ar X iv : h ep - p h / 99 12 37 6 v 1 1 6 D ec 1 99 9 On the twist - 3 contribution to h L in the instanton vacuum

We show that the instanton model of the QCD vacuum indicates the parametric smallness of the twist-3 contributions to the polarized structure function h L. This smallness is related to the diluteness of the QCD instanton vacuum. 1. Among higher twist parton distributions the twist-3 distributions play a special role. In many physical observables the twist-3 distributions enter not suppressed by powers of the hard scale relative to twist-2 distributions. Therefore the determination of twist-3 distributions does not encounter the conceptual problems of the separation of power suppressed contributions from those that are suppressed by only logarithms. Examples of such observables are spin asymmetries in DIS on transversely polarized targets (g 2) [1] and single spin azimuthal asymmetries in semi-inclusive production of hadrons (h L) [2, 3, 4]. The experimental data of DIS on transversely polarized targets have already reached the precision to estimate the twist-3 contributions to the observables, see recent measurements by E155 collaboration [6]. Recent HERMES and SMC data on single spin azimuthal asymmetries [5, 7] provide the possibility to estimate the quark transversity distribution h 1 in the nucleon if, among other things, one would be able to estimate the twist-3 contribution to h L. The objective of this report is to make an estimate of the size of the twist-3 contribution to h L in the instanton model of the QCD vacuum. The twist-3 distributions are given by nucleon matrix elements of mixed quark-gluon operators. These matrix elements are very sensitive to the correlations of non-perturbative gluon and quark fluctuations in the QCD vacuum. The theory of such fluctuations is provided by the instanton model of the QCD vacuum [8] (for a review see [9, 10]). A nice feature of the instanton model of the QCD vacuum is the existence of a small parameter– the ratio of the average instanton size ¯ ρ to the average distance between instantons ¯ R (¯ ρ/ ¯ R ≈ 1/3). This parameter was first anticipated in ref. [11] from phenomenological considerations, obtained in dynamical calculations of [12] and recently confirmed by direct measurements on the lattice [13]. In ref. [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 …