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$$\leftrightarrow$ 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${}_1{F}^2$+λ${}_2{G}^2$+λ${}_{3}FG$, 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.