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.
Highlights
We recall that the elementary level contribution only had a typical momentum of OðmWÞ ∼ OðmtÞ, and this feature, together with the GIM mechanism, forced the electric dipole moment (EDM) of charged leptons to have a suppression factor m2bm2cm2s due to the cancellation between terms with very close values
We evaluated for the first time the hadron level contribution to the EDM of charged leptons in the standard model (SM), where the CP violation is generated by the physical complex phase of the CKM matrix
We found that this long distance effect is much larger than the previously known one, which was estimated at the elementary level
Summary
The electric dipole moment (EDM) [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21] is a very sensitive observable for the detection of the CP violation in many candidate models of new physics beyond the standard model (SM) such as the supersymmetry [22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50], extended Higgs model [51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79], Majorana fermion [80,81,82,83], and other interesting models [66,84,85,86,87,88,89,90,91,92]. The hadronic contribution to the EDM of charged leptons has never been evaluated in the past. This is just the aim of this paper to quantify it. We calculate the hadronic long distance contribution to the charged lepton EDM generated by vector mesons at one-loop level. We review the quark-gluon level calculation of the CKM contribution to the EDM of charged leptons and prove that it is suppressed by factors of quark masses at all orders of perturbation.
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