Using probability is a good start I think. As I understand it, CERN should be able to find new particles below about 2–3 TeV in energy. It hasn't and physicists say it’s a reasonable assumption that there might not be anything new to find until energy scales of 100,000,000 TeV or more. You'll need to build and accelerator around the Sun to reach those energy levels. With that in mind, does it make sense to build something slightly larger than LHC? At billions of dollars?