Quark level and hadronic contributions to the electric dipole moment of charged leptons in the standard model
Yasuhiro Yamaguchi, Nodoka Yamanaka
Abstract
We evaluate the electric dipole moment of charged leptons in the standard model, where the complex phase of the Cabibbo-Kobayashi-Maskawa matrix is the only source of $CP$ violation. We first prove that, at the quark-gluon level, it is suppressed by a factor of ${m}_{b}^{2}{m}_{c}^{2}{m}_{s}^{2}$ at all orders of perturbation due to the Glashow-Iliopoulos-Maiani mechanism. We then calculate the hadronic long distance contribution generated by vector mesons at one-loop level. The $|\mathrm{\ensuremath{\Delta}}S|=1$ weak hadronic interaction is derived using the factorization, and the strong interaction is modeled by the hidden local symmetry framework. We find that the electric dipole moments of charged leptons obtained from this hadronic mechanism are much larger than the perturbative four-loop level quark-gluon process, by several orders of magnitude.