Space-time description of the hadron interaction at high energies

TL;DR

Gribov develops a space‑time, parton‑based framework for high‑energy hadron interactions using a toy λφ^3 theory to illustrate how fast hadrons can be described as evolving parton ensembles with limited transverse momenta. He derives a covariant hadron wave function composed of n‑parton states, analyzes their rapidity and spatial distributions, and shows that rapidity diffusion leads to Bjorken scaling in deep inelastic scattering and to universal, energy‑independent total cross sections at high energy. A Pomeron‑like exchange with slope α' = γ/4 emerges naturally, and the framework predicts vanishing zero‑angle inelastic diffractive amplitudes due to the orthogonality of slow‑parton states, with cross sections converging across different hadrons. Together these results connect DIS scaling, diffraction, and the asymptotic behavior of hadronic cross sections, laying foundational ideas later incorporated into QCD phenomenology.

Abstract

This is a classical paper by Vladimir Gribov (1930-97) which has influenced the understanding of high energy hadron collisions and deep inelastic scattering for several decades, and is still important today. Gribov's main assumption - that partons have limited transverse momenta - was later proved to be satisfied in QCD, modulo logarithmic corrections. However, QCD was just coming into existence at the time of the lecture, and Gribov used the super-renormalizable φ^3 theory to illustrate his points.

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