Leading logarithms of the b quark mass in inclusive B → Xs γ decay

Part of the order αs correction to the inclusive B → Xs γ photon spectrum is enhanced by log(mb2ms2). We discuss its origin and sum the corrections proportional to [αs log(mb2μ2)]n to all orders. These are the calculable leading logarithms in the parton fragmentation functions of a quark or gluon into a photon. Although the gluon fragmentation into a photon starts only at order αs2, its contribution is of the same order as the s quarkʹs in the leading log sum. For not too small values of the photon energy, the resummation.yields a moderate suppression. In the standard model, the coefficient of the operator whose matrix element gives rise to such terms is small. A measurement of the photon spectrum around 1 GeV would provide a theoretically clean determination of C8, the Wilson coefficient of the b → s g operator.