Skip to main content
Log in

CP-violation and unitarity triangle test of the Standard Model

  • Published:
Physics of Particles and Nuclei Aims and scope Submit manuscript

Abstract

Phenomenological issues of CP violation in the quark sector of the Standard Model are discussed. We consider quark mixing in the SM, standard, and Wolfenstein parametrization of the CKM mixing matrix and unitarity triangle. We discuss the phenomenology of CP violation in K 0 L and B 0 d (\( \bar B_d^0 \))-decays. The standard unitarity triangle fit of the existing data is discussed. In appendix A we compare the K 0\( \bar K^0 \), B 0 d,s \( \bar B_{d, s}^0 \) , etc. oscillations with neutrino oscillations. In Appendix B we derive the evolution equation for the M\( \bar M^0 \) system in the Weisskopf-Wigner approximation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. C. S. Wu et al., Phys. Rev. 105, 1413 (1957).

    Article  ADS  Google Scholar 

  2. L. Landau, Nucl. Phys. 3, 127 (1957).

    Article  Google Scholar 

  3. T. D. Lee and C. N. Yang, Phys. Rev. 105, 1671 (1957).

    Article  ADS  MathSciNet  Google Scholar 

  4. A. Salam, Nuovo Cimento 5, 299 (1957).

    Article  MathSciNet  Google Scholar 

  5. M. Goldhaber, L. Grodzins, and A. W. Sunyar, Phys. Rev. 109, 1015 (1958).

    Article  ADS  Google Scholar 

  6. J. H. Christenson, J. W. Cronin, V. L. Fitch, and R. Turlay, Phys. Rev. Lett. 13, 138 (1964).

    Article  ADS  Google Scholar 

  7. L. Wolfenstein, Phys. Rev. Lett. 33, 562 (1964).

    Article  ADS  Google Scholar 

  8. J. R. Batley et al. (NA48 Collab.), Phys. Lett. B 544, 97 (2002).

    Article  ADS  Google Scholar 

  9. A. Alavi-Harati et al. (KTeV Collab.), Phys. Rev. D 67, 012005 (2003).

    Google Scholar 

  10. S. L. Glashow, Nucl. Phys. 22, 597 (1961).

    Google Scholar 

  11. S. Weinberg, Phys. Rev. Lett. 19, 1264 (1967).

    Article  ADS  Google Scholar 

  12. A. Salam, in Proc. of the 8th Nobel Symposium on Elementary Particle Theory, Relativistic Groups, and Analyticity, Ed. by N. Svartholm (1969).

  13. A. J. Buras, in Proc. of the Intern. School on Subnuclear Physics, Ed. by A. Zichichi (World Sci., 2000), pp. 200–237; hep-ph/0101336.

  14. M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973).

    Article  ADS  Google Scholar 

  15. Proc. of CP Violation, Advanced Series in High Energy Physics, Ed. by C. Jarlskog (World Sci., Singapore, 1989), Vol. 3, p. 3.

    Google Scholar 

  16. The BaBar Physics Book, Ed. by P. Harrison and H. Quinn, SLAC-R-0504 (1998).

  17. Heavy Flavors II, Ed. by A. Buras and M. Lindner (World Sci., Singapore, 1998).

    Google Scholar 

  18. G. C. Branco, L. Lavoura, and J. P. Silva, CP Violation (Clarendon Press, Oxford, 1999).

    Google Scholar 

  19. I. I. Bigi and A. I. Sanda, CP Violation, Cambridge Monographs on Particle Physics, Nuclear Physics, and Cosmology (Cambridge Univ., Cambridge, 2000).

    MATH  Google Scholar 

  20. “B-Physics at the Tevatron: Run II and Beyond,” hep-ph/0201071.

  21. K. Kleinknecht, Springer Tracts Mod. Phys. 195, 1 (2003).

    Google Scholar 

  22. M. Battaglia et al., “The CKM Matrix and the Unitary Triangle 2003” (CERN, Geneva); hep-ph/0304132.

  23. J. P. Silva, “Phenomenological Aspects of CP Violation,” hep-ph/0410351.

  24. Y. Nir, “CP Violation in Meson Decays,” hep-ph/0510413.

  25. R. Fleisher, “Flavor Physics and CP Violation,” hep-ph/0608019.

  26. A. J. Buras, “Flavor Physics and CP Violation,” hep-ph/0505175.

  27. J. A. Hewett et al., “The Discovery Potential of a Super B Factory,” hep-ph/0503261.

  28. S. Weinberg, The Quantum Theory of Fields, Vol. I: Foundations (Cambridge Univ., Cambridge, 1995).

    Google Scholar 

  29. S. M. Bilenky, Introduction to Feynman Diagrams and Electroweak Interaction Physics (Energoatomizdat, Moscow, 1990; Editions Frontiers, Gif-sur-Yvette, 1994).

    Google Scholar 

  30. N. Cabibbo, Phys. Lett. 10, 531 (1963).

    Article  Google Scholar 

  31. C. Jarlskog, Phys. Rev. Lett. 55, 1039 (1985); Z. Phys. C 29, 491 (1985); C. Jarlskog and R. Stora, Phys. Lett. B 208, 268 (1988).

    Article  ADS  Google Scholar 

  32. W. M. Yao et al. (Particle Data Group.), J. Phys. G 33, 1 (2006).

    Article  ADS  Google Scholar 

  33. A. Ceccuci, Z. Ligeti, and Y. Sakai, “The CKM Quark-Mixing Matrix” in W. M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006).

    Article  Google Scholar 

  34. J. C. Hardy and I. S. Towner, Phys. Rev. Lett. 94, 092502 (2005).

    Google Scholar 

  35. G. Savard et al., Phys. Rev. Lett. 95, 102501 (2005).

  36. D. Pocanic et al., Phys. Rev. Lett. 93, 181803 (2004).

  37. E. Blucher and W. J. Marciano, “V ud, V us. The Cabibbo Angle and CKM Unitarity” in W. M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006).

  38. T. Alexopoulos et al. (KTeV Collab.), Phys. Rev. Lett. 93, 181802 (2004); Phys. Rev. D 70, 092006 (2004).

    Google Scholar 

  39. F. Ambrosino et al. (KLOE Collab.), Phys. Lett. B 632, 43 (2006).

    Article  ADS  Google Scholar 

  40. A. Lai et al. (NA48 Collab.), Phys. Lett. B 602, 41 (2004).

    Article  ADS  Google Scholar 

  41. H. Leutwyler and M. Roos, Z. Phys. C 25, 91 (1984).

    Article  ADS  Google Scholar 

  42. C. Bernard et al., PoS LAT2005 (2005), p. 025; hep-lat/0509137.

  43. N. Cabibbo, E. S. Swallow, and R. Winston, Phys. Rev. Lett. 92, 251803 (2004).

    Google Scholar 

  44. E. Gamiz et al., Phys. Rev. Lett. 94, 011803 (2005).

  45. C. Aubin et al., Phys. Rev. Lett. 94, 011601 (2005).

  46. M. Artuso, Int. J. Mod. Phys. A 21, 1697 (2006); hep-ex/0510052.

    Article  ADS  Google Scholar 

  47. P. Abren et al., Phys. Lett. B 439, 209 (1998).

    Article  ADS  Google Scholar 

  48. I. I. Y. Bigi et al., Phys. Rev. Lett. 71, 496 (1993).

    Article  ADS  Google Scholar 

  49. A. V. Manohar and M. B. Weise, Phys. Rev. D: Part. Fields 49, 1310 (1994).

    ADS  Google Scholar 

  50. B. Kowalewski and T. Mannel, “Determination of V cb and V ub,” in W. M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006).

    Article  Google Scholar 

  51. N. Isgur and M. B. Wise, Phys. Lett. B 232, 113 (1989); Phys. Lett. B 237, 527 (1990).

    Article  ADS  Google Scholar 

  52. M. A. Shifman and M. B. Voloshin, Sov. J. Nucl. Phys. 47, 511 (1988).

    Google Scholar 

  53. M. Okamoto et al., Nucl. Phys. B (Proc. Supp.) 140, 461 (2005).

    Article  ADS  Google Scholar 

  54. J. Shigemitsu et al., Nucl. Phys. B (Proc. Supp.) 140, 464 (2005).

    Article  ADS  Google Scholar 

  55. E. Barbero et al. (Heavy Flavor Averaging Group), hep-ex/0603003.

  56. A. Gray et al., Phys. Rev. Lett. 95, 212001 (2005).

  57. S. Aoki et al., Phys. Rev. Lett. 91, 212001 (2003).

  58. M. Okamoto et al., PoS LAT2005 (2005), p. 013.

  59. A. Abulencia et al. (CDF Collab.), Phys. Rev. Lett. 97, 062003 (2006); hep-ex/0606027.

    Google Scholar 

  60. D. Acosta et al. (CDF Collab.), Phys. Rev. Lett. 95, 102002 (2005).

  61. V. M. Abazov et al. (D0 Collab.), Phys. Lett. B 639, 616 (2006); hep-ex/0603002.

    Article  ADS  Google Scholar 

  62. L. Wolfenstein, Phys. Rev. Lett. 51, 1945 (1983).

    Article  ADS  Google Scholar 

  63. A. Buras, E. M. Lautenbacher, and G. Ostermaier, Phys. Rev. D: Part. Fields 50, 3433 (1994).

    ADS  Google Scholar 

  64. L. Wolfenstein and T. G. Trippe, “CP Violation in KL Decays” in W. M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006).

    Article  Google Scholar 

  65. G. Calangelo, J. Gasser, and H. Leutwyler, Nucl. Phys. B 603, 125 (2001).

    Article  ADS  Google Scholar 

  66. U. Nierste, hep-ph/0612310; A. Lenz and U. Nierste, hep-ph/0612167.

  67. A. B. Carter and A. I. Sanda, Phys. Rev. Lett. 45, 952 (1980); Phys. Rev. D 23, 1567 (1981); I. I. Bigi and A. I. Sandra, Nucl. Phys. 193, 85 (1981).

    Article  ADS  Google Scholar 

  68. B. Aubert et al. (BaBar Collab.), Phys. Rev. Lett. 66, 071102 (2002).

  69. K. Abe et al. (Belle Collab.), Phys. Rev. D: Part. Fields 89, 201802 (2002).

    Google Scholar 

  70. B. Aubert et al. (BaBar Collab.), hep-ex/0607107.

  71. K. Abe et al. (Belle Collab.), hep-ex/0608039.

  72. M. Bona et al. (UTfit Collab.), hep-ph/0501199.

  73. M. Bona et al. (UTfit Collab.), J. High Energy Phys. 0610, 081 (2006); hep-ph/0606167.

    ADS  Google Scholar 

  74. J. Charles et al. (CKMfitter Group), Eur. Phys. J. 41, 1 (2005); hep-ph/0406184; hep-ph/0606046.

    Article  ADS  Google Scholar 

  75. E. Barberio et al. (Heavy Flavor Averaging Group), hep-ex/0603003.

  76. M. Rama, in Proc. of XXI Rencontres de Physique de la Vallee d’Aoste, March 4–10, 2007.

  77. R. P. Feynman and M. Gell-Mann, Phys. Rev. 109, 193 (1958).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  78. E. C. G. Sudarshun and R. Marshak, Phys. Rev. 109, 1860 (1958).

    Article  ADS  Google Scholar 

  79. A. D. Sakharov, JETP Lett. 5, 24 (1967).

    ADS  Google Scholar 

  80. M. B. Gavela et al., Mod. Phys. Lett. A 9, 795 (1994).

    Article  ADS  Google Scholar 

  81. V. A. Rubakov and M. E. Shaposhnikov, Usp. Fiz. Nauk 166, 493 (1996) [Phys. Usp. 39, 461 (1996)].

    Article  Google Scholar 

  82. J. M. Cline, hep-ph/0609145.

  83. Y. Ashie et al. (Super-Kamiokande Collab.), Phys. Rev. Lett. 93, 101801 (2004); Phys. Rev. D 71, 11205 (2005).

  84. S. N. Ahmed et al. (SNO Collab.), Phys. Rev. Lett. 89, 011302 (2002); Phys. Rev. Lett. 92, 181301 (2004).

    Google Scholar 

  85. T. Araki et al. (KamLAND Collab.), Phys. Rev. Lett. 94, 081801 (2005); hep-ex/0406035.

    Google Scholar 

  86. B. T. Cleveland et al., Astrophys. J. 496, 505 (1998).

    Article  ADS  Google Scholar 

  87. W. Hampel et al. (GALLEX Collab.), Phys. Lett. B 447, 127 (1999); M. Altmann et al. (GNO Collab.), Phys. Lett. B 616, 174 (2005).

    Article  ADS  Google Scholar 

  88. J. N. Abdurashitov et al. (SAGE Collab.), Phys. Rev. C 60, 055801 (1999); Nucl. Phys. Proc. Suppl. 110, 315 (2002); Nucl. Phys. Proc. Suppl. 118, 39 (2003).

    Google Scholar 

  89. S. Fukuda et al. (Super-Kamiokande Collab.), Phys. Rev. Lett. 86, 5651 (2001).

    Article  ADS  Google Scholar 

  90. M. H. Ahn et al. (K2K Collab.), Phys. Rev. Lett. 90, 041801 (2003).

  91. D. G. Michael et al. (MINOS Collab.), Phys. Rev. Lett. 97, 191801 (2006); hep-ex/0607088.

    Google Scholar 

  92. S. M. Bilenky and C. Giunti, Int. J. Mod. Phys. A 16, 3931 (2001); hep-ph/0102320.

    Article  MATH  ADS  Google Scholar 

  93. S. M. Bilenky and M. D. Mateev, Phys. Part. Nucl. 8, 117 (2007); hep-ph/0604044.

    Article  Google Scholar 

  94. B. Pontecorvo, Zh. Eksp. Teor. Fiz. 33, 549 (1957) [Sov. Phys. JETP 6, 429 (1958)]; Zh. Eksp. Teor. Fiz. 34, 247 (1958) [Sov. Phys. JETP 7, 172 (1958)].

    Google Scholar 

  95. Z. Maki, M. Nakagawa, and S. Sakata, Prog. Theor. Phys. 28, 870 (1962).

    Article  MATH  ADS  Google Scholar 

  96. S. M. Bilenky and S. T. Petcov, Rev. Mod. Phys. 59, 671 (1987).

    Article  ADS  Google Scholar 

  97. S. M. Bilenky, C. Giunti, and W. Grimus, Prog. Part. Nucl. Phys. 43, 1 (1999).

    Article  ADS  Google Scholar 

  98. S. M. Bilenky, N. P. Nedelcheva, and S. T. Petcov, Nucl. Phys. B 247, 61 (1984); B. Kayser, Phys. Rev. D: Part. Fields 30, 1023 (1984).

    Article  ADS  Google Scholar 

  99. S. M. Bilenky, J. Hosek and S. T. Petcov, Phys. Lett. B 94, 495 (1980).

    Article  ADS  Google Scholar 

  100. S. M. Bilenky, Part. Nucl. 1, 228 (1970).

    Google Scholar 

  101. V. Weisskopf and E. Wigner, Z. Phys. 63, 54 (1930); Z. Phys. 65, 18 (1930).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

The text was submitted by the author in English.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bilenky, S.M. CP-violation and unitarity triangle test of the Standard Model. Phys. Part. Nuclei 39, 641–673 (2008). https://doi.org/10.1134/S1063779608050018

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063779608050018

PACS numbers

Navigation