Electric dipole moment of the $\mathcal{W}$ boson at the quark-gluon level

The electric dipole moment (EDM) of the $\mathcal{W}$ boson in a three-loop approximation at the quark-gluon level is investigated. The violation of combined $\mathcal{CP}$ symmetry is introduced through a complex phase in the Cabibbo–Kobayashi–Maskawa matrix, which characterizes the flavor structure of the quark loop. For the first time, an estimate for the EDM of the $\mathcal{W}$ boson is obtained taking into account the Glashow–Iliopoulos–Maiani mechanism: $d_{\mathcal{W}}\sim$ 10$^{-41}$ ecm. It is known that at the quark-gluon level, the EDM of the $\mathcal{W}$ boson can induce both the EDM of the electron and the EDM of the neutron. Thus, from experimental constraints on the EDM of these fermions, obtained through various spectroscopic methods, one can derive a constraint on the EDM of the $\mathcal{W}$ boson. It is shown that this constraint exceeds the predictions of the Standard Model for the EDM of the $\mathcal{W}$ boson obtained in this work by many orders of magnitude.