Induced CP-violation in the Euler–Heisenberg Lagrangian

Abstract

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, $$g_{v}$$ g v and $$g_{a}$$ g a , in terms of a new coupling $$\beta $$ β . Interestingly, this parametrization allows us to explore a hidden symmetry under the change of $$g_{v}\leftrightarrow g_{a}$$ g v ↔ g a in some diagrams. This symmetry is explicitly observed in the analysis of the box diagram, where we determine the $$\lambda _i$$ λ i coefficients of $${\mathcal {L}}_{\mathrm{ext.}}^\mathrm{\small EH}=\lambda _{1}{\mathcal {F}}^{2}+\lambda _{2}{\mathcal {G}}^{2}+ \lambda _{3}{\mathcal {F}}{\mathcal {G}}$$ L ext . E H = λ 1 F 2 + λ 2 G 2 + λ 3 F G , specially the coefficient $$\lambda _3$$ 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.