Quark level and hadronic contributions to the electric dipole moment of charged leptons in the standard model

TL;DR

This paper calculates the electric dipole moments of charged leptons in the Standard Model, showing that hadronic contributions dominate over suppressed quark-gluon level effects, with implications for CP violation studies.

Contribution

It provides a detailed analysis of both quark-gluon and hadronic contributions to lepton EDMs, highlighting the significance of long-distance hadronic effects.

Findings

Quark-gluon level contributions are highly suppressed by the GIM mechanism.

Hadronic long-distance effects are significantly larger than perturbative estimates.

Hadronic mechanisms can produce observable EDMs in charged leptons.

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 $|\Delta S|=1$ 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.