A New bound on CP Violation in the $\tau$ Lepton Yukawa Coupling and electroweak baryogenesis.

The origin of the matter-antimatter asymmetry in the Universe is a fundamental question of physics. Electroweak baryogenesis is a compelling scenario for explaining it but it requires beyond the Standard Model sources of the CP symmetry violation. The simplest possibility is CP violation in the third generation fermion Higgs couplings, widely investigated theoretically and searched for experimentally. It has been found that the experimental bounds on the CP violation in the quark Yukawa couplings exclude their significant role in the electroweak baryogenesis, but it can be still played by the $\tau$ lepton Yukawa coupling. It is shown in this paper that, within the context of the Standard Model Effective Field Theory and assuming an underlying flavour symmetry of the Wilson coefficients, the electron dipole moment bound on the $\tau$ lepton Yukawa coupling is two orders of magnitude stronger than previously reported. This sheds strong doubts on its role in the electroweak baryogenesis, further stimulates the interest in its experimental verification and makes electroweak baryogenesis even more difficult to explain.