Induced CP-violation in the Euler–Heisenberg Lagrangian

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 β . Interestingly, this parametrization allows us to explore a hidden symmetry under the change of g_v↔ g_a in some diagrams. This symmetry is explicitly observed in the analysis of the box diagram, where we determine the λ _i coefficients of ℒ_ext.^ EH=λ _1ℱ^2+λ _2𝒢^2+ λ _3ℱ𝒢 , specially the coefficient λ _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.