Measurements of double-helicity asymmetries in inclusive $J/ψ$ production in longitudinally polarized $p+p$ collisions at $\sqrt{s}=510$ GeV
We report the double helicity asymmetry, $A_{LL}^{J/ψ}$, in inclusive $J/ψ$ production at forward rapidity as a function of transverse momentum $p_T$ and rapidity $|y|$. The data analyzed were taken during $\sqrt{s}=510$ GeV longitudinally polarized $p$$+$$p$ collisions at the Relativistic Heavy Ion Collider (RHIC) in the 2013 run using the PHENIX detector. At this collision energy, $J/ψ$ particles are predominantly produced through gluon-gluon scatterings, thus $A_{LL}^{J/ψ}$ is sensitive to the gluon polarization inside the proton. We measured $A_{LL}^{J/ψ}$ by detecting the decay daughter muon pairs $μ^+ μ^-$ within the PHENIX muon spectrometers in the rapidity range $1.2<|y|<2.2$. In this kinematic range, we measured the $A_{LL}^{J/ψ}$ to be $0.012 \pm 0.010$~(stat)~$\pm$~$0.003$(syst). The $A_{LL}^{J/ψ}$ can be expressed to be proportional to the product of the gluon polarization distributions at two distinct ranges of Bjorken $x$: one at moderate range $x \approx 0.05$ where recent RHIC data of jet and $π^0$ double helicity spin asymmetries have shown evidence for significant gluon polarization, and the other one covering the poorly known small-$x$ region $x \approx 2\times 10^{-3}$. Thus our new results could be used to further constrain the gluon polarization for $x< 0.05$.