Comparison of the isolated direct photon cross sections in $p\overline{p}$ collisions at $\sqrt{s}=1.8\mathrm{}\hspace{0.5em}\mathrm{TeV}$ and $\sqrt{s}=0.63\mathrm{}\hspace{0.5em}\mathrm{TeV}$

We have measured the cross sections $d^2\sigma {/dP}_{T}d\eta$ for production of isolated direct photons in $p\overline{p}$ collisions at two different center-of-mass energies, 1.8 TeV and 0.63 TeV, using the Collider Detector at Fermilab. The normalization of both data sets agrees with the predictions of quantum chromodynamics for a photon transverse momentum ${(P}_T)$ of 25 GeV/c, but the shapes versus photon $P_T$ do not. These shape differences lead to a significant disagreement in the ratio of cross sections in the scaling variable $x_T(\equiv {2P}_T/\sqrt{s}).\mathrm{}$ This disagreement in the $x_T$ ratio is difficult to explain with conventional theoretical uncertainties such as scale dependence and parton distribution parametrizations.