Extraction ofαsfrom the Gross–Llewellyn Smith sum rule using Borel resummation

Abstract

Using the CCFR data for the Gross-Llewellyn Smith (GLS) sum rule, we extract the strong coupling constant via Borel resummation of the perturbative QCD calculation. The method incorporates the correct nature of the first infrared renormalon singularity, and employs a conformal mapping to improve the convergence of the QCD perturbation expansion. The important twist-four contribution is calculated from resummation of the perturbation theory, which is based on the ansatz that the higher-twist contribution has a cut singularity only along the positive real axis on the complex coupling plane. Thus obtained, the strong coupling constant corresponding to the central GLS experimental value is in good agreement with the world average.

Surviving the renormalon in the heavy quark potential

“…Clearly, this approach fails in the static potential because the potential of the OPE approach is just the truncated power series plus an r independent constant, which we know has a bad convergence and disagrees with the lattice calculation. As already discussed more extensively in the Gross-Llewellyn Smith sum rule [38] the solution to the problem is the Borel resummation that properly accounts for the renormalon. Without Borel resummation the bad convergence in the truncated power series results in wide fluctuations in the power corrections as the order of perturbation varies, which is observed in many cases.…”

Infrared renormalons and analyticity structure in perturbative QCD

“…The perturbative QCD (pQCD), involving the quark and gluon degrees of freedom, is usually expected to be unable to predict the strength of such terms. 1 Recently, a specific prescription, based on the IR renormalon considerations, has been proposed [6] to fix the strength of such higher-twist terms, and this method gave encouraging numerical results in the case of the resummation of the Gross-Lewellyn-Smith sum rule and of the heavy-quark potential [7]. The main observation was that the IR renormalon induces in the Borel-integrated quantity a nonphysical cut along the positive axis in the complex plane of the coupling parameter z, and that this cut structure can be naturally eliminated by subtracting a cut function proportional to (−z) ν where ν is related with the power coefficient of the renormalon singularity.…”

“…The imaginary part of this expression, i.e., expression (5), must be identified as the imaginary part of the contribution from the leading IR renormalon (2). The central assumption of the method is that the full first expression on the right-hand side of (7), which contains the full nonphysical cut (5) along z > 0 and no cut along z < 0, represents the nonphysical cut-function which is to be eliminated…”

“…( 12), the equality Re∆ (cut1) (|z| ± iε) = ± cot(πν) Im∆ (cut1) (|z| ± iε) was taken into account, a direct consequence of Eqs. ( 5), (7), and…”

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

“…[36]. In this reference only two data points were used and a Principal Valuelike Borel resummation prescription was used.…”