Abstract.
Using results on soft-collinear factorization for inclusive B-meson decay distributions, a systematic study of the partial \(B\to X_s\gamma\) decay rate with a cut \(E_\gamma\ge E_0\) on photon energy is performed. For values of E 0 below about 1.9 GeV, the rate can be calculated without reference to shape functions using a multi-scale operator product expansion (MSOPE). The transition from the shape-function region to the MSOPE region is studied analytically. The resulting prediction for the \(B\to X_s\gamma\) branching ratio depends on three large scales: m b , \(\sqrt{m_b\Delta}\), and \(\Delta = m_b-2E_0\). Logarithms associated with these scales are resummed at next-to-next-to-leading logarithmic order. While power corrections in \(\Lambda_{\mathrm {QCD}}/\Delta\) turn out to be small, the sensitivity to the scale \(\Delta\approx 1.1\) GeV (for \(E_0\approx 1.8\) GeV) introduces significant perturbative uncertainties, which so far have been ignored. The new theoretical prediction for the \(B\to X_s\gamma\) branching ratio with \(E_\gamma\ge 1.8\) GeV is \(\mbox{Br}(B\to X_s\gamma) = \smash{(3.38_{ -0.42}^{ + 0.31}\pm 0.31)}\times 10^{-4}\), where the first error is an estimate of perturbative uncertainties and the second one reflects uncertainties in input parameters. With this cut \(\smash{(89_{ -7}^{ + 6} \pm 1)}\%\) of all events are contained. When this fraction is combined with the previously best prediction for the total decay rate, one obtains \(\mbox{Br}(B\to X_s\gamma) = (3.30_{ -0.35}^{ + 0.31}\pm 0.17)\times 10^{-4}\), with a somewhat less conservative estimate of parametric uncertainties. The implications of larger theory uncertainties for new physics searches are briefly explored with the example of the type-II two-Higgs-doublet model, for which the lower bound on the charged-Higgs mass is reduced compared with previous estimates to approximately 200 GeV at 95% confidence level.
Similar content being viewed by others
References
For a review, see T. Hurth, Rev. Mod. Phys. 75, 1159 (2003) [hep-ph/0212304]
K. Bieri, C. Greub, M. Steinhauser, Phys. Rev. D 67, 114019 (2003) [hep-ph/0302051]
M. Misiak, M. Steinhauser, Nucl. Phys. B 683, 277 (2004) [hep-ph/0401041]
A.F. Falk, M.E. Luke, M.J. Savage, Phys. Rev. D 49, 3367 (1994) [hep-ph/9308288]
S. Chen et al. [CLEO Collaboration], Phys. Rev. Lett. 87, 251807 (2001) [hep-ex/0108032]
P. Koppenburg et al. [Belle Collaboration], Phys. Rev. Lett. 93, 061803 (2004) [hep-ex/0403004]
P. Gambino, M. Misiak, Nucl. Phys. B 611, 338 (2001) [hep-ph/0104034]
M. Neubert, Phys. Rev. D 49, 3392 (1994) [hep-ph/9311325]; D 49, 4623 (1994) [hep-ph/9312311]
I.I.Y. Bigi, M.A. Shifman, N.G. Uraltsev, A.I. Vainshtein, Int. J. Mod. Phys. A 9, 2467 (1994) [hep-ph/9312359]
T. Mannel, M. Neubert, Phys. Rev. D 50, 2037 (1994) [hep-ph/9402288]
A.F. Falk, E. Jenkins, A.V. Manohar, M.B. Wise, Phys. Rev. D 49, 4553 (1994) [hep-ph/9312306]
G.P. Korchemsky, G. Sterman, Phys. Lett. B 340, 96 (1994) [hep-ph/9407344]
R. Akhoury, I.Z. Rothstein, Phys. Rev. D 54, 2349 (1996) [hep-ph/9512303]
S.W. Bosch, B.O. Lange, M. Neubert, G. Paz, Nucl. Phys. B 699, 335 (2004) [hep-ph/0402094]
C.W. Bauer, A.V. Manohar, Phys. Rev. D 70, 034024 (2004) [hep-ph/0312109]
R.D. Dikeman, M.A. Shifman, N.G. Uraltsev, Int. J. Mod. Phys. A 11, 571 (1996) [hep-ph/9505397]
A.L. Kagan, M. Neubert, Eur. Phys. J. C 7, 5 (1999) [hep-ph/9805303]
B.O. Lange, M. Neubert, Phys. Rev. Lett. 91, 102001 (2003) [hep-ph/0303082]
C.W. Bauer, S. Fleming, D. Pirjol, I.W. Stewart, Phys. Rev. D 63, 114020 (2001) [hep-ph/0011336]; C.W. Bauer, D. Pirjol, I.W. Stewart, Phys. Rev. D 65, 054022 (2002) [hep-ph/0109045]
For a review, see M. Neubert, Phys. Rept. 245, 259 (1994) [hep-ph/9306320]
E. Braaten, S. Narison, A. Pich, Nucl. Phys. B 373, 581 (1992)
A. Czarnecki, W.J. Marciano, Phys. Rev. Lett. 81, 277 (1998) [hep-ph/9804252]
S.W. Bosch, R.J. Hill, B.O. Lange, M. Neubert, Phys. Rev. D 67, 094014 (2003) [hep-ph/0301123]
M. Beneke, G. Buchalla, M. Neubert, C.T. Sachrajda, Nucl. Phys. B 606, 245 (2001) [hep-ph/0104110]
K.G. Chetyrkin, M. Misiak, M. Münz, Phys. Lett. B 400, 206 (1997) [Erratum B 425, 414 (1998)] [hep-ph/9612313]
C. Greub, T. Hurth, D. Wyler, Phys. Rev. D 54, 3350 (1996) [hep-ph/9603404]
A.J. Buras, A. Czarnecki, M. Misiak, J. Urban, Nucl. Phys. B 631, 219 (2002) [hep-ph/0203135]
J.M. Soares, Nucl. Phys. B 367, 575 (1991)
A.L. Kagan, M. Neubert, Phys. Rev. D 58, 094012 (1998) [hep-ph/9803368]
P. Gambino, U. Haisch, JHEP 0009, 001 (2000) [hep-ph/0007259]
K. Baranowski, M. Misiak, Phys. Lett. B 483, 410 (2000) [hep-ph/9907427]
F. De Fazio, M. Neubert, JHEP 9906, 017 (1999) [hep-ph/9905351]
G.P. Korchemsky, A.V. Radyushkin, Nucl. Phys. B 283, 342 (1987); 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]
A. Vogt, Phys. Lett. B 497, 228 (2001) [hep-ph/0010146]
E. Gardi, JHEP 0404, 049 (2004) [hep-ph/0403249]; E. Gardi, R.G. Roberts, Nucl. Phys. B 653, 227 (2003) [hep-ph/0210429], and unpublished work
X. Garcia i Tormo, M. Neubert, I. Scimemi, in preparation
A.G. Grozin, G.P. Korchemsky, Phys. Rev. D 53, 1378 (1996) [hep-ph/9411323]
C. Balzereit, T. Mannel, W. Kilian, Phys. Rev. D 58, 114029 (1998) [hep-ph/9805297]
C.W. Bauer, M.E. Luke, T. Mannel, Phys. Rev. D 68, 094001 (2003) [hep-ph/0102089]
M. Neubert, T. Becher, Phys. Lett. B 535, 127 (2002) [hep-ph/0105217]
I.I.Y. Bigi, M.A. Shifman, N.G. Uraltsev, A.I. Vainshtein, Phys. Rev. D 50, 2234 (1994) [hep-ph/9402360]
M. Beneke, V.M. Braun, Nucl. Phys. B 426, 301 (1994) [hep-ph/9402364]
G. Martinelli, M. Neubert, C.T. Sachrajda, Nucl. Phys. B 461, 238 (1996) [hep-ph/9504217]
M. Neubert, Phys. Lett. B 393, 110 (1997) [hep-ph/9610471]
A. Ali, C. Greub, Phys. Lett. B 361, 146 (1995) [hep-ph/9506374]
R.J. Hill, T. Becher, S.J. Lee, M. Neubert, JHEP 0407, 081 (2004) [hep-ph/0404217]
T. Becher, R.J. Hill, B.O. Lange, M. Neubert, Phys. Rev. D 69, 034013 (2004) [hep-ph/0309227]
M.B. Voloshin, Phys. Lett. B 397, 275 (1997) [hep-ph/9612483]
Z. Ligeti, L. Randall, M.B. Wise, Phys. Lett. B 402, 178 (1997) [hep-ph/9702322]
A. Kapustin, Z. Ligeti, H.D. Politzer, Phys. Lett. B 357, 653 (1995) [hep-ph/9507248]
T. Becher, S. Braig, M. Neubert, A.L. Kagan, Phys. Lett. B 540, 278 (2002) [hep-ph/0205274]
A. Kapustin, Z. Ligeti, Phys. Lett. B 355, 318 (1995) [hep-ph/9506201]
Z. Ligeti, M.E. Luke, A.V. Manohar, M.B. Wise, Phys. Rev. D 60, 034019 (1999) [hep-ph/9903305]
I. Bigi, N. Uraltsev, Int. J. Mod. Phys. A 17, 4709 (2002) [hep-ph/0202175]
M. Beneke, A. Signer, Phys. Lett. B 471, 233 (1999) [hep-ph/9906475]
S. Eidelman et al. [Particle Data Group], Phys. Lett. B 592, 1 (2004)
V.M. Abazov et al. [D0 Collaboration], Nature 429, 638 (2004) [hep-ex/0406031]
J. Charles et al. [CKMfitter Group], hep-ph/0406184
D. Cronin-Hennessy et al. [CLEO Collaboration], Phys. Rev. Lett. 87, 251808 (2001) [hep-ex/0108033]; A.H. Mahmood et al. [CLEO Collaboration], Phys. Rev. D 67, 072001 (2003) [hep-ex/0212051]
B. Aubert et al. [BaBar Collaboration], hep-ex/0307046; Phys. Rev. D 69, 111103 (2004) [hep-ex/0403031]
B. Aubert et al. [BaBar Collaboration], Phys. Rev. Lett. 93, 011803 (2004) [hep-ex/0404017]
F.M. Borzumati, C. Greub, Phys. Rev. D 58, 074004 (1998) [hep-ph/9802391]
G.P. Korchemsky, G. Marchesini, Nucl. Phys. B 406, 225 (1993) [hep-ph/9210281]
E. Gardi reports that he has confirmed littlegamma with \(\kappa=4/3\) from an independent calculation of the anomalous dimension \(\gamma\) (private communication)
S.J. Brodsky, G.P. Lepage, P.B. Mackenzie, Phys. Rev. D 28, 228 (1983)
M. Neubert, Phys. Rev. D 51, 5924 (1995) [hep-ph/9412265]
F. Le Diberder, A. Pich, Phys. Lett. B 286, 147 (1992)
O.V. Tarasov, A.A. Vladimirov, A.Y. Zharkov, Phys. Lett. B 93, 429 (1980)
G. Korchemsky, private communication
A.K. Leibovich, I.Z. Rothstein, Phys. Rev. D 61, 074006 (2000) [hep-ph/9907391]
Author information
Authors and Affiliations
Additional information
Received: 18 September 2004, Revised: 18 January 2005, Published online: 21 February 2005
Rights and permissions
About this article
Cite this article
Neubert, M. Renormalization-group improved calculation of the \(B\to X_s\gamma\) branching ratio. Eur. Phys. J. C 40, 165–186 (2005). https://doi.org/10.1140/epjc/s2005-02141-1
Issue Date:
DOI: https://doi.org/10.1140/epjc/s2005-02141-1