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An exact CKM matrix related to the approximate Wolfenstein form · Around

2011

An exact CKM matrix related to the approximate Wolfenstein form

Kim, Jihn E., Seo, Min-Seok

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Noting the hierarchy between three mixing angles, $\theta_{2,3}={\cal O}(\theta_1^2)$, we present an exact form of the quark mixing matrix, replacing Wolfenstein's approximate form.

In addition, we suggest to rotate the unitarity triangle, using the weak CP phase convention where the phase is located at the (31) element $\sin\theta_1\sin\theta_2 e^{i\delta}$ while the (13) element $\sin\theta_1\sin\theta_3$ is real.
For the $(ab)$ unitarity triangle, the base line (x-axis) is defined from the product of the first row elements, $V_{1a}V^*_{1b}$, and the angle between two sides at the origin is defined to be the phase $\delta$.
This is a useful definition since every Jarlskog triangle has the angle $\delta$ at the origin, defined directly from the unitarity condition.

Built on

L. Wolfenstein, Phys. Rev. Lett. 51
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N. Cabibbo, Phys. Rev. Lett. 10
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M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49
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L. Maiani, in Proceedings of the 1977 International Symposium on Lepton and Photon Interactions at High Energies
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R. D. Peccei and H. R. Quinn, Phys. Rev. Lett. 38
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Earlier work this paper cites.

Similar

L. L. Chau and W. Y. Keung, Phys. Rev. Lett. 53
1984
Cited alongside, same era.
C. Jarlskog, Phys. Rev. Lett. 55
1985
Cited alongside, same era.
P. Ramond, R. G. Roberts, and G. G. Ross, Nucl. Phys. B406
Original
1993
Cited alongside, same era.
G. C. Branco, L. Lavoura and J. P. Silva, CP Violation
2009
Cited alongside, same era.

Then

K. Nakamura et al
2010
Later among the works it cites.
J. E. Kim, Phys. Rep. 150
2010
Later among the works it cites.
N. Qin, B. Q. Ma, Phys. Lett. B695
Original
2011
Closest in time.
J. E. Kim and M.-S. Seo, J. High Energy Phys. 1102
Original
2011
Closest in time.

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