Abstract
We compute NNLO (\(\mathcal{O}\)(αs 2)) corrections to the hard-scattering kernels entering the QCD factorization formula for B→Vγ decays, where V is a light vector meson. We give complete NNLO results for the dipole operators Q7 and Q8, and partial results for Q1 valid in the large-β0 limit and neglecting the NNLO correction from hard-spectator scattering. Large perturbative logarithms in the hard-scattering kernels are identified and resummed using soft-collinear effective theory. We use our results to estimate the branching fractions for B→K*γ and Bs→φγ decays at NNLO and compare them with the current experimental data.
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References
CLEO Collaboration, T.E. Coan et al., Phys. Rev. Lett. 84, 5283 (2000) [arXiv:hep-ex/9912057]
BABAR Collaboration, B. Aubert et al., Phys. Rev. D 70, 112006 (2004) [arXiv:hep-ex/0407003]
BELLE Collaboration, M. Nakao et al., Phys. Rev. D 69, 112001 (2004) [arXiv:hep-ex/0402042]
BELLE Collaboration, K. Abe et al., Phys. Rev. Lett. 96, 221601 (2006) [arXiv:hep-ex/0506079]
BABAR Collaboration, B. Aubert et al., SLAC-PUB-12025, BABAR-CONF-06-034 [arXiv:hep-ex/0607099]
BELLE Collaboration, M. Nakao, in: Proc. of the XXIII International Symposium on Lepton and Photon Interactions at High Energy (Lepton-Photon-2007), August 13–18, 2007, Daego, Korea
Heavy Flavor Averaging Group (April 2007 update), http://www.slac.stanford.edu/xorg/hfag/
Heavy Flavor Averaging Group, arXiv:0704.3575 [hep-ex]
CDF Collaboration, A. Abulencia et al., Phys. Rev. Lett. 97, 242003 (2006) [arXiv:hep-ex/0609040]
G. Buchalla, A.J. Buras, M.E. Lautenbacher, Rev. Mod. Phys. 68, 1125 (1996) [arXiv:hep-ph/9512380]
M. Beneke, G. Buchalla, M. Neubert, C.T. Sachrajda, Nucl. Phys. B 591, 313 (2000) [arXiv:hep-ph/0006124]
T. Hurth, Rev. Mod. Phys. 75, 1159 (2003) [arXiv:hep-ph/0212304]
C. Bobeth, M. Misiak, J. Urban, Nucl. Phys. B 574, 291 (2000) [arXiv:hep-ph/9910220]
M. Misiak, M. Steinhauser, Nucl. Phys. B 683, 277 (2004) [arXiv:hep-ph/0401041]
M. Gorbahn, U. Haisch, Nucl. Phys. B 713, 291 (2005) [arXiv:hep-ph/0411071]
M. Gorbahn, U. Haisch, M. Misiak, Phys. Rev. Lett. 95, 102004 (2005) [arXiv:hep-ph/0504194]
M. Czakon, U. Haisch, M. Misiak, JHEP 0703, 008 (2007) [arXiv:hep-ph/0612329]
A. Ali, A.Y. Parkhomenko, Eur. Phys. J. C 23, 89 (2002) [arXiv:hep-ph/0105302]
A. Ali, E. Lunghi, A.Y. Parkhomenko, Phys. Lett. B 595, 323 (2004) [arXiv:hep-ph/0405075]
M. Beneke, T. Feldmann, D. Seidel, Nucl. Phys. B 612, 25 (2001) [arXiv:hep-ph/0106067]
A.L. Kagan, M. Neubert, Phys. Lett. B 539, 227 (2002) [arXiv:hep-ph/0110078]
S.W. Bosch, G. Buchalla, Nucl. Phys. B 621, 459 (2002) [arXiv:hep-ph/0106081]
S.W. Bosch, G. Buchalla, JHEP 0501, 035 (2005) [arXiv:hep-ph/0408231]
M. Beneke, T. Feldmann, D. Seidel, Eur. Phys. J. C 41, 173 (2005) [arXiv:hep-ph/0412400]
A. Ali, A. Parkhomenko, DESY 06-187 (2006) [arXiv:hep-ph/0610149]
P. Ball, G.W. Jones, R. Zwicky, Phys. Rev. D 75, 054004 (2007) [arXiv:hep-ph/0612081]
Y.Y. Keum, M. Matsumori, A.I. Sanda, Phys. Rev. D 72, 014013 (2005) [arXiv:hep-ph/0406055]
C.D. Lü, M. Matsumori, A.I. Sanda, M.Z. Yang, Phys. Rev. D 72, 094005 (2005) [arXiv:hep-ph/0508300]
C.D. Lü, M. Matsumori, A.I. Sanda, M.Z. Yang, Phys. Rev. D 73, 039902 (2006) [Erratum]
C.W. Bauer, S. Fleming, M.E. Luke, Phys. Rev. D 63, 014006 (2001) [arXiv:hep-ph/0005275]
C.W. Bauer, S. Fleming, D. Pirjol, I.W. Stewart, Phys. Rev. D 63, 114020 (2001) [arXiv:hep-ph/0011336]
C.W. Bauer, D. Pirjol, I.W. Stewart, Phys. Rev. D 65, 054022 (2002) [arXiv:hep-ph/0109045]
M. Beneke, A.P. Chapovsky, M. Diehl, T. Feldmann, Nucl. Phys. B 643, 431 (2002) [arXiv:hep-ph/0206152]
J.G. Chay, C. Kim, Phys. Rev. D 68, 034013 (2003) [arXiv:hep-ph/0305033]
B. Grinstein, Y. Grossman, Z. Ligeti, D. Pirjol, Phys. Rev. D 71, 011504 (2005) [arXiv:hep-ph/0412019]
T. Becher, R.J. Hill, M. Neubert, Phys. Rev. D 72, 094017 (2005) [arXiv:hep-ph/0503263]
M. Beneke, T. Feldmann, Nucl. Phys. B 592, 3 (2001) [arXiv:hep-ph/0008255]
C.W. Bauer, D. Pirjol, I.W. Stewart, Phys. Rev. D 67, 071502 (2003) [arXiv:hep-ph/0211069]
M. Beneke, T. Feldmann, Nucl. Phys. B 685, 249 (2004) [arXiv:hep-ph/0311335]
B.O. Lange, M. Neubert, Nucl. Phys. B 690, 249 (2004) [arXiv:hep-ph/0311345]
B.O. Lange, M. Neubert, Nucl. Phys. B 723, 201 (2005) [Erratum]
M. Beneke, Y. Kiyo, D.S. Yang, Nucl. Phys. B 692, 232 (2004) [arXiv:hep-ph/0402241]
M. Beneke, D. Yang, Nucl. Phys. B 736, 34 (2006) [arXiv:hep-ph/0508250]
R.J. Hill, T. Becher, S.J. Lee, M. Neubert, JHEP 0407, 081 (2004) [arXiv:hep-ph/0404217]
T. Becher, R.J. Hill, JHEP 0410, 055 (2004) [arXiv:hep-ph/0408344]
I. Blokland, A. Czarnecki, M. Misiak, M. Slusarczyk, F. Tkachov, Phys. Rev. D 72, 033014 (2005) [arXiv:hep-ph/0506055]
H.M. Asatrian, A. Hovhannisyan, V. Poghosyan, T. Ewerth, C. Greub, T. Hurth, Nucl. Phys. B 749, 325 (2006) [arXiv:hep-ph/0605009]
H.M. Asatrian, T. Ewerth, A. Ferroglia, P. Gambino, C. Greub, G. Ossola, in preparation
C. Greub, T. Hurth, D. Wyler, Phys. Rev. D 54, 3350 (1996) [arXiv:hep-ph/9603404]
A.J. Buras, A. Czarnecki, M. Misiak, J. Urban, Nucl. Phys. B 611, 488 (2001) [arXiv:hep-ph/0105160]
A.J. Buras, A. Czarnecki, M. Misiak, J. Urban, Nucl. Phys. B 631, 219 (2002) [arXiv:hep-ph/0203135]
K. Bieri, C. Greub, M. Steinhauser, Phys. Rev. D 67, 114019 (2003) [arXiv:hep-ph/0302051]
R. Boughezal, M. Czakon, T. Schutzmeier, JHEP 0709, 072 (2007) [arXiv:0707.3090 [hep-ph]]
M. Beneke, V.M. Braun, Phys. Lett. B 348, 513 (1995) [arXiv:hep-ph/9411229]
M. Misiak, M. Steinhauser, Nucl. Phys. B 764, 62 (2007) [arXiv:hep-ph/0609241]
M. Misiak et al., Phys. Rev. Lett. 98, 022002 (2007) [arXiv:hep-ph/0609232]
M. Beneke, S. Jäger, Nucl. Phys. B 751, 160 (2006) [arXiv:hep-ph/0512351]
M. Beneke, S. Jäger, Nucl. Phys. B 768, 51 (2007) [arXiv:hep-ph/0610322]
M. Beneke, S. Jäger, Phys. Rev. Lett. 98, 022002 (2007) [arXiv:hep-ph/0609232]
M. Beneke, V.A. Smirnov, Nucl. Phys. B 522, 321 (1998) [arXiv:hep-ph/9711391]
G.G. Kirilin, arXiv:hep-ph/0508235
N. Kivel, JHEP 0705, 019 (2007) [arXiv:hep-ph/0608291]
A.V. Manohar, I.W. Stewart, MIT-CTP-3726, UCSD-PTH-06-04 (2006) [arXiv:hep-ph/0605001]
M. Steinhauser, Phys. Rep. 364, 247 (2002) [arXiv:hep-ph/0201075]
I.A. Korchemskaya, G.P. Korchemsky, Phys. Lett. B 287, 169 (1992)
S. Moch, J.A.M. Vermaseren, A. Vogt, Nucl. Phys. B 688, 101 (2004) [hep-ph/0403192]
M. Neubert, Eur. Phys. J. C 40, 165 (2005) [arXiv:hep-ph/0408179]
T. Becher, M. Neubert, Phys. Rev. Lett. 98, 022003 (2007) [arXiv:hep-ph/0610067]
T. Becher, M. Neubert, Phys. Lett. B 633, 739 (2006) [arXiv:hep-ph/0512208]
T. Becher, M. Neubert, Phys. Lett. B 637, 251 (2006) [arXiv:hep-ph/0603140]
S. Descotes-Genon, C.T. Sachrajda, Nucl. Phys. B 693, 103 (2004) [arXiv:hep-ph/0403277]
G.P. Lepage, S.J. Brodsky, Phys. Rev. D 22, 2157 (1980)
A.V. Efremov, A.V. Radyushkin, Phys. Lett. B 94, 245 (1980)
B.O. Lange, M. Neubert, Phys. Rev. Lett. 91, 102001 (2003) [arXiv:hep-ph/0303082]
S.W. Bosch, R.J. Hill, B.O. Lange, M. Neubert, Phys. Rev. D 67, 094014 (2003) [arXiv:hep-ph/0301123]
V.M. Braun, D.Y. Ivanov, G.P. Korchemsky, Phys. Rev. D 69, 034014 (2004) [arXiv:hep-ph/0309330]
X.D. Ji, M.J. Musolf, Phys. Lett. B 257, 409 (1991)
M. Neubert, Phys. Rev. D 72, 074025 (2005) [arXiv:hep-ph/0506245]
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Ali, A., Pecjak, B. & Greub, C. Towards B→Vγ decays at NNLO in SCET. Eur. Phys. J. C 55, 577–595 (2008). https://doi.org/10.1140/epjc/s10052-008-0623-5
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DOI: https://doi.org/10.1140/epjc/s10052-008-0623-5