Cross Section and Transverse Single-Spin Asymmetry of $\eta$ Mesons in $p^{\uparrow }+p$ Collisions at $\sqrt{s}=200$ GeV at Forward Rapidity

We present a measurement of the cross section and transverse single-spin asymmetry ($A_N$) for $\eta$ mesons at large pseudorapidity from $\sqrt{s}=200$~GeV $p^{\uparrow }+p$ collisions. The measured cross section for $0.5<p_T<5.0$~GeV/$c$ and $3.0<\mathrm{\mid }\eta \mathrm{\mid }<3.8$ is well described by a next-to-leading-order perturbative-quantum-chromodynamics calculation. The asymmetries $A_N$ have been measured as a function of Feynman-$x$ ($x_F$) from $0.2<\mathrm{\mid }{x}_F\mathrm{\mid }<0.7$, as well as transverse momentum ($p_T$) from $1.0<p_T<4.5$~GeV/$c$. The asymmetry averaged over positive $x_F$ is $⟨A_N⟩=0.061\pm 0.014$. The results are consistent with prior transverse single-spin measurements of forward $\eta$ and ${\pi }^0$ mesons at various energies in overlapping $x_F$ ranges. Comparison of different particle species can help to determine the origin of the large observed asymmetries in $p^{\uparrow }+p$ collisions.