Nucleon matrix elements of higher-twist operators from the instanton vacuum

Abstract

We compute the nucleon matrix elements of QCD operators of twist 3 and 4 in the instanton vacuum. We consider the operators determining 1/Q 2 -power corrections to the Bjorken, Ellis-Jaffe and Gross-Llewellyn-Smith sum rules. The nucleon is described as a soliton of the effective chiral theory derived from instantons in the 1/N c -expansion. QCD operators involving the gluon field are systematically represented by effective operators in the effective chiral theory. We find that twist-3 matrix elements are suppressed relative to twist-4 by a power of the packing fraction of the instanton medium. Numerical results for the spin-dependent (d (2) , f (2) ) and spin-independent twist-3 and 4 matrix elements are compared with results of other approaches and with experimental estimates of power corrections. The methods developed can be used to evaluate a wide range of matrix elements relevant to DIS.

Twist-3 contribution tohLin the instanton vacuum

“…We shall compute the matrix element (8) in the instanton model of the QCD vacuum using the technique of refs. [14,15]. The effective low-energy theory one derives from the instanton vacuum is formulated in terms of degrees of freedom which are pions (Goldstone bosons) and massive "constituent" quarks.…”

“…[14] a method was developed to calculate hadronic matrix elements of mixed quark gluon operators in the instanton vacuum. Later this method was applied to estimates of higher twist operators [15]. In particular it was shown that the twist-3 contribution to the structure function g 2 is parametrically small relative to twist-2 and twist-4 contributions.…”

“…(see [15] for details). This strong suppression of the twist-3 contribution relative to twist-2 one is related to the specific spin-colour structure of the instanton field and its properties under conformal transformations.…”

Heavy-quark-mass expansion of vector and tensor currents and intrinsic charm in nucleon form factors

“…(6.5). One of possibilities to estimate these form factors is the theory of instanton vacuum [28,29]. However, one can easily see that the gluon operator (6.5) is exactly zero on the instanton field.…”

Imaging the Transverse (Spin) Structure of Hadrons

“…The interpretation of 2M 2 d 2 as an average transverse force also illustrates why d 2 is so small [27,[29][30][31]. Compared to the QCD string tension σ ≈ 1 GeV f m , the factor multiplying d 2 is rather large: 2M 2 ≈ 2GeV 2 ≈ 10σ .…”