Reducing Complex Phases and other Subtleties of CP Violation

TL;DR

This paper introduces a method to reduce the number of CP-violating phases in models extending the Standard Model with vector-like quarks, simplifying the analysis of CP violation.

Contribution

It develops a systematic approach to minimize complex phases in VLQ models and provides an explicit parametrization, including applications to the Nelson-Barr solution.

Findings

VLQ models can be described with fewer physical phases

Explicit parametrization for quark mixing matrix with reduced phases

Application to the BBP model recovers single phase formulation

Abstract

When extending the SM, e.g. with vector-like quarks (VLQ), one inevitably encounters more than one CP violating complex phases. In this work, we develop a method useful in reducing the number of complex phases in scenarios with one and two VLQs. We show that these VLQ-models can be described with just one or two physical complex phases respectively and present an explicit alternative parametrization for the quark mixing matrix. Making use of this Reduction of Complex Phases in the case of the Bento-Branco-Parada (BBP) model, i.e. the simplest implementation of the Nelson-Barr solution to the strong CP problem, one also recovers the single phase formulation of BBP model. We comment on how this specific scenario can be distinguished from the general VLQ case with weak-basis invariants