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 ${\mathcal{L}}_{ext.}^{\mathrm{EH}}={\lambda }_1{\mathcal{F}}^2+{\lambda }_2{\mathcal{G}}^2+{\lambda }_3\mathcal{F}\mathcal{G}$, 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.

19 pages

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Cited by in corpus (1)

• Euler-Heisenberg Lagrangian under an axial gauge field