Rapidity Correlations and $\mathrm{\Delta }G$ from Prompt Photon plus Jet Production in Polarized $pp$ Collisions

A study of prompt photon plus associated jet production is performed at next-to-leading order (O($\alpha {\alpha }_s^2$)) in QCD at $\sqrt{S}=200-500$ GeV, appropriate for the RHIC polarized $\vec{p}\vec{p}$ collider experiment. Momentum correlations between the jet and photon are examined and the utility of the process as a method for constraining the size and shape of the polarized gluon density of the proton $\mathrm{\Delta }G$ is examined.