<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>CP</mi></math> violation in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow><mo>→</mo><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow><mrow><msup><mrow><mi>D</mi></mrow><mrow><mi>−</mi></mrow></msup></mrow><mo>,</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mi>*</mi><mo>+</mo></mrow></msup></mrow><mrow><msup><mrow><mi>D</mi></mrow><mrow><mi>−</mi></mrow></msup></mrow><mo>,</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow><mrow><msup><mrow><mi>D</mi></mrow><mrow><mi>*</mi><mi>−</mi></mrow></msup></mrow><mo>,</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mi>*</mi><mo>+</mo></mrow></msup></mrow><mrow><msup><mrow><mi>D</mi></mrow><mrow><mi>*</mi><mi>−</mi></mrow></msup></mrow></math> decays

Zhi-zhong Xing

doi:10.1103/PhysRevD.61.014010

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$CP$ violation in $B_{d} \to D^{+} D^{-},$ $D^{* +} D^{-},$ $D^{+} D^{* -},$ and $D^{* +} D^{* -}$ decays

Zhi-zhong Xing^*

Sektion Physik, Universität München, Theresienstrasse 37A, 80333 München, Germany

^*Email address: Xing@hep.physik.uni-muenchen.de

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Phys. Rev. D 61, 014010 – Published 9 December, 1999

DOI: https://doi.org/10.1103/PhysRevD.61.014010

Abstract

$CP$ asymmetries in $B_{d} \to D^{+} D^{-},$ $D^{* +} D^{-},$ $D^{+} D^{* -}$ and $D^{* +} D^{* -}$ decays are investigated with the help of the factorization approximation and isospin relations. We find that direct $CP$ violation is governed only by the short-distance penguin mechanism, while the indirect $CP$ asymmetries in $B_{d} \to D^{\pm} D^{* \mp}$ transitions may be modified due to the final-state rescattering effect. An updated numerical analysis shows that the direct $CP$ asymmetry in $B_{d}^{0}$ vs $B_{d}^{0} \to D^{+} D^{-}$ decays can be as large as 3%. The $CP$ -even and $CP$ -odd contributions to the indirect $CP$ asymmetry in $B_{d}^{0}$ vs $B_{d}^{0} \to D^{* +} D^{* -}$ decays are found to have the rates 89% and 11 %, respectively. Some comments on the possibilities to determine the weak phase $β$ and to test the factorization hypothesis are also given.

References (22)

CDF Collaboration, Report No. CDF/PUB/BOTTOM/CDF/4855, 1999.
CLEO Collaboration, M. Artuso et al., Phys. Rev. Lett. 82, 3020 (1999).
F. Parodi, P. Roudeau, and A. Stocchi, hep-ex/9903063.
The BABAR Physics Book, edited by P. F. Harrison and H. R. Quinn, Report No. SLAC-R-504, 1998.
R. Aleksan, A. Le Yaouanc, L. Oliver, O. Péne, and J. C. Raynal, Phys. Lett. B 317, 173 (1993).
A. I. Sanda and Z. Z. Xing, Phys. Rev. D 56, 341 (1997).
Z. Z. Xing, Phys. Lett. B 443, 365 (1998).
I. Dunietz, H. R. Quinn, A. Snyder, W. Toki, and H. J. Lipkin, Phys. Rev. D 43, 2193 (1991); ibid.G. Kramer and W. F. Palmer, 45, 193 (1992).
See, e.g., A. Deandrea, N. Di Bartolomeo, R. Gatto, and G. Nardulli, Phys. Lett. B 320, 170 (1994); G. Kramer, W. F. Palmer, and H. Simma, Z. Phys. C 66, 429 (1995).
G. Buchalla, A. J. Buras, and M. E. Lautenbacher, Rev. Mod. Phys. 68, 1125 (1996).
Z. Z. Xing, Phys. Rev. D 53, 2847 (1996).
R. Fleischer, Z. Phys. C 62, 81 (1994).
N. G. Deshpande and C. O. Dib, Phys. Lett. B 319, 313 (1993).
M. Neubert, Phys. Lett. B 424, 152 (1998).
M. Bander, D. Silverman, and A. Soni, Phys. Rev. Lett. 43, 242 (1979).
D. Du and Z. Z. Xing, Phys. Rev. D 48, 4155 (1993); Z. Phys. C 66, 129 (1995).
N. G. Deshpande and X. G. He, Phys. Lett. B 336, 471 (1994).
I. Dunietz and J. L. Rosner, Phys. Rev. D 34, 1404 (1986).
A. I. Sanda and Z. Z. Xing, Phys. Rev. D 56, 6866 (1997).
X. Y. Pham and Z. Z. Xing, Phys. Lett. B 458, 375 (1999).
G. Valencia, Phys. Rev. D 39, 3339 (1989).
M. Bauer, B. Stech, and M. Wirbel, Z. Phys. C 34, 103 (1987).

[c1] CDF Collaboration, Report No. CDF/PUB/BOTTOM/CDF/4855, 1999.

[c2] CLEO Collaboration, M. Artuso et al., Phys. Rev. Lett. 82, 3020 (1999).

[c3] F. Parodi, P. Roudeau, and A. Stocchi, hep-ex/9903063.

[c4] The BABAR Physics Book, edited by P. F. Harrison and H. R. Quinn, Report No. SLAC-R-504, 1998.

[c5] R. Aleksan, A. Le Yaouanc, L. Oliver, O. Péne, and J. C. Raynal, Phys. Lett. B 317, 173 (1993).

[c6] A. I. Sanda and Z. Z. Xing, Phys. Rev. D 56, 341 (1997).

[c7] Z. Z. Xing, Phys. Lett. B 443, 365 (1998).

[c8] I. Dunietz, H. R. Quinn, A. Snyder, W. Toki, and H. J. Lipkin, Phys. Rev. D 43, 2193 (1991); ibid.G. Kramer and W. F. Palmer, 45, 193 (1992).

[c9] See, e.g., A. Deandrea, N. Di Bartolomeo, R. Gatto, and G. Nardulli, Phys. Lett. B 320, 170 (1994); G. Kramer, W. F. Palmer, and H. Simma, Z. Phys. C 66, 429 (1995).

[c10] G. Buchalla, A. J. Buras, and M. E. Lautenbacher, Rev. Mod. Phys. 68, 1125 (1996).

[c11] Z. Z. Xing, Phys. Rev. D 53, 2847 (1996).

[c12] R. Fleischer, Z. Phys. C 62, 81 (1994).

[c13] N. G. Deshpande and C. O. Dib, Phys. Lett. B 319, 313 (1993).

[c14] M. Neubert, Phys. Lett. B 424, 152 (1998).

[c15] M. Bander, D. Silverman, and A. Soni, Phys. Rev. Lett. 43, 242 (1979).

[c16] D. Du and Z. Z. Xing, Phys. Rev. D 48, 4155 (1993); Z. Phys. C 66, 129 (1995).

[c17] N. G. Deshpande and X. G. He, Phys. Lett. B 336, 471 (1994).

[c18] I. Dunietz and J. L. Rosner, Phys. Rev. D 34, 1404 (1986).

[c19] A. I. Sanda and Z. Z. Xing, Phys. Rev. D 56, 6866 (1997).

[c20] X. Y. Pham and Z. Z. Xing, Phys. Lett. B 458, 375 (1999).

[c21] G. Valencia, Phys. Rev. D 39, 3339 (1989).

[c22] M. Bauer, B. Stech, and M. Wirbel, Z. Phys. C 34, 103 (1987).

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$CP$ violation in $B_{d} \to D^{+} D^{-},$ $D^{* +} D^{-},$ $D^{+} D^{* -},$ and $D^{* +} D^{* -}$ decays

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CP violation in Bd→D+D−, D*+D−, D+D*−, and D*+D*− decays

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$CP$ violation in $B_{d} \to D^{+} D^{-},$ $D^{* +} D^{-},$ $D^{+} D^{* -},$ and $D^{* +} D^{* -}$ decays