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There are three Sakharov conditions of baryogenesis:

  1. CP symmetry violation.

  2. Baryon number conservation violation.

  3. Thermodynamical equilibrium violation.

In SM the first one is satisfied by CKM phases, the second one is satisfied by instanton-like transitions for zero temperature and sphaleron-like transitions for non-zero temperatures. As for the third one, I've thought that EW phase transition provides violation of equilibrium, but after reading Gorbunov and Rubakov book "Introduction to the Theory of the Early Universe: Hot Big Bang Theory" I've started to doubt. They write that this transition is of second type one; thus it doesn't provide sufficient thermodynamical equilibrium violation.

So can EW phase transition provide baryogenesis?

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Within the standard model: It cannot!

Even though there is CP violation in the SM (as you state), the amount is not enough to give the ratio of

$ \frac{n_B}{n_\gamma} \sim 10^{-10} \ .$

Furthermore, the electroweak phase transition (EWPT) in the SM is not even a second order transition, but merely a crossover.

In order to render the transition (strongly) first order and to account for enough CP violation, new physics beyond the standard model is needed. Supersymmetry (SUSY) is just one of the theories in the literature. One simple extension of the SM is the inert doublet model (IDM) which has a first order EWPT, but unfortunately no additional CP violation.

Although we have not yet found signs of new physics at colliders, the EWPT is still a hot candidate for baryogenesis.

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