PHYSICAL PARAMETERS AND RENORMALIZATION OF U(1)(A)XU(1)(B) MODELS

We analyze the structure of models with unbroken and spontaneously bro ken U(1)(a) x U(1)(b) gauge symmetry. We show that the quantum correct ions to the 2N gauge charges, with N = number of fermions + number of scalars, can be absorbed in the redefinition of three independent gaug e couplings (g(a), g(b), and g(ab)). We establish the (one-loop) condi tions on the matter content for g(ab) = 0 (a value usually assumed in the literature) and we show that in the minimal extensions of the Stan dard Model with an extra U(1) symmetry the choice g(ab) = 0 is not sta ble under radiative corrections induced by the standard Higgs fields. Moreover, g(ab) = 0 to all orders seems to require an exact symmetry. The spontaneous breaking of the gauge symmetry induces further mixing between the two gauge bosons and introduces a fourth independent physi cal parameter. A consequence of our analysis is that the usual tree-le vel description with only three physical parameters (i.e., two gauge c ouplings and one gauge boson mixing angle) is not in general a justifi ed zero order limit of the treatment including radiative corrections.