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In the process of Baryogenesis through Leptogenesis from the decay of heavy Majorana neutrinos, the necessary CP violation is perhaps provided only by the CP phases in the PMNS matrix. But the Weak interactions in the SM also violate CP through the CKM matrix. However, since Leptogenesis talks about the lepton sector and since the CKM matrix talks about CP violation in the quark sector, I guess that the CKM matrix cannot supply CP asymmetry for Leptogenesis. For Leptogenesis, it is the complex phases of PMNS matrix (not the CKM matrix) that supply the necessary CP asymmetry. Correct me if wrong.

Question If the CKM matrix cannot contribute to Leptogenesis, can it supply the CP violation some other way, at least in principle, through some other mechanism of baryogenesis (no matter how small)?

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    $\begingroup$ For electroweak baryogenesis the CKM phases are not enough and you need new physics. I don't know about other models though. $\endgroup$ – FrodCube Nov 7 '18 at 23:46
  • $\begingroup$ @FrodCube I think you can put your comment as the answer. Also, I hope that in my guess that the quark CKM phase $\delta$ have no reason to appear in Leptogenesis. Right? $\endgroup$ – SRS Nov 10 '18 at 0:06
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No. The baryon-to-photon ratio observed in the universe is $10^{-10}$, whereas the calculations done in [1] imply that the CP violation induced in CKM matrix can at most produces ratio $10^{-20}$. Baryon asymmetry is only generated at seven loop level (a huge suppression!), and the calculation involves the sum of over 10000 Feynman diagrams. For similar reason, the yet unconfirmed leptonic CP violation cannot supply the necessary amount of CP asymmetry for baryogenesis.

[1] Nuclear Physics B Volume 287, 1987, Pages 757-775, https://www.sciencedirect.com/science/article/pii/0550321387901271

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  • $\begingroup$ But people do study baryogenesis through leptogenesis whee the necessary CP asymmetry is provided by the complex phases in PMNS matrix. Isn't it? @Zeick $\endgroup$ – SRS Nov 10 '18 at 0:01
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    $\begingroup$ Not from PMNS matrix. In order to have a working leptogenesis, one needs heavy right-handed neutrinos. The CP asymmetry arises from one-loop corrections to heavy neutrino decay to leptons and Higgs bosons. See for example, scholarpedia.org/article/Leptogenesis. $\endgroup$ – Zeick Nov 12 '18 at 11:19

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