Understanding Hard Interaction in QCD and the Search for the Gluon Spin Contribution to the Spin of the Proton

In the following discourse unpolarized cross sections and double helicity asymmetries of single inclusive positive and negative charged hadrons at mid-rapidity from p + p collisions at p s = 62:4 GeV are presented. Measurements for the transverse momentum range 1:0 \u3c pT \u3c 4:5 GeV/c are done with PHENIX detector at Relativistic Heavy-Ion Collider (RHIC) and are consistent with calculations based on perturbative quantum chromodynamics (pQCD) at next-to-leading order (NLO) in the strong coupling constant, s. Resummed pQCD calculations including terms with next-to-leading log (NLL) accuracy, yielding reduced theoretical uncertainties, also agree with the data. The double helicity asymmetry, sensitive at leading order to the gluon polarization in a momentum fraction range of 0:0