On effective Chern-Simons Term induced by a Local CPT-Violating Coupling using $γ_5$ in Dimensional Regularization

We resume a long-standing, yet not forgotten, debate on whether a Chern-Simons birefringence can be generated by a local term $b_μ\barψγ^μγ_5ψ$ in the Lagrangian (where $b_μ$ are constants). In the present paper we implement a new way of managing $γ_5$ in dimensional regularization. Gauge invariance in the underlying theory (QED) is enforced by this choice of defining divergent amplitudes. We investigate the singular behavior of the vector meson two-point-function around the $m^2=0$ and $p^2=0$ point. We find that the coefficient of the effective Chern-Simons can be finite or zero. It depends on how one takes the limits: they cannot be interchanged due to the associate change of symmetry. For $m^2=0$ we evaluate also the self-mass of the photon at the second orderin $b_μ$. We find zero.

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