Leading logarithmic QCD corrections to the Bs → γγ decay rate including long-distance effects through Bs → φγ → γγ

Abstract

We present leading logarithmic QCD corrections to the decay B s → γγ in the Standard Model. Further, the form factor F 1 (0) of B s → φγ is calculated in the framework of QCD sum rules and found to be in agreement with the result existing in the literature. Using Vector Meson Dominance model, the amplitude for B s → φγ → γγ is calculated as an estimate of the O 7 -type contributions to the long-distance effects in the B s → γγ decay. The resulting branching ratio B(B s → γγ) SD+LDO 7 is analysed in view of its strong dependence on the non-perturbative parameterΛ s , describing bound state effects, and the renormalization scale µ. * ‡ Supported by TUBITAK 1 We adopt the convention T r(γ µ γ ν γ α γ β γ5) = 4iǫ µναβ , with ǫ 0123 = +1. 2 In an earlier version of this paper the contributions of the operators O1,3...6 in the irreducible part in A + and A − were not completely taken into account. This is corrected here. As a second improvement we give the amplitudes in a formalism inspired by HQET to estimate the uncertainties coming from the bound state.

(O8,O8) contribution toAsatrian1, Greub2, Kokulu3 2016Phys. Rev. D

“…Also the corresponding exclusive modes, B s → γγ and B → Kγγ, have been examined before, both in the SM [9,[26][27][28][29][30][31][32][33][34] and in its extensions [25,30,31,[35][36][37][38][39][40][41][42][43]. We should add that the long-distance resonant effects were also discussed in the literature (see e.g.…”

Technicolor corrections onBs,d→γγdecays in QCD factorization

“…Both inclusive and exclusive processes, such as the decays B → X s γ, X s γγ and B s,d → γγ, have been studied in great detail [1][2][3][4][5][6][7][8][9][10][11].…”

“…In other words, the excellent agreement between SM theory and experimental data results in a strong constraint on many new physics models beyond the SM. Within the SM, the electroweak contributions to b → sγγ and B → γγ decays have been calculated some time ago [1]; the leading-order QCD corrections and the long-distance contributions were evaluated recently by several groups [6,14]. The new physics corrections were also considered, for example, in the two-Higgs doublet model [15,16] and the supersymmetric model [17].…”

“…In Q 7,8 , the terms proportional to m s are usually neglected because of the strong suppression m The Wilson coefficients C i (µ) in Eq. (6) are known currently at next-to-leading order (NLO) [2,3]. Within the SM and at scale m W , the Wilson coefficients C i (m W ) at the leading order (LO) approximation have been given for example in [3],…”

“…The first approach was proposed ten years ago and has been employed by many authors [1,6]. Under this approach, one simply evaluates the hadronic element of the amplitudes for one-particle reducible (1PR) and one-particle irreducible (1PI) diagrams, relying on a phenomenological model.…”