Isolated Photons at Hadron Colliders at O($\alpha alpha_s^2$) (I): Spin Averaged Case

The cross sections for isolated and non-isolated prompt photon production with unpolarized hadron beams are studied at order $\alpha\alpha_s^2$. Two methods of performing the calculations are compared. One uses purely analytic techniques and the second uses a combination of analytic and Monte Carlo techniques to perform the phase-space integrations. The results of the analytic and Monte Carlo methods are compared both before and after isolation cuts are placed on the photon. Fragmentation contributions are included at next-to-leading order in the analytic case, and the question of the infrared sensitivity of this contribution once isolation is implemented is addressed. Numerical results are presented and compared with the latest CDF data for $p\bar{p} \to \gamma+X$ using the latest parton densities for the proton.