Model for next-to-leading order threshold resummed form factors

Abstract

We present a model for next-to-leading order resummed threshold form factors based on a time-like coupling recently introduced in the framework of small x physics. Improved expressions for the form factors in N -space are obtained which are not plagued by Landau-pole singularities, as the included absorptive effects -usually neglected -act as regulators. The physical reason is that, because of faster decay of gluon jets, there is not enough resolution time to observe the Landau pole. Our form factors reduce to the standard ones when the absorptive parts related to the coupling are neglected. The inverse transform from N -space to x-space can be done directly without any prescription and we obtain analytical expressions for the form factors, which are well defined in all x-space.

Semileptonic B decays

“…Very roughly speaking, the BLNP approach by Bosch, Lange, Neubert, and Paz [33] and the GGOU one by Gambino, Giordano, Ossola and Uraltsev [34] differ in their treatment of Sudakov double logarithms resumming and subleading shape function modeling. The DGE, the dressed gluon exponentiation, by Andersen and Gardi [35,36] and the ADFR approach, by Aglietti, Di Lodovico, Ferrara, and Ricciardi, [37,38,39] start analyzing the singularities of the perturbative expansion in moment space; in the ADFR approach, an effective running coupling is introduced to help estimating nonperturbative corrections. The results listed in Table 1 are consistent within the errors, but the theoretical uncertainty among determinations can reach 10%.…”

Status of |Vcb| and |Vub| CKM matrix elements

“…The analyses from BaBar [102] and Belle [101] collaborations, as well as the HFAG averages [39], rely on at least four theoretical different QCD calculations of the inclusive partial decay rate: BLNP by Bosch, Lange, Neubert, and Paz [103,104,105]; GGOU by Gambino, Giordano, Ossola and Uraltsev [106]; ADFR by Aglietti, Di Lodovico, Ferrara, and Ricciardi [107,108,109]; DGE, the dressed gluon exponentiation, by Andersen and Gardi [110]. They can be roughly divided into approaches based on the estimation of the shape function (BLNP, GGOU) and on resummed perturbative QCD (ADFR, DGE).…”

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

“…In fact we have constructed our model among different possibilities (f.i. 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].…”

“…The perturbative expansion of spectra in the threshold region is affected by large logarithms ≈ α n S log 2n (2E X /m X ), which must be resummed to all orders in α S in order to have a reliable result [7][8][9]. Consistent inclusion of subleading logarithms requires a prescription for the QCD coupling in the low-energy region ∼ Λ -in principle completely arbitrary -which in our model is the analyticity condition.…”