Double parton scattering in the ultraviolet: addressing the double counting problem

An important question in the theory of double parton scattering is how to incorporate the possibility of the parton pairs being generated perturbatively via $1 \to 2$ splitting into the theory, whilst avoiding double counting with single parton scattering loop corrections. Here, we describe a consistent approach for solving this problem, which retains the notion of double parton distributions (DPDs) for individual hadrons. Further, we discuss the construction of appropriate model DPDs in our framework, and the use of these to compute the DPS part, presenting DPS 'luminosities' from our model DPDs for a few sample cases.