Long distance effects in semi-inclusive B decays

We discuss some issues on factorization of long distance effects for semi-inclusive B decay spectra in full QCD and in the effective theory.Comment: Contribution to the Proceedings of 1st Workshop on Theory, Phenomenology and Experiments in Heavy Flavour Physics, Anacapri, Italy, 29-31 May, 2006, to be published on Nucl. Phys. B Proceeding

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.

Matching of the Shape Function

The shape function f(k_+) describes Fermi motion effects in inclusive semi-leptonic decays such as B -> X_u+e+nu near the end-point of the lepton spectrum. We compute the leading one-loop corrections to the shape function f(k_+) in the effective theory with a hard cut-off regularization. The matching constant onto full QCD is infrared safe, i.e. the leading infrared singularity represented by the term log^2(k_+) cancels in the difference of integrals. We compare the hard cut-off result with the result in dimensional regularization, the latter containing an additional factor of two in the coefficient of the log^2(k_+) term, and consequently requiring an oversubtraction.Comment: 11 pages, 1 figure added, minor changes in the tex

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

Transverse Momentum Distributions in B-Decays

We consider transverse momentum distributions in B-decays. The O(alpha_S) coefficients for soft and collinear logarithms are computed to next-to-leading accuracy. Resummation of large logarithmic contributions is performed in impact parameter space within the general formalism for transverese momentum distributions. It is shown that the shape-function approach as used for the threshold distribution case cannot be extended to the transverse momentum one.Comment: LaTex file, 8 pages, 1 postscript figur

Semi-Inclusive B Decays and a Model for Soft-Gluon Effects

We compare experimental spectra of radiative and semileptonic B decays with the predictions of a model based on soft-gluon resummation to next-to-next-to leading order and on a ghost-less time-like coupling. We find a good agreement with photon spectra in the radiative decay and with hadron mass distributions in the semileptonic one: the extracted values for alpha_S(m_Z) are in agreement with the current PDG average within at most two standard deviations. The agreement is instead less good for the electron spectra measured by BaBar and Belle in semileptonic decays for small electron energies (< 2.2 GeV): our spectrum is harder. We also show that, in general, the inclusion of next-to-next-to-leading order effects is crucial for bringing the model closer to the data and that the non-power expansion introduced in the framework of analytic coupling studies does not accurately describe soft-gluon effects.Comment: 28 pages, 12 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

Transverse Momentum Distribution in b-> s Gamma

We present the complete calculation of the transverse momentum distribution for the decay b->s Gamma. The contributions of the leading operator O_7 are computed: infrared logarithms are resummed with next-to-leading accuracy, according to usual techniques of resummation. Non logarithmic terms are evaluated to O(alpha_S) by calculating one loop diagrams.Comment: Talk given 10th International QCD Conference (QCD 03), Montpellier, France, 2-9 Jul 2003. 4 page

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