What stays the same when you reshuffle two U(1) forces?

When a theory has two U(1) gauge symmetries, their interaction—kinetic mixing—evolves differently at different energies. Using a reformulation that treats gauge bosons symmetrically, the authors derive clean two-loop equations showing how this mixing scales up and down, then identify mathematical invariants that survive arbitrary field redefinitions. These invariants connect directly to measurable millicharges, making it easier to predict what experiments should see.