Dispersive approach to power-behaved contributions in QCD hard processes

Abstract

We consider power-behaved contributions to hard processes in QCD arising from non-perturbative effects at low scales which can be described by introducing the notion of an infrared-finite effective coupling. Our method is based on a dispersive treatment which embodies running coupling effects in all orders. The resulting power behaviour is consistent with expectations based on the operator product expansion, but our approach is more widely applicable. The dispersively-generated power contributions to different observables are given by (log-)moment integrals of a universal low-scale effective coupling, with process-dependent powers and coefficients. We analyse a wide variety of quark-dominated processes and observables, and show how the power contributions are specified in lowest order by the behaviour of one-loop Feynman diagrams containing a gluon of small virtual mass. We discuss both collinear safe observables (such as the e + e − total cross section and τ hadronic width, DIS sum rules, e + e − event shape variables and the Drell-Yan K-factor) and collinear divergent quantities (such as DIS structure functions, e + e − fragmentation functions and the Drell-Yan cross section).

New and old jet clustering algorithms for electron-positron events

“…(4.1) and, for a more theoretically sound basis, also ref. [59]. That a p ⊥ -based measure is indeed a better choice is confirmed not only by the fact that also the various Luclus algorithms can boast a power-suppression similar to that of the Durham scheme, see eq.…”

A novel integral representation for the Adler function

“…The value of the scale parameter Λ = 335 MeV has been estimated for the case of n f = 2 active flavors by fitting D(Q 2 ) (17) (17) corresponding to ρ (1) pert (σ) (solid curve) with its experimental behavior (•) extracted from [13]. The zeroth order prediction for D(Q 2 ) (10) is shown by the dashed curve, the massless APT case (19) is denoted by the dot-dashed curve, and the dot-dot-dashed curve corresponds to the one-loop perturbative approximation (20) of the Adler function.…”

“…3), but fails to describe the experimental behavior of the Adler function in the low-energy domain Q 1 GeV, where the effects due to the pion mass become appreciable. Of course, in the framework of the massless APT, the infrared behavior of the Adler function can be greatly improved following the procedure introduced in [34]; this consists essentially in carrying out an appropriate resummation of threshold singularities, and introducing into (18) and (19) effects from nonperturbative light quark masses. The necessary nonperturbative information on the quark masses is furnished from the study of Schwinger-Dyson equations and quark condensates.…”

On the 1/Q correction to the C-parameter at two loops

“…and the different colour factor, the only difference is in the coefficients of the two terms inside the curly brackets -recall that in (2.10) we had: 4) where the total characteristic function is now…”

“…However, no such expansion is available for event shape variables, so some physically reasonable (and experimentally testable) assumptions are required before progress can be made. Either renormalon methods are employed (for a review see [2]) with the assumption of ultra-violet dominance [3], or else assumptions are made concerning the behaviour of the non-perturbative strong coupling in the infra-red, leading to the dispersive approach [4]. In practice the two methods give consistent results, but in the calculations that follow the dispersive approach will be adopted.…”