Basis invariant measure of CP-violation and renormalization

TL;DR

This paper investigates how different renormalization schemes affect the CP-violation properties of a simple model, showing that certain schemes preserve CP-properties and that basis invariants can characterize CP-violation.

Contribution

It demonstrates that minimal subtraction and on-shell schemes preserve CP-properties of the bare and finite parts, and introduces basis invariants to characterize CP-violation in renormalized theories.

Findings

CP-properties coincide in minimal subtraction and on-shell schemes

CP-odd basis invariants vanish in CP-conserving theories at all scales

In CP-violating theories, invariants are not RG invariant

Abstract

We analyze, in the context of a simple toy model, for which renormalization schemes the CP-properties of bare Lagrangian and its finite part coincide. We show that this is the case for the minimal subtraction and on-shell schemes. The CP-properties of the theory can then be characterized by CP-odd basis invariants expressed in terms of renormalized masses and couplings. For the minimal subtraction scheme we furthermore show that in CP-conserving theories the CP-odd basis invariants are zero at any scale but are not renormalization group invariant in CP-violating ones.