https://doi.org/10.1140/epjc/s10052-022-11145-8
Regular Article - Theoretical Physics
Induced CP-violation in the Euler–Heisenberg Lagrangian
1
Department of Physics, Shahid Beheshti University, 1983969411, Tehran, Iran
2
Departamento de Física, Universidade Federal de Lavras, Caixa Postal 3037, 37200-900, Lavras, MG, Brazil
3
Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia
4
School of Mathematics, Statistics and Physics, Newcastle University, NE1 7RU, Newcastle upon Tyne, UK
Received:
11
November
2022
Accepted:
16
December
2022
Published online:
19
January
2023
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, 
and 
, in terms of a new coupling 
. Interestingly, this parametrization allows us to explore a hidden symmetry under the change of 
in some diagrams. This symmetry is explicitly observed in the analysis of the box diagram, where we determine the 
coefficients of 
, specially the coefficient 
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.
© The Author(s) 2023
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