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

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.