Threshold resummed spectra in B -> Xu l nu decays in NLO (II)

We resum to next-to-leading order the distribution in the ratio of the invariant hadron mass mX to the total hadron energy EX and the distribution in mX in the semileptonic decays B -> Xu l nu. By expanding our formulas, we obtain the coefficients of all the infrared logarithms at O(alphaS^2) and of the leading ones at O(alphaS^3). We explicitly show that the relation between these semileptonic spectra and the photon spectrum in the radiative decay B -> Xs gamma is not a purely short-distance one. There are long-distance effects in the semileptonic spectra which are not completely factorized by the structure function as measured in the radiative decay and have to be modelled in some way.Comment: 16 pages, no figure

The shape function in field theory

The shape function describes (non-perturbative) Fermi motion effects in semi-inclusive heavy flavour decay. Its renormalization properties are substantially dependent on the kind of ultraviolet regulator used. For example, the double logarithm that appears at one loop is larger by a factor 2 in dimensional regularization than in lattice regularization. We show that factorization of long-distance effects inside the shape function is achieved with any regulator considered.Comment: Latex, 7 pages, 2 postscript figures, invited talk at the QCD 00 Euroconference, Montpellier, 6-13 July 200

Resummed coefficient function for the shape function

We present a leading evaluation of the resummed coefficient function for the shape function. It is also shown that the coefficient function is short-distance-dominated. Our results allow relating the shape function computed on the lattice to the physical QCD distributions.Comment: LaTex file, 12 pages, 1 postscript figur

Non-Universal Effects in Semi-Inclusive B Decays

We show that most spectra in the semileptonic decay B -> X_u + l + nu, such as for example the distribution in the light-cone momentum p_+ = E_X - p_X recently considered, do not have the same long-distance structure of the photon spectrum in the radiative decay B -> X_s + gamma. On the contrary, the semileptonic distribution in the final hadron energy E_X is connected to the radiative spectrum via short-distance factors only. The E_X distribution also has a specific infrared structure known as the ``Sudakov shoulder''. We also discuss an explicit check of the resummation formula for the semileptonic decays, based on a recent second-order computation.Comment: LaTeX file, 6 pages, no figures. To appear in the Proceedings of the 7th International Symposium on Radiative Corrections (application of quantum field theory to phenomenology) Shonan Village, Japan October 2-7, 2005 (Nucl. Phys. B Proc. Suppl.

The evaluation of loop amplitudes via differential equations

The evaluation of loop amplitudes via differential equations and harmonic polylogarithms is discussed at an introductory level. The method is based on evolution equations in the masses or in the external kinematical invariants and on a proper choice of the basis of the trascendental functions. The presentation is pedagogical and goes through specific one-loop and two-loop examples in order to illustrate the general elements and ideas.Comment: LaTex file, 16 pages, no figures, talk presented at IFAE (Incontri di Fisica delle Alte Energie), Torino 14-16 April 200

Next-to-leading resummed coefficient function for the shape function

We present a next-to-leading evaluation of the resummed coefficient function for the shape function. The results confirm our previous leading order analysis, namely that the coefficient function is short-distance-dominated, and allow relating the shape function computed with a non-perturbative technique to the physical QCD distributions