Comment by at_a_remove

How I learned it, as a mere undergrad, was that the mass of the virtual particle for the field in question determined exactly how long it could exist, just by the uncertainty principle -- much like the way the virtual particles drive Hawking radiation.

In short, a massive virtual particle can exist only briefly before The Accountant comes looking to balance the books. And if you give it a speed of c, it can travel only so far during its brief existence before the books get balanced. And therefore the range of the force is determined by the mass of the force carrier virtual particle.

There's probably some secondary and tertiary "loops" as the virtual particle possibly decays during its brief existence, influencing the math a little further, but that is beyond me.