The electric dipole moment (EDM) and the anomalous magnetic moment (g 2) are physical observables sensitive to quantum corrections induced by the virtual particles that populate the vacuum. For this reason they are well suited to test the Standard Model (SM) of particle physics and to unveil unknown New Physics (NP) hidden at high energy. The electron and muon g 2 have been measured with the wonderful precision of 0.24 ppb and 0.54 ppm and they agree with SM prediction at the level of 1.3 and 3.7 standard deviations, respectively. They represent two of the most precise tests of the SM and greatest achievements in Quantum Field Theory.
In spite of that, the SM is insu cient to explain well-establish observations in various ﬁelds of physics: the nature of dark matter and dark energy, the cosmological inﬂation, the neutrino oscillations and their masses, the strong CP problem, the naturalness of the SM and the origin of matter-antimatter asymmetry. All of these call for NP that should lie at a mass scale higher that the electroweak scale.
Since the NP contribution to the dipole moments of a fermion is expected to scale with the square of its mass, from the theoretical point of view the dipole moments of heavy particles, such as the top quark or the tau lepton, are much more sensitive to NP e↵ects than the electron or muon ones. However their very short lifetime makes it impossible to directly measure their electromagnetic properties, but indirect information may be obtained by precisely measuring cross sections and decay rates in processes involving the emission of a real photon by the heavy fermion.