The decay b→sgg in the standard model and a nonsoft bremsstrahlung extension of the low-energy theorem

An extension to the low-energy theorem for a flavor-changing two-gluon decay is discussed. It is shown that in cases where external momenta are much smaller than MW but not small compared with the mass of the decaying particle, contributions with the lowest powers of external momenta are only proportional to the corresponding one-gluon decay dipole-moment form factor. In particular, contributions from the color charge-radius form factor must cancel by gauge invariance. As an illustration, an explicit calculation for the decay b→sgg is carried out in the standard model. The result o the calculation agrees with our theorem. We estimate that the branching ratio B(b→sgg) is roughly approx-lt 10-4 and hence completely negligible in the study of nonleptonic inclusive charmless B decays. This differs from other estimates