How much color do we really need? Two-loop subleading-color effects in photon and jet physics

In recent years, the complete set of cross sections for Large Hadron Collider (LHC) processes ending with three resolved final states consisting of either photons or jets has been evaluated at next-to-next-to-leading order in QCD and leading order in QED. Results for three photons or three jets have only been obtained using the leading-color approximation of the virtual two-loop amplitudes. In the meantime, the required amplitudes have become available without recourse to the color expansion. In the present publication, we quantify the effects of the subleading-color contributions, and show that they do not exceed 2\% for most of the previously published results. The one exception is the ratio of three- to two-jet cross sections, where subleading-color effects can reach up to 5\%. Furthermore, we show that these conclusions hold for both popular infrared renormalization schemes, minimal subtraction and Catani's. The size of the effects is usually overshadowed by the size of the remaining uncertainty due to the truncation of the perturbation series. This is particularly important in the case of three-jet distributions that have already been used for the extraction of the strong-coupling constant at the very high energies available at the LHC.