Resummed B -> Xᵤ l nu Decay Distributions to Next-to-Leading Order

الأصل · EN

We perform factorization of the most general distribution in semileptonic B -> Xᵤ decays and we resum the threshold logarithms to next-to-leading order. From this (triple-differential) distribution, any other distribution is obtained by integration. As an application of our method, we derive simple analytical expressions for a few distributions, resummed to leading approximation. It is shown that the shape function can be directly determined by measuring the distribution in mₓ²/Eₓ², not in mₓ²/mB². We compute the resummed hadron energy spectrum, which has a ``Sudakov shoulder'', and we show how the distribution in the singular region is related to the shape function. We also present an improved formula for the photon spectrum in B->Xₛ gamma which includes soft-gluon resummation and non-leading operators in the effective hamiltonian. We explicitly show that the same non-perturbative function - namely the shape function - controls the non-perturbative effects in all the distributions in the semi-leptonic and in the rare decay.