Isospin-breaking effects on α extracted in B→ππ, ρρ, ρπ

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 71, Issue 7, 2005, Pages 1-11

  Gronau, M ^a   Zupan, J ^b,c  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b CARNEGIE MELLON UNIVERSITY   (United States)

^c JO EF STEFAN INSTITUTE   (Slovenia)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MOLECULAR DYNAMICS; MOLECULAR PHYSICS;

EID: 18544363895     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.71.074017     Document Type: Article

References (84)

1. M. Gronau and D. London, Phys. Rev. Lett. 65, 3381 (1990).
2. Y. Grossman and H. R. Quinn, Phys. Rev. D 58, 017504 (1998); J. Charles, Phys. Rev. D 59, 054007 (1999); M. Gronau, D. London, N. Sinha, and R. Sinha, Phys. Lett. B 514, 315 (2001).
3. Y. Grossman and H. R. Quinn, Phys. Rev. D 58, 017504 (1998); J. Charles, Phys. Rev. D 59, 054007 (1999); M. Gronau, D. London, N. Sinha, and R. Sinha, Phys. Lett. B 514, 315 (2001).
4. Y. Grossman and H. R. Quinn, Phys. Rev. D 58, 017504 (1998); J. Charles, Phys. Rev. D 59, 054007 (1999); M. Gronau, D. London, N. Sinha, and R. Sinha, Phys. Lett. B 514, 315 (2001).
5. BABAR Collaboration, B. Aubert et al., Phys. Rev. D 69, 031102 (2004); Phys. Rev. Lett. 93, 231801 (2004).
6. BABAR Collaboration, B. Aubert et al., Phys. Rev. D 69, 031102 (2004); Phys. Rev. Lett. 93, 231801 (2004).
7. H. J. Lipkin, Y. Nir, H. R. Quinn, and A. Snyder, Phys. Rev. D 44, 1454 (1991); M. Gronau, Phys. Lett. B 265, 389 (1991).
8. H. J. Lipkin, Y. Nir, H. R. Quinn, and A. Snyder, Phys. Rev. D 44, 1454 (1991); M. Gronau, Phys. Lett. B 265, 389 (1991).
9. A. E. Snyder and H. R. Quinn, Phys. Rev. D 48, 2139 (1993); H. R. Quinn and J. P. Silva, Phys. Rev. D 62, 054002 (2000).
10. A. E. Snyder and H. R. Quinn, Phys. Rev. D 48, 2139 (1993); H. R. Quinn and J. P. Silva, Phys. Rev. D 62, 054002 (2000).
11. BABAR Collaboration, B. Aubert et al., hep-ex/0408099; hep-ex/0412037 [Phys. Rev. Lett. (to be published)]; Phys. Rev. Lett. 94, 131801 (2005); hep-ex/0501071 [Phys. Rev. Lett. (to be published)].
12. BABAR Collaboration, B. Aubert et al., hep-ex/0408099; hep-ex/0412037 [Phys. Rev. Lett. (to be published)]; Phys. Rev. Lett. 94, 131801 (2005); hep-ex/0501071 [Phys. Rev. Lett. (to be published)].
13. BABAR Collaboration, B. Aubert et al., hep-ex/0408099; hep-ex/0412037 [Phys. Rev. Lett. (to be published)]; Phys. Rev. Lett. 94, 131801 (2005); hep-ex/0501071 [Phys. Rev. Lett. (to be published)].
14. Belle Collaboration, K. Abe et al., Phys. Rev. Lett. 93, 021601 (2004); hep-ex/0408101; Phys. Rev. Lett. 91, 221801 (2003); J. Zhang et al., Phys. Rev. Lett. 94, 031801 (2005); C. C. Wang et al., Phys. Rev. Lett. 94, 121801 (2005).
15. Belle Collaboration, K. Abe et al., Phys. Rev. Lett. 93, 021601 (2004); hep-ex/0408101; Phys. Rev. Lett. 91, 221801 (2003); J. Zhang et al., Phys. Rev. Lett. 94, 031801 (2005); C. C. Wang et al., Phys. Rev. Lett. 94, 121801 (2005).
16. Belle Collaboration, K. Abe et al., Phys. Rev. Lett. 93, 021601 (2004); hep-ex/0408101; Phys. Rev. Lett. 91, 221801 (2003); J. Zhang et al., Phys. Rev. Lett. 94, 031801 (2005); C. C. Wang et al., Phys. Rev. Lett. 94, 121801 (2005).
17. Belle Collaboration, K. Abe et al., Phys. Rev. Lett. 93, 021601 (2004); hep-ex/0408101; Phys. Rev. Lett. 91, 221801 (2003); J. Zhang et al., Phys. Rev. Lett. 94, 031801 (2005); C. C. Wang et al., Phys. Rev. Lett. 94, 121801 (2005).
18. The CKMfitter Group, J. Charles et al., hep-ph/0406184; http://www.slac.stanford.edu/xorg/ckmfitter.
19. A somewhat larger error is obtained using broken flavor SU(3). See M. Gronau and J. L. Rosner, Phys. Lett. B 595, 339 (2004); M. Gronau and J. Zupan, Phys. Rev. D 70, 074031 (2004).
20. A somewhat larger error is obtained using broken flavor SU(3). See M. Gronau and J. L. Rosner, Phys. Lett. B 595, 339 (2004); M. Gronau and J. Zupan, Phys. Rev. D 70, 074031 (2004).
21. M. Gronau, E. Lunghi, and D. Wyler, Phys. Lett. B 606, 95 (2005).
22. BABAR Collaboration, B. Aubert et al., hep-ex/0408081; Belle Collaboration, Y. Chao et al., hep-ex/0408101.
23. C. W. Bauer, D. Pirjol, I. Z. Rothstein, and I. W. Stewart, Phys. Rev. D 70, 054015 (2004).
24. C. W. Bauer, I. Z. Rothstein, and I. W. Stewart, hep-ph/0412120.
25. A. J. Buras and R. Fleischer, Eur. Phys. J. C 11, 93 (1999); M. Gronau, D. Pirjol and T. M. Yan, Phys. Rev. D 60, 034021 (1999).
26. A. J. Buras and R. Fleischer, Eur. Phys. J. C 11, 93 (1999); M. Gronau, D. Pirjol and T. M. Yan, Phys. Rev. D 60, 034021 (1999).
27. S. Gardner, Phys. Rev. D 59, 077502 (1999); hep-ph/9906269.
28. A. Ali, G. Kramer and C.-D. Lü, Phys. Rev. D 58, 094009 (1998).
29. S. Gardner and U. Meissner, Phys. Rev. D 65, 094004 (2002).
30. R. Enomoto and M. Tanabashi, Phys. Lett. B 386, 413 (1996).
31. S. Gardner, H. B. O'Connel, and A. W. Thomas, Phys. Rev. Lett. 80, 1834 (1998).
32. O. Leitner, X. H. Guo, and A. W. Thomas, Eur. Phys. J. C 31, 215 (2003); J. Phys. G 31, 199 (2005).
33. O. Leitner, X. H. Guo, and A. W. Thomas, Eur. Phys. J. C 31, 215 (2003); J. Phys. G 31, 199 (2005).
34. D. Zeppenfeld, Z. Phys. C 8, 77 (1981).
35. L. L. Chau et al., Phys. Rev. D 43, 2176 (1991).
36. M. Gronau, O. Hernández, D. London, and J. L. Rosner, Phys. Rev. D 50, 4529 (1994).
37. M. Gronau and J. L. Rosner, Phys. Rev. D 53, 2516 (1996); A. S. Dighe, Phys. Rev. D 54, 2067 (1996).
38. M. Gronau and J. L. Rosner, Phys. Rev. D 53, 2516 (1996); A. S. Dighe, Phys. Rev. D 54, 2067 (1996).
39. C. W. Bauer and D. Pirjol, Phys. Lett. B 604, 183 (2004).
40. M. Gronau, O. Hernández, D. London, and J. L. Rosner, Phys. Rev. D 52, 6374 (1995).
41. R. Escribano and J.-M. Frère, hep-ph/0501072; see also Th. Feldman, P. Kroll, and B. Stech, Phys. Rev. D 58, 114006 (1998).
42. C. W. Chiang, M. Gronau, and J. L. Rosner, Phys. Rev. D 68, 074012 (2003); C. W. Chiang, M. Gronau, J. L. Rosner, and D. A. Suprun, Phys. Rev. D 70, 034020 (2004).
43. C. W. Chiang, M. Gronau, and J. L. Rosner, Phys. Rev. D 68, 074012 (2003); C. W. Chiang, M. Gronau, J. L. Rosner, and D. A. Suprun, Phys. Rev. D 70, 034020 (2004).
44. H. Leutwyler, Phys. Lett. B 374, 181 (1996).
45. P. Kroll, hep-ph/0409141.
46. Field operators creating a state consisting of two identical particles can do this in two different ways implying a factor of 2 in the amplitude. However, when integrating over the final states, one has to avoid double counting of configurations with identical momenta, so the rate is cut by a factor of 2 and the net result is a factor of √2 in the amplitude.
47. The correction to the angle φ in (5) is given by Δφ=(e 0/sinφ)(√2|A+0|/|A+-|-cosφ). A similar expression describes the correction to the angle φ̄.
48. Heavy Flavor Averaging Group, J. Alexander et al., hepex/0412073.
49. Belle Collaboration, Y. Chao et al., Phys. Rev. D 69, 111102 (2004).
50. BABAR Collaboration, B. Aubert et al., hep-ex/0408081.
51. BABAR Collaboration, B. Aubert et al., Phys. Rev. D 70, 032006 (2004).
52. Belle Collaboration, K. Abe et al., hep-ex/0408131; P. Chang, hep-ex/0412043.
53. BABAR Collaboration, B. Aubert et al., Phys. Rev. Lett. 92, 061801 (2004).
54. BABAR Collaboration, B. Aubert et al., hep-ex/0408058.
55. M. Gronau, J. L. Rosner, and J. Zupan, Phys. Lett. B 596, 107 (2004); For earlier but less stringent constraints, see Y. Grossman, Z. Ligeti, Y. Nir, and H. Quinn, Phys. Rev. D 68, 015004 (2003); C. W. Chiang, M. Gronau, and J. L. Rosner, Ref. [28].
56. M. Gronau, J. L. Rosner, and J. Zupan, Phys. Lett. B 596, 107 (2004); For earlier but less stringent constraints, see Y. Grossman, Z. Ligeti, Y. Nir, and H. Quinn, Phys. Rev. D 68, 015004 (2003); C. W. Chiang, M. Gronau, and J. L. Rosner, Ref. [28].
57. Belle Collaboration, K. Abe et al., hep-ex/0409049; BABAR Collaboration, B. Aubert et al., hep-ex/0502017 [Phys. Rev. Lett. (to be published)].
58. A. F. Falk, Z. Ligeti, Y. Nir, and H. Quinn, Phys. Rev. D 69, 011502 (2004).
59. H. B. O'Connell, B. C. Pearce, A. W. Thomas, and A. G. Williams, Prog. Part. Nucl. Phys. 39, 201 (1997); K. Maltman, H. B. O'Connell, and A. G. Williams, Phys. Lett. B 376, 19 (1996); H. B. O'Connell, A. W. Thomas, and A. G. Williams, Nucl. Phys. A623, 559 (1997).
60. H. B. O'Connell, B. C. Pearce, A. W. Thomas, and A. G. Williams, Prog. Part. Nucl. Phys. 39, 201 (1997); K. Maltman, H. B. O'Connell, and A. G. Williams, Phys. Lett. B 376, 19 (1996); H. B. O'Connell, A. W. Thomas, and A. G. Williams, Nucl. Phys. A623, 559 (1997).
61. H. B. O'Connell, B. C. Pearce, A. W. Thomas, and A. G. Williams, Prog. Part. Nucl. Phys. 39, 201 (1997); K. Maltman, H. B. O'Connell, and A. G. Williams, Phys. Lett. B 376, 19 (1996); H. B. O'Connell, A. W. Thomas, and A. G. Williams, Nucl. Phys. A623, 559 (1997).
62. Particle Data Group, S. Eidelman et al., Phys. Lett. B 592, 1 (2004).
63. P. F. Harrison and H. R. Quinn, SLAC Report No. SLACR-0504, 1998 (unpublished).
64. S. Gardner and H. B. O'Connell, Phys. Rev. D 57, 2716 (1998); 62, 019903(E) (2000).
65. S. Gardner and H. B. O'Connell, Phys. Rev. D 57, 2716 (1998); 62, 019903(E) (2000).
66. BABAR Collaboration, B. Aubert et al., Phys. Rev. Lett. 91, 171802 (2003); Belle Collaboration, J. Zhang et al.. Phys. Rev. Lett. 91, 221801 (2003).
67. BABAR Collaboration, B. Aubert et al., Phys. Rev. Lett. 91, 171802 (2003); Belle Collaboration, J. Zhang et al.. Phys. Rev. Lett. 91, 221801 (2003).
68. BABAR Collaboration, B. Aubert et al., Phys. Rev. D 71, 031103 (2005).
69. M. Gronau and J. L. Rosner, Phys. Rev. D 66, 053003 (2002).
70. A. S. Dighe, M. Gronau, and J. L. Rosner, Phys. Rev. D 57, 1783 (1998).
71. A similar effect can be observed in D0→K Sπ+π-. See CLEO Collaboration, H. Muramatsu et al., Phys. Rev. Lett. 89, 251802 (2002); 90, 059901(E) (2003); BABAR Collaboration, B. Aubert et al., hep-ex/0408088; Belle Collaboration, K. Abe et al., hep-ex/0411049.
72. A similar effect can be observed in D0→K Sπ+π-. See CLEO Collaboration, H. Muramatsu et al., Phys. Rev. Lett. 89, 251802 (2002); 90, 059901(E) (2003); BABAR Collaboration, B. Aubert et al., hep-ex/0408088; Belle Collaboration, K. Abe et al., hep-ex/0411049.
73. M. Gronau, Phys. Rev. Lett. 63, 1451 (1989).
74. J. Charles, LPT-Orsay Report No. 99-31, 1999; available (in French) at http://www.tel.ccsd.cnrs.fr (ID 00002502);M. Gronau, Phys. Rev. D 62, 014031 (2000).
75. J. Charles, LPT-Orsay Report No. 99-31, 1999; available (in French) at http://www.tel.ccsd.cnrs.fr (ID 00002502);M. Gronau, Phys. Rev. D 62, 014031 (2000).
76. M. Beneke and M. Neubert, Nucl. Phys. B675, 333 (2003).
77. C. W. Chiang, M. Gronau, Z. Luo, J. L. Rosner, and D. A. Suprun, Phys. Rev. D 69, 034001 (2004). Here and in [56] the c-convention has been used, related to the t-convention by [49] |Pt|/|Pc|=sinγ/ sinα, |Tt|e-iδt-|Tc|e -iδc=(sinβ/sinα)|Pc| where δc,t are strong phase differences between penguin and tree amplitudes. We checked that the bounds on amplitude ratios (57) hold in both conventions.
78. M. Gronau and J. Zupan, Ref. [9].
79. A. Deandrea et al., Phys. Rev. D 62, 036001 (2000); A. Deandrea and A. D. Polosa, Phys. Rev. Lett. 86, 216 (2001); J. Tandean and S. Gardner, Phys. Rev. D 66, 034019 (2002).
80. A. Deandrea et al., Phys. Rev. D 62, 036001 (2000); A. Deandrea and A. D. Polosa, Phys. Rev. Lett. 86, 216 (2001); J. Tandean and S. Gardner, Phys. Rev. D 66, 034019 (2002).
81. A. Deandrea et al., Phys. Rev. D 62, 036001 (2000); A. Deandrea and A. D. Polosa, Phys. Rev. Lett. 86, 216 (2001); J. Tandean and S. Gardner, Phys. Rev. D 66, 034019 (2002).
82. Belle Collaboration, J. Dradic et al., Phys. Rev. Lett. 93, 131802 (2004).
83. BABAR Collaboration, B. Aubert et al., Phys. Rev. Lett. 93, 051802 (2004).
84. BABAR Collaboration, B. Aubert, Phys. Rev. D 70, 032006 (2004).