Toward the non-perturbative description of high energy processes

Abstract

General implications of existence of non-perturbative scales and hadronic sub-structure for high energy processes are discussed. We propose that the dependence of the cross section of $\bar q q$ dipoles on their size d should deviate from $d^2$ when d becomes comparable to substructure scale. Then we discuss Kharzeev-Levin pomeron model \cite{KL}, based on ladder-type diagrams with $scalar$ resonances (scalar $\pi\pi$ or $\sigma$ and the scalar glueball $G_0$). This channel is truly unique, because instanton-induced attractive gg interaction \cite{Shu_82} leads to unusually small sizes and strong coupling constants of these states, supplemented by unusually large mass scale, $M_0\approx 4 GeV$, of the transition boundary to the perturbative regime. As pomeron is a small-size object by itself, these resonances may play a special role in its dynamics. Furthermore, we use more realistic description of the scalar gluonic spectral density without free parameters, and slightly modify the model to get correct chiral limit. We conclude that the non-perturbative part of the scalar contribution to the soft pomeron intercept is $\Delta = >.05\pm 0.015$, with comparable contributions from both $\sigma$ and $G_0$.