Transverse single-spin asymmetry of forward $\eta$ mesons in $p^{\uparrow }+p$ collisions at $\sqrt{s}=200$ GeV

Utilizing the 2012 transversely polarized proton data from the Relativistic Heavy Ion Collider at Brookhaven National Laboratory, the forward $\eta$-meson transverse single-spin asymmetry ($A_N$) was measured for $p^{\uparrow }+p$ collisions at $\sqrt{s}=200$ GeV as a function of Feynman-x ($x_F$) for $0.2<\mathrm{\mid }{x}_F\mathrm{\mid }<0.8$ and transverse momentum ($p_T$) for $1.0<p_T<5.0$ GeV/$c$. Large asymmetries at positive $x_F$ are observed ($<A_N>=0.086\pm 0.019$), agreeing well with previous measurements of ${\pi }^0$ and $\eta$ $A_N$, but with reach to higher $x_F$ and $p_T$. The contribution of initial-state spin-momentum correlations to the asymmetry, as calculated in the collinear twist-3 framework, appears insufficient to describe the data and suggests a significant impact on the asymmetry from fragmentation.