Nuclear dependence of the transverse single-spin asymmetry in the production of charged hadrons at forward rapidity in polarized $p+p$, $p+$Al, and $p+$Au collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV

We report on the nuclear dependence of transverse single-spin asymmetries (TSSAs) in the production of positively-charged hadrons 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 rapidity ($1.4<\eta <2.4$) over the range of $1.8<p_T<7.0$ GeV$\mathrm{/}c$ and $0.1<x_F<0.2$. We observed a positive asymmetry $A_N$ for positively-charged hadrons in \polpp collisions, and a significantly reduced asymmetry in $p^{\uparrow }$+$A$ collisions. These results reveal a nuclear dependence of charged hadron $A_N$ in a regime where perturbative techniques are relevant. These results provide new opportunities to use \polpA collisions as a tool to investigate the rich phenomena behind TSSAs in hadronic collisions and to use TSSA as a new handle in studying small-system collisions.