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What is the effect on leptogenesis in the standard model if the electroweak phase transition is (i) first order and (ii) second order?

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In the Standard Model there is neither first nor second order electroweak phase transition (EWPT), but rather a crossover. To get a first order transition, additional particles are needed. There are many different theories (2HDM, Higgs portal, MSSM, ...) covering this topic.

Considering leptogenesis $\Delta L \neq 0$ we need a first order PT, since non-equilibrium is one of the Sakharov conditions required for leptogenesis. If these conditions are fulfilled, sphaleron processes violate lepton (or baryon) number by "jumping" from the symmetric $(\phi = 0)$ to the broken $(\phi=\phi_0)$ phase. I found this plot: (Never mind the numbers, in the case of EWPT the critical temperature $T_c \sim \mathcal{O}(100 GeV)$ )

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    $\begingroup$ This looks like a first order transition to me, or am I misreading the plot? $\endgroup$ Apr 4, 2019 at 13:16

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