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

TL;DR

This paper investigates the all-order renormalization of non-semisimple gauge models using the Background Field Method, ensuring consistency with symmetries and addressing issues like CKM matrix renormalization and CP violation.

Contribution

It demonstrates that the Background Field Method provides suitable normalization conditions for various field mixings in non-semisimple gauge theories, including handling anomalies.

Findings

Proper normalization conditions established for fermion, scalar, and gauge fields.

Analysis of anomalies shows conditions for their absence.

Framework applicable to models with CKM matrix and CP violation.

Abstract

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.