Simultaneous binary collisions in the planar four-body problem

We consider simultaneous binary collisions in the general planar four-body problem. We prove they are regularizable in the sense of continuity with respect to initial conditions using a blow-up of the singularity. Furthermore, numerical evidence is given that the differentiability of the regularization should be, in general, less than C8/3. As a simple example, the double isosceles four-body problem, displays that kind of behaviour.