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 $3.0<|eta|<3.8$ 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 $0.2<|x_{F}|<0.7$, as well as transverse momentum ($p_T$) from $1.0<p_T<4.5$~GeV/$c$. The asymmetry averaged over positive $x_F$ is $langle{A_{N}}rangle=0.061{pm}0.014$. 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.