J/ψ Longitudinal Double Spin Asymmetry Measurement at Forward Rapidity in p + p Collisions at s = 510 GeV

The polarized gluon distribution, as described by the polarized parton distribution function [Formula: see text], is an important part of the spin structure of the nucleon; however the current data have very limited constraints on [Formula: see text] for [Formula: see text]. During the 2013 RHIC run, the PHENIX experiment collected 146 pb[Formula: see text] of longitudinally polarized [Formula: see text] data at [Formula: see text] GeV with an average beam polarization of 52%. At this energy, [Formula: see text] particles are predominantly produced through gluon-gluon interactions and thus the longitudinal double spin asymmetry, [Formula: see text], is sensitive to the gluon polarization inside the proton. We measure the [Formula: see text] [Formula: see text] in the rapidity range [Formula: see text] by detecting the decay [Formula: see text] pairs using the PHENIX muon detector arms. In this kinematic range, [Formula: see text] is sensitive to the polarized gluon distribution at small [Formula: see text] as well as at moderate [Formula: see text] where recent RHIC data on jet and [Formula: see text] production show possible evidence for significant gluon polarization. Compared to previous measurements in 2005 and 2006, the Run 2013 data set has roughly twenty times more statistics and will allow us to measure [Formula: see text] with a statistical uncertainty at [Formula: see text]% level. In these preceedings, the latest status of this analysis will be presented.