Charm quark mass dependence of the electromagnetic dipole operator contribution to anti-B -.pdf

a r X i v : h e p - p h / 0 6 1 1 1 2 3 v 2 2 J u n 2 0 0 7 Charm quark mass dependence of the electromagnetic dipole operator contribution to B? → Xsγ at O(α 2 s) H. M. Asatriana, T. Ewerthb, H. Gabrielyana, and C. Greubb aYerevan Physics Institute, 375036 Yerevan, Armenia bInstitute for Theoretical Physics, Univ. Berne, CH-3012 Berne, Switzerland Abstract We extend existing calculations of the electromagnetic dipole operator contribution to the total decay rate and the photon energy spectrum of the decay B? → Xsγ at O(α2s) by working out the exact dependence on the charm quark mass. 1 Introduction As a flavor changing neutral current process the inclusive decay B? → Xsγ is loop-induced and therefore highly sensitive to new degrees of freedom beyond the Standard Model. To tap the full potential of this decay channel in deriving constraints on the parameter space of new physics models both the experiments and the Standard Model calculations should be known as accurately as possible. On the experimental side, the latest measurements by Belle and BABAR are reported in [1, 2], and the world average performed by the Heavy Flavor Averaging Group [3] for Eγ 1.6GeV reads Br(B? → Xsγ) = ( 3.55± 0.24+0.09 ?0.10 ± 0.03 )× 10?4 , (1.1) where the errors are statistical, systematical, due to the extrapolation to the common lower- cut in the photon energy, and due to the B? → Xdγ contamination, respectively. In order to compete with the given experimental accuracy the theoretical prediction of the B? → Xsγ branching ratio has to be known at the next-to-next-to-leading order (NNLO) level. There have been great efforts of several groups within the last few years to achieve this goal. The three-loop dipole operator matching was found in [4], the three-loop mixing of the four- quark operators in [5], and the three-loop mixing of the dipole operators was calculated in [6]. Furthermore, the four-loop mixing of the four-quark operators into the dipole operators was calculated in [