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ON MANIFESTATION OF QUARK-HADRON DUALITY
VIA THE ADLER D-FUNCTION
O.P. Solovtsova 1,2† and V.G. Teplyakov 2
(1) Gomel Technical University, Gomel 246746, Belarus
(2) BLTP, JINR, Dubna 141980, Russia
† E-mail: olsol@theor.jinr.ru
To compare theoretical results and experimental data one often uses the concept of
quark-hadron duality, which establishes a bridge between quarks and gluons, a language
oftheoreticians, andreal measurements withhadrons performedby experimentalists. The
ideaquark-hadrondualitywasformulatedinthepaperbyPoggio, Quinn,andWeinberg[1]
as follows: Inclusive hadronic cross sections, once they are appropriately averaged over an
energy interval, must approximately coincide with the corresponding quantities derived
from the quark-gluon picture. It is clear that it will be most fruitful to connect measured
quantities with “simplest” theoretical objects. Some single-argument functions which are
directly connected with experimentally measured quantities can play the role of these
objects.
In this talk we concentrate on physical quantities and functions connected with the
Adler D-function [2]. This function defined in the Euclidean region for positive momentum,
Q 2 = −q 2 > 0, is a smooth function without traces of the resonance structure.
Therefore one might expect that use of the Adler function is useful and that it more precisely
reflects the quark-hadron duality, than, for example, use of the smeared quantity,
R ∆ (q 2 ), defined in the timelike region [1]. The D-function was studied in a number of
papers (see [4] for more details).
Thetheoretical approachthatweuse hereisbased onthenonperturbative a-expansion
method (see [3]) which leads to a new small expansion parameter. Even going into the
infrared region of small momenta where the running coupling becomes large and the
standard perturbative expansion fails, the nonperturbative expansion parameter remains
small and the approach holds valid. It is important that this method supports the correct
analytic properties of the Adler function. Using the D-function in the theoretical description,
we found good agreement between our results and corresponding experimental data
downtothelowest energyscale (thatisnot calculablewithin standardperturbative QCD)
both for the timelike and Euclidean quantities. We investigate the reason of such good
agreement and as a result we formulate a criterion which we call as the R – D self-duality.
References
[1] E.C. Poggio, H.R. Quinn, and S. Weinberg, Phys. Rev. D13, 1958 (1976).
[2] S.L. Adler, Phys. Rev. D10, 3714 (1974).
[3] A.N. Sissakian and I.L. Solovtsov, Phys. Part. Nucl. 30, 461 (1999).
[4] S.L. Adler, “Adventures in theoretical physics: Selected papers of Stephen L. Adler:
Drafts of commentaries”, hep-ph/0505177, 117 pp.
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