Abstract
The strong phases and CP violation in the rare B̄0→K+K-, K*±K∓, K*+K*- decays are investigated. As these decays proceed only via annihilation type diagrams in the standard model (SM), a dynamical gluon mass is introduced to avoid the infrared divergence in the soft endpoint regions. The Cutkosky rule is adopted to deal with a physical-region singularity of the on-mass-shell quark propagators, which leads to a big imaginary part and hence a large strong phase. As a consequence, large CP asymmetries are predicted in those decay modes due to a big interference between the annihilation amplitudes from penguin and tree operators, which may be tested in future more precise experiments.
Similar content being viewed by others
References
BaBar Collaboration, B. Aubert et al., Phys. Rev. Lett. 87, 091801 (2001)
Bell Collabration, K. Abe et al., Phys. Rev. Lett. 87, 091802 (2001)
Belle Collaboration, K. Abe et al., Phys. Rev. Lett. 93, 021601 (2004)
BaBar Collaboration, B. Aubert et al., Phys. Rev. Lett. 93, 131801 (2004)
Belle Collaboration, Y. Chao et al., Phys. Rev. Lett. 93, 191802 (2004)
J.H. Christenson, J.W. Cronin, V.L. Fitch, R. Turlay, Phys. Rev. Lett. 13, 138 (1964)
NA48 Collaboration, J.R. Batley et al., Phys. Lett. B 544, 97 (2002)
KTeV Collaboration, A. Alavi-Harati et al., Phys. Rev. D 67, 012005 (2003)
Y.L. Wu, Phys. Rev. D 64, 016001 (2001)
Y.L. Wu, Intern. Conf. on Flavor Physics (ICFP2001), ed. by Y.-L. Wu (World Scientific Pub. Co., 2001), pp. 217–236
Y.L. Wu, Int. J. Mod. Phys. A 7, 2863 (1992)
J. Heinrich, E.A. Paschos, J.M. Schwarz, Y.L. Wu, Phys. Lett. B 279, 140 (1992)
Y.L. Wu, ICHEP92 (Dallas, 1992), p. 506
A.J. Buras et al., Phys. Rev. Lett. 92, 101804 (2004)
T. Yoshikawa, Phys. Rev. D 68, 054023 (2003)
D. Atwood, G. Hiller, hep-ph/0307251
S. Mishima, T. Yoshikawa, hep-ph/0408090
S. Nandi, A. Kundu, hep-ph/0407061
Y.L. Wu, Y.F. Zhou, Phys. Rev. D 71, 021701 (2005)
Y.L. Wu, Y.F. Zhou, Phys. Rev. D 72, 034037 (2005)
M. Kobayashi, T. Maskawa, Prog. Theor. Phys. 49, 652 (1973)
Y.L. Wu, CMU-Report, hep-ph/9404241 (1994)
Y.L. Wu, L. Wolfenstein, Phys. Rev. Lett. 73, 1762 (1994)
L. Wolfenstein, Y.L. Wu, Phys. Rev. Lett. 73, 2809 (1994)
Y.L. Wu, Y.F. Zhou, Phys. Rev. D 61, 096001 (2000)
M. Wirbel, B. Stech, M. Bauer, Z. Phys. C 29, 637 (1985)
M. Bauer, B. Stech, M. Wirbel, Z. Phys. C 34, 103 (1987)
L.L. Chau, H.Y. Cheng, W.K. Sze, H. Yao, B. Tseng, Phys. Rev. D 43, 2176 (1991)
L.L. Chau, H.Y. Cheng, W.K. Sze, H. Yao, B. Tseng, Phys. Rev. D 58, 019902 (1998)
M. Beneke, G. Buchalla, M. Neubert, C.T. Sachrajda, Phys. Rev. Lett. 83, 1914 (1999)
M. Beneke, G. Buchalla, M. Neubert, C.T. Sachrajda, Nucl. Phys. B 579, 313 (2000)
H.N. Li, H.L. Yu, Phys. Rev. Lett. 74, 4388 (1995)
H.N. Li, H.L. Yu, Phys. Lett. B 353, 301 (1995)
Y.Y. Keum, H.N. Li, A.I. Sanda, Phys. Rev. D 63, 054008 (2001)
Y.Y. Keum, H.N. Li, A.I. Sanda, Phys. Lett. B 504, 6 (2001)
Y.Y. Keum, H.N. Li, Phys. Rev. D 63, 074006 (2001)
BaBar Collaboration, hep-ex/0508046
A.J. Buras, R. Fleischer, S. Recksiegel, F. Schwab, Nucl. Phys. B 697, 133 (2004)
A. Kagan, Phys. Lett. B 601, 151 (2004)
J.M. Cornwall, Phys. Rev. D 26, 1453 (1982)
J.M. Cornwall, J. Papavasiliou, Phys. Rev. D 40, 3474 (1989)
J.M. Cornwall, J. Papavasiliou, Phys. Rev. D 44, 1285 (1991)
R. Alkofer, L. von Smekal, Phys. Rep. 353, 281 (2001)
L. von Smekal, R. Alkofer, A. Hauck, Phys. Rev. Lett. 79, 3591 (1997)
D. Zwanziger, Phys. Rev. D 69, 016002 (2004)
D.M. Howe, C.J. Maxwell, Phys. Lett. B 541, 129 (2002)
R. Alkofer, Phys. Rev. D 70, 014002 (2004)
A.C. Aguilar, A.A. Natale, P.S. Rodrigues da Silva, Phys. Rev. Lett. 90, 152001 (2003)
S. Furui, H. Nakajima, AIP Conf. Proc. 717, 685 (2004)
S. Brodsky, S. Menke, C. Merino, J. Rathsman, Phys. Rev. D 67, 055008 (2003)
A.C. Mattingly, P.M. Stevenson, Phys. Rev. D 49, 437 (1994)
M. Baldicchi, G.M. Prosperi, Phys. Rev. D 66, 074008 (2002)
R.E. Cutkosky, J. Math. Phys. 1, 429 (1960)
G. Buchalla, A.J. Buras, M.E. Lautenbacher, Rev. Mod. Phys. 68, 1125 (1996)
W.F. Palmer, Y.L. Wu, Phys. Lett. B 350, 245 (1995)
M. Beneke, M. Neubert, Nucl. Phys. B 675, 333 (2003)
M. Beneke et al., Nucl. Phys. B 606, 245 (2001)
S.W. Bosch, G. Buchalla, Nucl. Phys. B 621, 459 (2002)
M. Beneke, T. Feldmann, D. Seidel, Nucl. Phys. B 612, 25 (2001)
J.F. Sun, G.H. Zhu, D.S. Du, Phys. Rev. D 68, 054003 (2003)
S.B. Shalom, G. Eilam, Y.D. Yang, Phys. Rev. D 67, 014007 (2003)
Y.D. Yang, F. Su, G.R. Lu, H.J. Hao, Eur. Phys. J. C 44, 243 (2005)
A.G. Williams et al., hep-ph/0107029 and references therein
C.D. Lu, K. Ukai, M.Z. Yang, Phys. Rev. D 63, 074009 (2001)
S. Eidelman et al., Phys. Lett. B 592, 1 (2004)
C.H. Chen, H.N. Li, Phys. Rev. D 63, 014003 (2001)
J. Zhu, Y.L. Shen, C.D. Lü, Phys. Rev. D 72, 054015 (2005)
Y.L. Wu, Int. J. Mod. Phys. A 18, 5363 (2003)
Y.L. Wu, Mod. Phys. Lett. A 19, 2191 (2004)
H.Y. Cheng, K.C. Yang, Phys. Lett. B 511, 40 (2001)
H.Y. Cheng, K.C. Yang, Phys. Rev. D 64, 074004 (2001)
M. Beneke, T. Feldmann, Nucl. Phys. B 592, 3 (2001)
S. Descotes-Genon, C.T. Sachrajda, Nucl. Phys. B 625, 239 (2002)
P. Ball, V.M. Braun, Nucl. Phys. B 543, 201 (1999)
Author information
Authors and Affiliations
Corresponding author
Additional information
PACS
13.25.Hw; 11.30.Er; 12.38.Bx
Rights and permissions
About this article
Cite this article
Su, F., Wu, YL., Yang, YD. et al. Large strong phases and CP violation in the annihilation processes B̄0→K+K-, K*±K∓, K*+K*- . Eur. Phys. J. C 48, 401–411 (2006). https://doi.org/10.1140/epjc/s10052-006-0029-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjc/s10052-006-0029-1