UV ASYMPTOTICALLY FREE QED AS A BROKEN YM THEORY IN THE UNITARY GAUGE

We compute the beta-function of a YM theory, broken to U(1), by evalua ting the coupling constant renormalization in the broken phase. We per form the calculation in the unitary gauge where only physical particle s appear and the theory looks like a version of QED containing massive charged spin-1 particles. We consider an on-shell scattering process and after verifying that the non-renormalizable divergences which appe ar in the Green's functions cancel in the expression of the amplitude, we show that the coupling constant renormalization is entirely due to the photon self-energy, as in QED. However we get the expected asympt otic freedom and the physical charge decreases logarithmically as a fu nction of the symmetry breaking scale.