CPT-Odd effects on the electromagnetic properties of charged leptons in the Standard Model Extension

Abstract

The impact of the CPT-Odd electroweak gauge sector of the Standard Model Extension on the electromagnetic properties of charged leptons is studied. This gauge sector is characterized by the $(k_1)_\mu$ and $(k_2)_\mu$ Lorentz violation (LV) coefficients, which have positive mass dimension because they are associated with a $U_Y(1)$-invariant and with an $SU_L(2)$-invariant dimension-three operators, respectively. We present a comprehensive study on the impact of this sector on the magnetic dipole moment (MDM) and the electric dipole moment (EDM) of charged leptons, up to second order in these LV coefficients, both at the tree and one-loop levels.The contributions of $O(k_i)$ to the MDM are found to be suppressed relative to the corresponding contributions to the EDM by approximately three orders of magnitude. Using a recent experimental limit on the electron EDM the $|(k_2)_0-|\mathbf{k_2}|\cos\theta_\gamma|<0.86\, m_e$ bound was obtained. As far as the contributions of $O(k^2_i)$ are concerned, we find that the tree-level contributions are suppressed with respect to the one-loop ones by at least a factor of $\left(m^2_l/m^2_Z\right)$. We find that the contribution to the electron MDM is by far the dominant one, as it can be up to four and seven orders of magnitude greater than those of the muon and tau, respectively. The Lorentz coefficient $(k_{AF})_\mu$ of the Carroll-Field-Jackiw's QED is given by a linear combination of $(k_1)_\mu$ and $(k_2)_\mu$. Assuming that $|k^2_1|, |k^2_2|\gg |k^2_{AF}|$ and taking $(k_{AF})_\mu=0$, which implies that $(k_1)_\mu$ and $(k_2)_\mu$ are collinear, we obtain an upper bound of $\left|\frac{ k^2_2}{m^2_e} \right|<4.36\times 10^{-10}$. The fact that $k^2_2$ is an observer Lorentz invariant allows us to introduce a new-physics scale through $\sqrt{k^2_2}=\Lambda_{CPT}$, for which we obtain the upper limit $\Lambda_{CPT}< 2.08 \times 10^{-5}\, m_e$.