Renormalization of Non-Semisimple Gauge Models with the Background Field Method

We study the renormalization of non-semisimple gauge models quantized in the `t Hooft-background gauge to all orders. We analyze the normalization conditions for masses and couplings compatible with the Slavnov-Taylor and Ward-Takahashi Identities and with the IR constraints. We take into account both the problem of renormalization of CKM matrix elements and the problem of CP violation and we show that the Background Field Method (BFM) provides proper normalization conditions for fermion, scalar and gauge field mixings. We discuss the hard and the soft anomalies of the Slavnov-Taylor Identities and the conditions under which they are absent.