# Can the CKM matrix supply the CP asymmetry as required by baryogenesis, in principle?

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)?

• For electroweak baryogenesis the CKM phases are not enough and you need new physics. I don't know about other models though. Nov 7 '18 at 23:46
• @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?
– SRS
Nov 10 '18 at 0:06

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.

• 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
– SRS
Nov 10 '18 at 0:01
• 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. Nov 12 '18 at 11:19

In the quark sector of SM, CP violation comes from a complex phase in the CKM matrix which is a product of two unitary matrices Uu and Ud which diagonalize the quark mass matrices Mu and Md, respectively. In our recent investigations (arXiv:1902.08749), a general pattern of Hermitian mass matrices was diagonalized analytically. A CP-violating CKM matrix is thus derived. In some discussions of that article, SN symmetries among quark generations can give us a CP strength orders stronger than that SM can provide.

The CKM matrix is for quarks and the PMNS matrix is for leptons. In a broken SN symmetry model the strength of CPV is unfixed. An Improved Standard Model Comes with Explicit CPV and Productive of BAU. JMP, 11, 1157-1169.

The CPV strength characterized by Jarlskog invariant is much stronger than the value given by present standard model. Thus, there could have some BAU-productive stages in the early universe in which the CPV strength was much stronger than what we see nowadays.

• Hi @ChilongLin, for your information, Physics.SE has a policy that it is OK to cite oneself, but it should be stated clearly and explicitly in the answer itself.
– Urb
Nov 25 '20 at 15:20
• Well, in the SM with S2 symmetries, the fermion mass matrices can be diagonalized analytically and then gives a complex CKM matrix, which indicates the violation of CP symmetry. The predicted Jarlskog invariant J=0.171 for the S2 model is about 5700 times that J=3.0 x 10^{-5} given by current SM. Though it is still not enough to account for all BAU. At least it answered part of it. Dec 17 '20 at 1:50