VirtualO(αs)corrections to the inclusive decayb→sγ

Abstract

We present in detail the calculation of the O(α s ) virtual corrections to the matrix element for b → sγ. Besides the one-loop virtual corrections of the electromagnetic and color dipole operators O 7 and O 8 , we include the important two-loop contribution of the four-Fermi operator O 2 . By applying the Mellin-Barnes representation to certain internal propagators, the result of the two-loop diagrams is obtained analytically as an expansion in m c /m b . These results are then combined with existing O(α s ) Bremsstrahlung corrections in order to obtain the inclusive rate for B → X s γ. The new contributions drastically reduce the large renormalization scale dependence of the leading logarithmic result. Thus a very precise Standard Model prediction for this inclusive process will become possible once also the corrections to the Wilson coefficients are available.

Constraints on light bottom squarks from radiative B-meson decays

“…Using (11), (12), and the wellknown anomalous dimensions of the SM operators [10], we obtain for the anomalous dimension matrix γ Q = αs 4π γ (0) Q + O(α 2 s ), where (setting N = 3 and …”

Radiative corrections to radiative B decays: Exclusive B → Vγ at NLO

“…This feature was already observed in the context of the inclusive case in [ 9]. A complex phase is generated at NLO, where the T I -corrections and the hard-spectator interactions (T II ) yield comparable effects.…”

“…The result for the diagrams in Figs. 2 and 3, which enter the hard-scattering kernels T I 1 , T I 8 , can be infered from [ 9]. In these papers the diagrams were computed to obtain the matrix elements for the inclusive mode b → sγ at next-to-leading order.…”

Rare B decays in the Standard Model

“…The higher order matching conditions, i.e., C i (m W ), are known up to the desired accuracy, i.e., up to O(α s (M W )) terms [14]. The next-to-leading order virtual corrections have also been calculated [15]. They reduce the scale-dependence of the inclusive decay width.…”

“…These functions were first calculated in [11] in the leading logarithmic approximation. Recently, these estimates have been improved in [19], making use of the NLO calculations in [15]. To get an estimate of the inclusive branching ratio, the CKM parameters ρ and η have to be constrained from the unitarity fits.…”