Isolated Prompt Photon Cross Sections

In ee and in hadron-hadron reactions at collider energies, prompt photons are observed and their cross sections are measured only if the photons are relatively isolated in phase space. Isolation is required to reduce various hadronic backgrounds including those from the electromagnetic decay of mesons, e.g., π → 2γ. The essence of isolation is that a cone of half-angle δ is drawn about the direction of the photon’s momentum, and the isolated cross section is defined for photons accompanied by less than a specified amount of hadronic energy in the cone, e.g., E h ≤ Emax = ǫhEγ ; Eγ denotes the energy of the photon. Theoretical predictions will therefore depend upon the additional parameters δ and ǫh. Isolation removes backgrounds, but it also reduces the signal. For example, it reduces the contribution from processes in which the photon emerges from the long-distance fragmentation of quarks and gluons, themselves produced in short-distance hard collisions. Hard photons in ee processes arise as QED bremsstrahlung from the initial beams, radiation that is directed along angles near θγ = 0 and π, and as final state radiation from direct and fragmentation processes. The final state radiation populates all angles, with a distribution having both transverse, 1 + cosθγ , and longitudinal components . Much of the predictive power of perturbative QCD derives from factorization theorems . Conventional factorization expresses a physical quantity as the convolution of a partonic term with a nonperturbative long-distance matrix element, and it requires that the partonic term, calculated perturbatively order-by-order in the the strong coupling strength αs, have no infrared singularities. Using ee → γX as an example, we demonstrate that the