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

The polarized gluon distribution, as described by the polarized parton distribution function Delta g(x), is an important part of the spin structure of the nucleon; however the current data have very limited constraints on Delta g(x) for x < 0.01. During the 2013 RHIC run, the PHENIX experiment collected 146 pb(-1) of longitudinally polarized p + p data at root s = 510 GeV with an average beam polarization of 52%. At this energy, J/psi particles are predominantly produced through gluon-gluon interactions and thus the longitudinal double spin asymmetry, A(LL)(J/psi), is sensitive to the gluon polarization inside the proton. We measure the J/. ALL in the rapidity range 1.2 < vertical bar eta vertical bar < 2.4 by detecting the decay mu(+)mu(-) pairs using the PHENIX muon detector arms. In this kinematic range, A(LL) is sensitive to the polarized gluon distribution at small x similar to 2x10(-3) as well as at moderate x similar to 0.05 where recent RHIC data on jet and pi(0) 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 A(LL)(J/psi) with a statistical uncertainty at similar to 1% level. In these preceedings, the latest status of this analysis will be presented.