  We present a detailed study of the double parton scattering (DPS)
singularity, which is a specific type of Landau singularity that can occur in
certain one-loop graphs in theories with massless particles. A simple formula
for the DPS singular part of a four-point diagram with arbitrary
internal/external particles is derived in terms of the transverse momentum
integral of a product of light cone wavefunctions with tree-level matrix
elements. This is used to reproduce and explain some results for DPS
singularities in box integrals that have been obtained using traditional loop
integration techniques. The formula can be straightforwardly generalised to
calculate the DPS singularity in loops with an arbitrary number of external
particles. We use the generalised version to explain why the specific MHV and
NMHV six-photon amplitudes often studied by the NLO multileg community are not
divergent at the DPS singular point, and point out that whilst all NMHV
amplitudes are always finite, certain MHV amplitudes do contain a DPS
divergence. It is shown that our framework for calculating DPS divergences in
loop diagrams is entirely consistent with the `two-parton GPD' framework of
Diehl and Schafer for calculating proton-proton DPS cross sections, but is
inconsistent with the `double PDF' framework of Snigirev.
