Multiplicative BRST renormalization of the SU(2) Higgs model.

We reformulate the proof of the renormalization of a spontaneously broken gauge theory by multiplicatively renormalizing the vacuum expectation value of the Higgs field in the SU(2) Higgs model. After BRST symmetry was discovered [1], it was noted that the renormalization of gauge theories [2] can be simplified by using BRST methods. In [3] Becchi, Rouet and Stora considered the SU(2) Higgs model, introduced sources for the BRST variations of the gauge and ghost fields, and made an analysis of the two-point-functions, the S-matrix, unitarity, and even an cohomologic analysis of anomalies. However, they did not give a systematic loop by loop proof of renormalizability. Also, their work was complicated because the non-nilpotency of the BRST transformations of the antighost introduces ghost equations of motion at various places. At about the same time, Zinn-Justin [4] considered the renormalization of gauge theories loop by loop using BRST Ward identities. For spontaneously broken gauge theories these Ward identities remain valid because they are independent of the value (in particular the sign) of the mass term in the matter section. Using this approach, B.Lee [5] gave a systematic analysis of the multiplicative loop-by-loop renormalization of unbroken gauge theories. This account supercedes his earlier treatments [6] which did not use BRST methods and were much less clear. At the end of his analysis he also briefly considered spontaneously broken gauge theories where he started a proof of the renormalizability of a