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We discuss two topics in double parton scattering (DPS) theory that have beenthe subject of recent research interest. First, the role of `double partonsplitting' diagrams in DPS is discussed. We outline the `double PDF'description of DPS, which was introduced a number of years ago. It is pointedout that under this framework, a certain structure is anticipated in the crosssection expression for a `double perturbative splitting' diagram, which in theframework is regarded as DPS. We show that although this structure does indeedappear in the `double perturbative splitting' diagrams, there is no naturalreason to demarcate specifically this part of the graph as the DPS part, andindeed there is no natural part of these diagrams that can be regarded as DPS.There therefore appear to be some unsatisfactory features in the double PDFapproach to describing DPS. The second issue we discuss is that of interferenceand correlated parton contributions to proton-proton DPS. We explain in simpleterms why there can be such contributions to the DPS cross section. Thepotential existence of such contributions was pointed out long ago by Mekhfiand more recently by Diehl and Schafer, but has been largely ignored inphenomenological investigations of DPS.

Double Parton Splitting Diagrams and Interference and Correlation Effects in Double Parton Scattering