) results. A scale uncertainty from the polarization (3%) is not included.