Modelling non-perturbative corrections to bottom-quark fragmentation

Abstract

We describe B-hadron production in e(+)e(-) annihilation at the Z(0) pole by means of a model including non-perturbative corrections to b-quark fragmentation as originating, via multiple soft emissions, from an effective QCD coupling constant, which does not exhibit the Landau pole any longer and includes absorptive effects due to parton branching. We work in the framework of perturbative fragmentation functions at NLO, with NLL DGLAP evolution and NNLL large-x resummation in both coefficient function and initial condition of the perturbative fragmentation function. We include hadronization corrections via the effective coupling constant in the NNLO approximation and do not add any further non-perturbative fragmentation function. As part of our model, we perform the Mellin transforms of our resummed expressions exactly. We present results on the energy distribution of b-flavored hadrons, which we compare with LEP and SLD data, in both x- and N-spaces. We find that, within the theoretical uncertainties on our calculation, our model is able to reasonably reproduce the data at x less than or similar to 0.92 and the first five moments of the B cross section. (C) 2007 Elsevier B.V. All rights reserved

Inclusive measure of |V ub | with the analytic coupling model

“…For a fixed experimental rate, a smaller Sudakov suppression implies indeed larger hadronic form factors and smaller |V ub |'s. As discussed above, our confidence in the model is also based on phenomenological grounds; we have checked it in beauty fragmentation [5], where soft contributions are similar to those in b decay 12 . In conclusion, the inclusive extraction of |V ub | requires the calculation of inclusive quantities, strongly dependent on b and c masses, as well as the evaluation of thresholdsuppressed quantities, the latter containing large infrared logarithms and Fermi-motion (non-perturbative) effects.…”

“…different possible prescriptions for the low energy behavior of the QCD coupling) (see f.i [8]). A further goal has been to describe at the best the very accurate data in B fragmentation [5]. Then, by using the discussed perturbative analogy in the resummation formulas, we have made predictions for the spectra B decays [1].…”

Charm-quark fragmentation with an effective coupling constant

“…The inclusion of NNLL terms in the resummed exponents shifted the B-hadron spectrum towards lower x B values and played a crucial role to obtain a reasonable description of LEP and SLD data (see figure 4 in ref. [4]).…”

“…Although the results in [3,4] are encouraging, it is nonetheless mandatory to consider more data and observables to validate the effective-coupling model. In this paper, we consider charm-quark fragmentation in e + e − processes and investigate how our nonperturbative model fares against D-meson data from LEP and B-factories.…”

extraction using the Analytic Coupling model

“…This model, which has no free parameters, describes B-meson fragmentation data at the Z 0 peak rather well [5], where -unlike B decaysaccurate data are available and there is no uncertainty coming from the CKM matrix elements. In the following, we describe the phenomelogical model used, then the extraction of |V ub |, and finally the results, followed by the conclusions.…”