The electromagnetic dipole operator effect on B -> Xs gamma at O(alpha_s^2)
Abstract
The flavor-changing electromagnetic dipole operator O_7 gives the dominant contribution to the B -> Xs gamma decay rate. We calculate two-loop QCD corrections to its matrix element together with the corresponding bremsstrahlung contributions. The optical theorem is applied, and the relevant imaginary parts of three-loop diagrams are computed following the lines of our recent t -> Xb W calculation. The complete result allows us to test the validity of the naive non-abelianization (NNA) approximation that has been previously applied to estimate the NNLO QCD correction to Gamma(B -> Xs gamma)/Gamma(B -> Xu e nu). When both decay widths are normalized to m^5_{b,R} in the same renormalization scheme R, the calculated O(alpha_s^2) correction is sizeable (~ 6%), and the NNA estimate is about 1/3 too large. On the other hand, when the ratio of the decay widths is written as S*(m_b(m_b)/m_{b,pole})^2, the calculated O(alpha_s^2) correction to S is at the level of 1% for both the complete and the NNA results.
Cite
@article{arxiv.hep-ph/0506055,
title = {The electromagnetic dipole operator effect on B -> Xs gamma at O(alpha_s^2)},
author = {I. Blokland and A. Czarnecki and M. Misiak and M. Slusarczyk and F. Tkachov},
journal= {arXiv preprint arXiv:hep-ph/0506055},
year = {2013}
}
Comments
Corrected pi^2 terms in the description of intermediate steps in Section II. Final results unchanged