Abstract
The integrated branching fraction of the process B→X s l + l − is dominated by resonance background from narrow charmonium states, such as B→X s ψ→X s l + l −, which exceeds the non-resonant charm-loop contribution by two orders of magnitude. The origin of this fact is discussed in view of the general expectation of quark–hadron duality. The situation in B→X s l + l − is contrasted with charm-penguin amplitudes in two-body hadronic B decays of the type B→π π, for which it is demonstrated that resonance effects and the potentially non-perturbative \(c\bar{c}\) threshold region do not invalidate the standard picture of QCD factorization. This holds irrespective of whether the charm quark is treated as a light or a heavy quark.
Similar content being viewed by others
References
E.C. Poggio, H.R. Quinn, S. Weinberg, Phys. Rev. D 13, 1958 (1976)
M. Beneke, G. Buchalla, M. Neubert, C.T. Sachrajda, Phys. Rev. Lett. 83, 1914 (1999). hep-ph/9905312
M. Beneke, G. Buchalla, M. Neubert, C.T. Sachrajda, Nucl. Phys. B 591, 313 (2000). hep-ph/0006124
M. Beneke, G. Buchalla, M. Neubert, C.T. Sachrajda, Nucl. Phys. B 606, 245 (2001). hep-ph/0104110
M. Misiak, hep-ph/0002007
G. Buchalla, A.J. Buras, M.E. Lautenbacher, Rev. Mod. Phys. 68, 1125 (1996). hep-ph/9512380
C. Amsler (Particle Data Group), Phys. Lett. B 667, 1 (2008)
P. Ko, J. Lee, H.S. Song, Phys. Rev. D 53, 1409 (1996). hep-ph/9510202
M. Beneke, F. Maltoni, I.Z. Rothstein, Phys. Rev. D 59, 054003 (1999). hep-ph/9808360
F. Krüger, L.M. Sehgal, Phys. Lett. B 380, 199 (1996). hep-ph/9603237
A.J. Buras, M. Münz, Phys. Rev. D 52, 186 (1995). hep-ph/9501281
M. Misiak, Nucl. Phys. B 393, 23 (1993) [Erratum-ibid. B 439, 461 (1995)]
B. Chibisov, R.D. Dikeman, M.A. Shifman, N. Uraltsev, Int. J. Mod. Phys. A 12, 2075 (1997). hep-ph/9605465
B. Blok, M.A. Shifman, D.X. Zhang, Phys. Rev. D 57, 2691 (1998) [Erratum-ibid. D 59, 019901 (1999)]. hep-ph/9709333
A. Sommerfeld, Ann. Phys. 403, 257 (1931)
M. Beneke, in Proceedings of the 8th International Symposium on Heavy Flavor Physics (Heavy Flavours 8), Southampton, UK (July 1999). hep-ph/9911490
M.B. Voloshin, Sov. J. Nucl. Phys. 36, 143 (1982) [Yad. Fiz. 36, 247 (1982)]
V.A. Novikov, L.B. Okun, M.A. Shifman, A.I. Vainshtein, M.B. Voloshin, V.I. Zakharov, Phys. Rev. Lett. 38, 626 (1977) [Erratum-ibid. 38, 791 (1977)]
J.H. Kühn, M. Steinhauser, C. Sturm, Nucl. Phys. B 778, 192 (2007). hep-ph/0702103
E. Braaten, S. Narison, A. Pich, Nucl. Phys. B 373, 581 (1992)
Z. Ligeti, L. Randall, M.B. Wise, Phys. Lett. B 402, 178 (1997). hep-ph/9702322
S.J. Lee, M. Neubert, G. Paz, Phys. Rev. D 75, 114005 (2007). hep-ph/0609224
C. Bobeth, M. Misiak, J. Urban, Nucl. Phys. B 574, 291 (2000). hep-ph/9910220
G. Buchalla, G. Isidori, S.J. Rey, Nucl. Phys. B 511, 594 (1998). hep-ph/9705253
M. Bander, D. Silverman, A. Soni, Phys. Rev. Lett. 43, 242 (1979)
A.J. Buras, R. Fleischer, Phys. Lett. B 341, 379 (1995). hep-ph/9409244
M. Ciuchini, E. Franco, G. Martinelli, L. Silvestrini, Nucl. Phys. B 501, 271 (1997). hep-ph/9703353
C.W. Bauer, D. Pirjol, I.Z. Rothstein, I.W. Stewart, Phys. Rev. D 70, 054015 (2004). hep-ph/0401188
M. Beneke, G. Buchalla, M. Neubert, C.T. Sachrajda, Phys. Rev. D 72, 098501 (2005). hep-ph/0411171
C.W. Bauer, D. Pirjol, I.Z. Rothstein, I.W. Stewart, Phys. Rev. D 72, 098502 (2005). hep-ph/0502094
I.I.Y. Bigi, M.A. Shifman, N.G. Uraltsev, A.I. Vainshtein, Phys. Rev. Lett. 71, 496 (1993). hep-ph/9304225
A.V. Manohar, M.B. Wise, Phys. Rev. D 49, 1310 (1994). hep-ph/9308246
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Beneke, M., Buchalla, G., Neubert, M. et al. Penguins with charm and quark–hadron duality. Eur. Phys. J. C 61, 439–449 (2009). https://doi.org/10.1140/epjc/s10052-009-1028-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjc/s10052-009-1028-9