CP Phases in 2HDM and Effective Potential: A Geometrical View

TL;DR

This paper uses a geometric approach to classify CP invariants in 2HDM, calculates the thermal effective potential invariantly, and explores how CP violation sources influence the potential and symmetry restoration at high temperatures.

Contribution

It introduces a basis-invariant geometric classification of CP invariants in 2HDM and analyzes their effects on the thermal effective potential and CP symmetry restoration.

Findings

CP violation in Yukawa interactions affects the effective potential at one loop.

The CKM matrix CP phase does not influence the effective potential at any order.

High temperature thermal corrections tend to restore CP symmetry in 2HDM with softly broken Z_2 symmetry.

Abstract

Using a geometric description of 2HDM, we classify CP invariants into three independent sectors such as scalar potential, Yukawa interaction and CKM matrix. Thermal effective potential of 2HDM is calculated in a basis invariant way. It is shown that the CP violation in Yukawa interactions can contribute to effective potential at one loop level but the CP phase in the CKM matrix cannot leak to effective potential at all orders. In the 2HDM with a softly broken Z_2 symmetry, the leading thermal correction tends to restore the CP symmetry at high temperature.