Next-to-leading logarithmic QCD contribution of the electromagnetic dipole operator toB¯→Xsγγwith a massive st

Abstract

We calculate the O(α s ) corrections to the double differential decay width dΓ 77 /(ds 1 ds 2 ) for the processB → X s γγ originating from diagrams involving the electromagnetic dipole operator O 7 . The kinematical variables s 1 and s 2 are defined as s i = (p b − q i ) 2 /m 2 b , where p b , q 1 , q 2 are the momenta of b-quark and two photons. We introduce a nonzero mass m s for the strange quark to regulate configurations where the gluon or one of the photons become collinear with the strange quark and retain terms which are logarithmic in m s , while discarding terms which go to zero in the limit m s → 0. When combining virtual-and bremsstrahlung corrections, the infrared and collinear singularities induced by soft and/or collinear gluons drop out. By our cuts the photons do not become soft, but one of them can become collinear with the strange quark. This implies that in the final result a single logarithms of m s survives. In principle the configurations with collinear photon emission could be treated using fragmentation functions. In a related work we found that similar results can be obtained when simply interpreting m s appearing in the final result as a constituent mass. We do so in the present paper and vary m s between 400 MeV and 600 MeV in the numerics. This work extends a previous paper of us, where only the leading power terms w.r.t. the (normalized) hadronic mass s 3 = (p b − q 1 − q 2 ) 2 /m 2 b were taken into account in the underlying triple differential decay width dΓ 77 /(ds 1 ds 2 ds 3 ).

Improved analysis of the (O_7, O_7) contribution to $\bar{B} \rightarrow X_s γγ$ at $O(α_s)$

“…the reviews [10,11] and references therein). On the other hand, the matrix elements sγγ|O i |b and sgγγ|O i |b , which in a NLL calculation are needed to order g 2 s and g s , respectively, are only partially known by now (see [16][17][18] for the details of the provided NLL contributions and [43] for a recent summary).…”

“…[10,11] for reviews). Regarding the B → X s γγ decay, the leading logarithmic (LL) prediction for the branching ratio was known since a long time [12][13][14][15], while the first attempts towards a NLL calculation were only made years later by us [16,17], in which the QCD corrections to the numerically dominant (O 7 , O 7 ) contribution were worked out in certain approximations which will be detailed in the next paragraph. In 2015, we also provided the contributions stemming from the self-interference of chromomagnetic dipole operator O 8 [18].…”

“…In Ref. [17], we worked out the double differential decay width based on the triple differential width, retaining all powers w.r.t. s 3 .…”

“…We denote these results as exact results and the results of Ref. [17] as results in the limit m s → 0.…”

One-loop SQCD corrections to the decay of top squarks to charm and neutralino in the generic MSSM

“…In Refs. [89,90] useful parametrizations for the phasespace factors D<F(1 -n) have been given for n = 3,4, for the case where all final-state particles are massive. In our problem we only use the case n = 3 where only the neutralino is massive; this means that the general formula simplifies.…”