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The STAR Collaboration reports a measurement of the transverse single-spinasymmetries, $A_{N}$, for neutral pions produced in polarized proton collisionswith protons ($pp$), with aluminum nuclei ($p\rm{Al}$) and with gold nuclei($p\rm{Au}$) at a nucleon-nucleon center-of-mass energy of 200 GeV. Neutralpions are observed in the forward direction relative to the transverselypolarized proton beam, in the pseudo-rapidity region $2.7<\eta<3.8$. Resultsare presented for $\pi^0$s observed in the STAR FMS electromagnetic calorimeterin narrow Feynman x ($x_F$) and transverse momentum ($p_T$) bins, spanning therange $0.17<x_F<0.81$ and $1.7<p_{T}<6.0$ GeV/$c$. For fixed $x_F<0.47$, theasymmetries are found to rise with increasing transverse momentum. For larger$x_F$, the asymmetry flattens or falls as ${p_T}$ increases. Parametrizing theratio $r(A) \equiv A_N(pA)/A_N(pp)=A^P$ over the kinematic range, the ratio$r(A)$ is found to depend only weakly on $A$, with ${\langle}P{\rangle} =-0.027 \pm 0.005$. No significant difference in $P$ is observed between thelow-$p_T$ region, $p_T<2.5$ GeV/$c$, where gluon saturation effects may play arole, and the high-$p_T$ region, $p_T>2.5$ GeV/$c$. It is further observed thatthe value of $A_N$ is significantly larger for events with a large-$p_T$isolated $\pi^0$ than for events with a non-isolated $\pi^0$ accompanied byadditional jet-like fragments. The nuclear dependence $r(A)$ is similar forisolated and non-isolated $\pi^0$ events.

physical review. d/physical review. d.

Comparison of transverse single-spin asymmetries for forward $\pi^{0}$  production in polarized $pp$, $p\rm{Al}$ and $p\rm{Au}$ collisions at nucleon  pair c.m. energy $\sqrt{s_{\mathrm{NN}}}= 200$ GeV