Infrared renormalons and analyticity structure in perturbative QCD

Abstract

The relation between the infrared renormalons, the Borel resummation prescriptions, and the analyticity structure of Green's functions in perturbative QCD is investigated. A specific recently suggested Borel resummation prescription resulted in a principal value and an additional power-suppressed correction that is consistent with operator product expansion. Arguments requiring the finiteness of the result for any power coefficient of the leading infrared renormalon, and consistency in the case of the absence of that renormalon, require that this prescription be modified. The apparently most natural modification leads to the result represented by the principal value. The analytic structure of the amplitude in the complex coupling plane, obtained in this way, is consistent with that obtained in the literature by other methods.

Fit to the Bjorken, Ellis-Jaffe and Gross-Llewellyn-Smith sum rules in a renormalon based approach

“…This is still an open question and, actually, it has been criticised by one of the authors in Ref. [53].…”

“…(45)(46)(47)(48)(49) after performing the renormalization group running of Eqs. (51)(52)(53)(54). If we perform such running we obtain…”

Calculations of binding energies and masses of heavy quarkonia using renormalon cancellation

“…For that, 1 See, for example, Ref. [22] for some algebraic details of obtaining the typical renormalon ambiguity ImS(z = 2β 0 a(µ) ± iε).…”

“…[14,18]. In the Borel integration, we choose the (generalized) principal value (PV) prescription [19,20,21,22]. The ratio S = (m q /m q − 1) has perturbation expansion in MS scheme which is at present known to order ∼ α 3 s (Ref.…”

“…[14,18]; (b) using a new "σ-regularized" full bilocal expansion introduced in the present work; (c) using the form of the Borel transform where the leading IR renormalon structure is a common factor of the transform [19,20] (we call it R-method). The Borel integrations for both m q and E qq (s) are performed by the same prescription (generalized principal value PV [19,20,21,22]) so as to ensure the numerical cancellation of the renormalon contributions in the sum 2m q + E qq (s). Furthermore, we demonstrate numerically that in the latter sum the residues at the renormalons are really consistent with the renormalon cancellation when a reasonable factorization scale parameter for the s-us separation is used, while they become incosistent with the aforementioned cancellation when no such separation is used.…”