Induced CP-violation in the Euler–Heisenberg Lagrangian

Abstract

In this paper, we examine the behaviour of the Euler–Heisenberg effective action in the presence of a novel axial coupling among the gauge field and the fermionic matter. This axial coupling is responsible to induce a CP-violating term in the extended form of the Euler–Heisenberg effective action, which is generated naturally through the analysis of the box diagram. However, this anomalous model is not a viable extension of QED, and we explicitly show that the induced CP-violating term in the Euler–Heisenberg effective Lagrangian is obtained only by adding an axial coupling to the ordinary QED Lagrangian. In order to perform our analysis, we use a parametrization of the vector and axial coupling constants, g_{v} and g_{a}, in terms of a new coupling beta . Interestingly, this parametrization allows us to explore a hidden symmetry under the change of g_{v}leftrightarrow g_{a} in some diagrams. This symmetry is explicitly observed in the analysis of the box diagram, where we determine the lambda _i coefficients of {mathcal {L}}_{mathrm{ext.}}^mathrm{small EH}=lambda _{1}{mathcal {F}}^{2}+lambda _{2}{mathcal {G}}^{2}+ lambda _{3}{mathcal {F}}{mathcal {G}}, specially the coefficient lambda _3 related with the CP-violating term due to the axial coupling. As a phenomenological application of the results, we compute the relevant cross section for the light by light scattering through the extended Euler–Heisenberg effective action.