Exploring the Origin of CP Violation in the Standard Model
Abstract
In this article, we present a very general but not ultimate solution of CPV problem in the standard model.
Our study starts from a naturally Hermitian \(M^2 ≡ M^q \cdot M^{q^†}\) rather than the previously assumed Hermitian
Mq. The only assumption employed here is that the real part and imaginary part of \(M^2\) can be,
respectively, diagonalized by a common \(U^q\) matrix. Such an assumption leads to an \(M^2\) pattern which depends
on only five parameters and can be diagonalized analytically by a \(U^q\) matrix which depends on only
two of the parameters. Two of the derived mass eigenvalues are predicted to be degenerate if one of the
parameters \(C (C′)\) in up- (down-) quark sector is zero. As the \(U^q\) patterns are obtained, thirty-six \(V_{CKM}\)
candidates are yielded, and only eight of them, classified into two groups, fit empirical data within the
order of \(O(\lambda)\). One of the groups is further excluded in a numerical test, and the surviving group predicts
that the degenerate pair in a quark type are the lightest and the heaviest generations rather than the lighter
two generations assumed in previous researches. However, there is still one unsatisfactory prediction in
this research, a quadruple equality in which four CKM elements of very different values are predicted to
be equal. It indicates that the \(M^2\) pattern studied here is still oversimplified by that employed assumption
and the ultimate solution can only be obtained by diagonalizing the unsimplified \(M^2\) matrix containing
nine parameters directly. The VCKM presented here is already very close to such an ultimate CPV solution.
References
Phys. Rev. Lett. 13, 138 (1964)
[2] N. Cabibbo, Phys. Rev. Lett. 10, 531 (1963)
[3] M. Kobayashi and T. Maskawa, Prog. of Theor. Phys. 49(2),
652-657 (1973)
[4] T. D. Lee, Phys. Rev. D 8, 1226 (1973)
[5] H. Fritzsch, Phys. Lett. B 73, 317 (1978)
[6] H. Fritzsch, Nucl. Phys. B 155, 189 (1979)
[7] T. P. Cheng and M. Sher, Phys. Rev. D 35, 3484 (1987)
[8] D. Du and Z. Z. Xing, Phys. Rev. D 48, 2349 (1993)
[9] A. Carcamo, R. Martinez, and J.-Alexis Rodriguez,
Eur. Phys. J. C 50, 935-948 (2007)
[10] K. Matsuda, H. Nishiura, and T. Fukuyama, Phys. Rev. D
61, 053001 (2000)
[11] C.L. Lin, C.E. Lee, and Y.W. Yang, Chin. J. Phys. 26, 180
(1988), arXiv:1703.07941
[12] E. Derman and H. S. Tsao, Phys. Rev. D 20, 1207 (1979)
[13] C. L. Lin, J. of Mod. Phys. 11, 1157-1169 (2020),
arXiv:1902.08749
[14] C.E. Lee, Y.W. Yang, Y.L. Chang, and S.N. Lai,
Chin. J. Phys. 24, 188 (1986)
[15] C.E. Lee, Y.W. Yang, S.N. Lai, and Y.L. Chang,
Chin. J. Phys. 24, 254 (1986)
[16] C. Jarlskog, Phys. Rev. Lett. 55, 1039 (1985)
[17] C. L. Lin, J. of Mod. Phys. 10, 35-42 (2019), arXiv:1403.348
[18] G. C. Branco, A. J. Buras, and J. M. Gerard, Nucl. Phys. B
259, 306 (1985)
[19] C.E. Lee, C.L. Lin, and Y.W. Yang, Phys. Rev. D 42, 2355
(1990)
[20] C. L. Lin, C. E. Lee, and Y. W. Yang, Phys. Rev. D 50(1),
558-564 (1994)
[21] Particle Data Group Collaboration, P. A. Zyla, et. al.,
Prog. Theor. Exp. Phys. , 083C01 (2020)
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