Double-Spin Asymmetry in Neutral Pion ($\pi^0$) Production in Longitudinally Polarized $p+p$ Collisions

Beyond the valence quarks' spin contribution to the total spin of a proton, gluon and sea quark contributions are becoming clear as well. For proton+proton collisions at a center of mass energy of 510 GeV, neutral pion production is dominated by gluon-gluon and gluon-quark scattering. An avenue to constrain the gluon polarization is the asymmetry, $A_{LL}$, in the production of neutral pions from collisions of longitudinally spin-polarized proton beams. Our experiment was performed with the STAR detector at the Relativistic Heavy Ion Collider (RHIC), unique for its ability to collide spin-polarized proton beams.The Endcap Electromagnetic Calorimeter (EEMC) of the STAR detector with its pseudorapidity $\left( \eta \right) $ range between 1.09 and 2.00 and full azimuthal coverage measures energies of photons from $\pi^0$ decays. We consider the invariant mass of all photon pairs in the EEMC as we identify $\pi^0$ candidates. We will present the current status of the analysis of the $\pi^0$ $A_{LL}$ as measured by the EEMC at STAR in 2012 data with center-of-mass energy of 510 GeV.