Measurement of the transverse single-spin asymmetry for forward neutron production in a wide $p_T$ range in polarized $p+p$ collisions at $\sqrt{s} = 510$ GeV

Transverse single-spin asymmetries $A_{\textrm{N}}$ of forward neutrons at pseudorapidities larger than 6 had only been studied in the transverse momentum range of $p_{\textrm{T}} < 0.4$ GeV/$c$. The RHICf Collaboration has extended the previous measurements up to 1.0 GeV/$c$ in polarized $p+p$ collisions at $\sqrt{s}~=~510$GeV, using an electromagnetic calorimeter installed in the zero-degree area of the STAR detector at the Relativistic Heavy Ion Collider. The resulting $A_{\textrm{N}}$s increase in magnitude with $p_{\textrm{T}}$ in the high longitudinal momentum fraction $x_{\textrm{F}}$ range, but reach a plateau at lower $p_{\textrm{T}}$ for lower $x_{\textrm{F}}$. For low transverse momenta the $A_{\textrm{N}}$s show little $x_{\textrm{F}}$ dependence and level off from intermediate values. For higher transverse momenta the $A_{\textrm{N}}$s show also an indication to reach a plateau at increased magnitudes. The results are consistent with previous measurements at lower collision energies, suggesting no $\sqrt{s}$ dependence of the neutron asymmetries. A theoretical model based on the interference of $\pi$ and $a_1$ exchange between two protons could partially reproduce the current results, however an additional mechanism is necessary to describe the neutron $A_{\textrm{N}}$s over the whole kinematic region measured.