The double radiative B̄ → Xsγγ decay at O(σs) in QCD

Abstract

In these proceedings, we briefly review the individual interference contribution of the electromagnetic dipole operator O7 to the double differential decay width dΓ77/(ds1 ds2) for the process B̄ → Xsγγ at O(σs) in QCD, which is based on our work in [1]. We define two kinematical variables s1 and s2 as si = (pb - qi)2/m2b, where pb, q1 - q2 are the momenta of b- quark and two photons. While the (renormalized) virtual corrections are worked out exactly for a certain range of s1 and s2, we retained in the gluon bremsstrahlung process only the leading power w.r.t. the (normalized) hadronic mass s3 = (pb - q1 - q2)2/m2b in the underlying triple differential decay width dΓ77/(ds1ds2ds3). We found that the double differential decay width, based on this approximation, is free of infrared- and collinear singularities when summing up the virtual- and real-radiation corrections, while this was not the case when keeping all powers in s3 in the gluon bremsstrahlung process due to the configurations allowing collinear photon emission from the (massless) s-quark. Lastly, we compare our analytical results with those obtained in a recently extended work [2], where a non-zero strange quark mass was introduced to regulate the collinear photon configurations.