Transverse single-spin asymmetry of charged hadrons at forward and backward rapidity in polarized $p$+$p$, $p$+Al, and $p$+Au collisions at $\sqrt{s_{NN}}=200$ 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 $p^{\uparrow }$+$p$, $p^{\uparrow }$+Al, and $p^{\uparrow }$+Au collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV. The measurements have been performed at forward and backward rapidity ($1.4<\mathrm{\mid }\eta \mathrm{\mid }<2.4$) over the range of $1.5<p_T<7.0\mathrm{G}\mathrm{e}\mathrm{V}\mathrm{/}c$ and $0.04<\mathrm{\mid }{x}_F\mathrm{\mid }<0.2$. A nonzero asymmetry is observed for positively charged hadrons at forward rapidity ($x_F>0$) in $p^{\uparrow }$+$p$ collisions, whereas the $p^{\uparrow }$+Al and $p^{\uparrow }$+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.