Constraining $\Delta G$ at low-x with Double Longitudinal Spin Asymmetries for Forward Hadrons in PHENIX

Recent global analyses that include polarized p+p data from RHIC through 2009 suggest for the first time a positive contribution of the gluon polarization, $\Delta G$, to the overall proton spin. The data sets included in the analysis constrain $\Delta g(x)$ in the range $0.05< x <0.2$, leaving the lower x region nearly unconstrained. This low-x region can be accessed via a double helicity asymmetry in hadron production at large pseudorapidity, with a dominant contribution from collisions between a high-momentum quark and a low-momentum gluon. At PHENIX, we measure cluster $A_{LL}$ at large pseudorapidity ($3.1<\eta<3.9$) using the Muon Piston Calorimeter (MPC). The majority of the clusters ($>80\%$) come from $\pi^{0}$ decay where the photon showers in the calorimeter overlap. Simulations using the event generator PYTHIA have shown that measuring forward $\pi^{0}$'s can access $\Delta g(x)$ for $x \sim$ $10^{-2}$ for inclusive $\pi^{0}$'s or down to $x \sim$ $10^{-3}$ for the dihadron channel. Here, we present the status of $A_{LL}$ measurements in the MPC at $\sqrt{s}=500\: GeV$ from the 2011 through 2013 runs. This data will help to provide stronger constraints on the form of $\Delta g(x)$ in ongoing global analyses.