One of the biggest quests in nuclear and particle physics in the last three decades is to unravel the spin structure of hadrons like protons and neutrons. Spin not only plays a central role in the strong force connecting the elementary constituents of matter, but is also responsible for many of its fundamental properties including the magnetic moment which defines the magnetic properties, the different phases in low temperature physics, and the stability of the universe in general. The origin of the spin of particles like protons and neutrons, which make up to 99.9% of the visible universe, has been the focus of experimental and theoretical efforts. Experiments at European Muon Collaboration (EMC) found that our knowledge of how the spin of the nucleon is derived from its elementary constituents is naive, and our interpretations are not valid. This was termed the spin crisis, an outstanding puzzle for more than three decades and is still not solved. Deciphering the spin puzzle requires knowing the spin of elementary constituents of these particles, quarks and gluons.

One of the major objectives of the Relativistic Heavy Ion Collider (RHIC) spin program at Brookhaven National Laboratory is the measurement of the gluon helicity contribution to the proton spin via measuring the double helicity asymmetry (A_LL) in various channels. In Pioneering High Energy Nuclear Interaction eXperiment (PHENIX) we measure A_LL in π⁰ meson production. The π⁰ meson is reconstructed through its di-photon decay channel. The photons are detected by the PHENIX Electromagnetic Calorimeter, which consists of lead glass and lead scintillator detectors and covers a rapidity of |η|< 0.35 and azimuthal angle of

180°.

In this dissertation, the results of A_LLin π⁰ production from the data collected in 2013 at center of mass energy = 510 GeV are presented. In 2013, the total integrated luminosity is 150 pb^-1 which is almost ten times the total luminosity recorded in 2009 at center of mass energy = 200 GeV. Due to the increase in the center of mass energy and integrated luminosity, these measurements cover the Bjorken x range down to ~0.01. A non-zero A_LL result is observed that is consistent with positive gluon polarization in the probed kinematics.