  This Letter reports a measurement of the cross section for producing pairs of
central prompt isolated photons in proton-antiproton collisions at a total
energy of 1.96 TeV using data corresponding to 9.5/fb integrated luminosity
collected with the CDF II detector at the Fermilab Tevatron. The measured
differential cross section is compared to three calculations derived from the
theory of strong interactions. These include a prediction based on a leading
order matrix element calculation merged with parton shower, a next-to-leading
order, and a next-to-next-to-leading order calculation. The first and last
calculations reproduce most aspects of the data, thus showing the importance of
higher-order contributions for understanding the theory of strong interaction
and improving measurements of the Higgs boson and searches for new phenomena in
diphoton final states.
