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Electroweak Baryogenesis(EWBG) aims to explain the matter anti-matter asymmetry at the Electroweak energy level. However the Standard Model alone is not enough to provide all the three Sakharov Criteria, so we turned to the MSSM. First, we discussed the maximum CP Violation(CPV) that could exist in the neutral Higgs sector of MSSM, especially in the lightest neutral Higgs. We found that there is a constraint from the lightest Higgs mass and that the observed mass 126~$GeV$ has already put a rather strong upper bound on CPV. Because the existence of CP-violating phases also modifies $hVV$ and $hb\bar{b}$ coupling, the CPV also receives constraints from Higgs precision measurements. After taking EDM and flavor physics constraints into account, we showed that the maximal CPV we can get from the lightest neutral Higgs is no higher than $3\%$. In the second part of this thesis, we looked into another necessary condition of EWBG, a strong first-order Electroweak phase transition(EWPT). We discussed the order of EWPT in the most general effective Higgs potential and especially the interesting correlation between this order and the triple Higgs self-coupling. We showed that a strong first-order EWPT could lead to a large modification of the Higgs self-coupling and could even change its sign. And this possible deviation could be detected through the channel $H\rightarrow HH\rightarrow b\bar{b}\gamma\gamma$. We reported a significance of 7.5~$\sigma$ for $\lambda_3 = -\lambda_3^{SM}$ at the LHC(14~$TeV$ and 3000~$fb^{-1}$).


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