Leading order one-loop CP and P violating effective action in the Standard Model

TL;DR

This paper calculates the leading CP and P violating effective operators in the Standard Model after integrating out fermions, revealing they are of dimension eight and providing explicit computations of these operators.

Contribution

It explicitly confirms that no CP and P violating operators of dimension six or less exist at zero temperature, and computes the leading dimension eight operators in the Standard Model.

Findings

Leading CP and P violating operators are of dimension eight.

Explicit computation of a non-vanishing dimension eight operator involving Z and W bosons.

Infrared enhancement observed in CP-violating results at dimension six.

Abstract

The fermions of the Standard Model are integrated out to obtain the effective Lagrangian in the sector violating P and CP at zero temperature. We confirm that no contributions arise for operators of dimension six or less and show that the leading operators are of dimension eight. To assert this we explicitly compute one such non-vanishing contribution, namely, that with three Z^0, two W^+ and two W^-. Terms involving just gluons and W's are also considered, however, they turn out to vanish in the P-odd sector to eighth order. The analogous gluonic term in the CP-odd and P-even (C-odd) sector is non-vanishing and it is also computed. The expressions derived apply directly to Dirac massive neutrinos. All CP-violating results display the infrared enhancement already found at dimension six.