Relating CKM parametrizations and unitarity triangles

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 55, Issue 1, 1997, Pages 348-352

  Lebed, Richard F ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0642272651     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.55.348     Document Type: Article

References (15)

1. N. Cabibbo, Phys. Rev. Lett.10, 531 (1963);
2. M. Kobayashi and T. Maskawa, Prog. Theor. Phys.49, 552 (1973).
3. C. Jarlskog, in CP Violation, edited by C. Jarlskog (World Scientific, Singapore, 1989), p. 3.
4. Particle Data Group, R. M. Barnett et al., Phys. Rev. D54, 1 (1996).
5. L.-L. Chau and W.-Y. Keung, Phys. Rev. Lett.53, 1802 (1984).
6. Nevertheless, it is possible to reconstruct all four invariant quantities of the CKM matrix (but not the sign of the Jarlskog parameter) using only four independent moduli (Formula presented): see C. Jarlskog and R. Stora, Phys. Lett. B208, 268 (1988).
7. Another interesting set of four invariants consists of the Jarlskog parameter, two off-diagonal asymmetries, and the modulus (Formula presented), which form a hierarchy of increasing magnitude: see Z.-Z. Xing, Nuovo Cimento A109, 115 (1996); and in Proceedings of the International Europhysics Conference on High Energy Physics, Brussels, Belgium, 1995, edited by J. Lemonne, C. Vander Velde, and F. Verbeure (World Scien-tific, Singapore, 1996), p. 181.
8. The idea of picturing unitarity conditions in this way appears to have originated independently with J. D. Bjorken and C. Jarlskog (see first reference in 5).
9. C. Jarlskog, Phys. Rev. Lett.55, 1039 (1985).
10. A. Ali, lectures given at the 20th International Nathiagali Summer College on Physics and Contemporary Needs, Bhurban, Pakistan, 1995 (unpublished), DESY Report No. DESY 96-106, hep-ph/9606324 (unpublished).
11. R. Aleksan, B. Kayser, and D. London, Phys. Rev. Lett.73, 18 (1994).
12. In fact, the sign of (Formula presented) appears to be already experimentally determined as +1. In the Wolfenstein parametrization (Formula presented), and (Formula presented) as determined through (Formula presented) mixing is positive, assuming the bag parameter (Formula presented) from short-distance calculations is also positive (see, for example, Ref. 8). (Formula presented) could have been negative, for example, if the neutral (Formula presented) eigenstate mass difference (Formula presented) had been negative.
13. L. Wolfenstein, Phys. Rev. Lett.51, 1945 (1983).
14. One such extension is that of M. Kobayashi, Prog. Theor. Phys.92, 287 (1994);
15. 92, 289 (1994).