Threshold resummed spectra in B ---> X(u) l nu decays in NLO. I

We evaluate threshold resummed spectra in B→Xulν decays in next-to-leading order. We present results for the distribution in the hadronic variables EX and mX2/EX2, for the distribution in EX and for the distribution in EX and El, where EX and mX are the total energy and the invariant mass of the final hadronic state Xu respectively and El is the energy of the charged lepton. We explicitly show that all these spectra (where there is no integration over the hadronic energy) can be directly related to the photon spectrum in B→Xsγ via short-distance coefficient functions.