Single and Double Perturbative Splitting Diagrams in Double Parton Scattering

We discuss the role of two different types of diagram in the proton-proton double parton scattering (DPS) cross section - single and double perturbative splitting graphs. Using explicit calculations of simple graphs from these classes we show that the treatment of these graphs by the 'double PDF' framework for describing the DPS cross section, introduced a number of years ago by Snigirev and collaborators, is unsatisfactory. We suggest that a contribution from single perturbative splitting graphs should be included in the DPS cross section, albeit with a different geometrical prefactor to the contribution from 'zero perturbative splitting' graphs.