Electromagnetic dipole moments of fermions

The electric (EDM) and magnetic (g-2) dipole moments are static properties sensitive to quantum corrections induced by the virtual particles that populate the vacuum. Indeed, they are well suited to test the Standard Model of Elementary 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, respectively, and thus they represent one of the strongest confirmation of the SM and greatest achievement in Quantum Field Theory. Nonetheless the SM deficiencies, the explanation of dark matter and dark energy, cosmological inflaton, neutrino oscillations and masses, the strong CP problem and the origin of matter-antimatter asymmetry, call for new physics beyond the SM. Since NP contribution to the dipole moments of a fermion f is expected to be proportional to m_f^2, dipole moments of heavy fermions, such as the top quark or the tau lepton, are much more sensitive to NP effects than the electron or muon ones. However the very short lifetime of these unstables particle makes it impossible to directly measure their electromagnetic properties. Therefore, indirect information must be obtain by precisely measuring cross sections and decay rates in processes involving the emission of a real photon by the heavy fermion. In this thesis, we investigate the possibility to measure the anomalous magnetic moment and the electric dipole moment of the top quark at the LHC and tau lepton at future high luminosity B-factories.