Varying alpha and the electroweak model

Inspired by recent claims for a varying fine structure constant, alpha, we investigate the effect of “promoting coupling constants to variables” upon various parameters of the standard model. We first consider a toy model: Proca theory of the massive photon. We then explore the electroweak theory with one and two dilaton fields. We find that a varying alpha unavoidably implies varying W and Z masses. This follows from gauge invariance, and is to be contrasted with Proca theory. For the two dilaton theory the Weinberg angle is also variable, but Fermi's constant and the tree level fermion masses remain constant unless the Higgs potential becomes dynamical. We outline some cosmological implications.