Appendix A - Space-time description of the hadron interactions at high energies

Summary

Here we consider the strong and electromagnetic interactions of hadrons in a unified way. It is assumed that there exist point-like particles (partons) in the sense of quantum field theory and that a hadron with large momentum p consists of ∼ ln(p/µ) partons which have restricted transverse momenta, and longitudinal momenta which range from p to zero. The density of partons increases with the increase of the coupling constant. Since the probability of their recombination also increases, an equilibrium may be reached. In this lecture we will consider consequences of the hypothesis that the equilibrium really occurs. We demonstrate that it leads to constant total cross sections at high energies, and to the Bjorken scaling in the deep inelastic ep scattering. The asymptotic value of the total cross sections of hadron–hadron scattering turns out to be universal, while the cross sections of quasi-elastic scattering processes at zero angle tend to zero.

The multiplicity of the outgoing hadrons and their distributions in longitudinal momenta (rapidities) are also discussed.

Introduction

In this lecture we will try to describe electromagnetic and strong interactions of hadrons in the same framework which follows from general quantum field theory considerations without the introduction of quarks or other exotic objects.

We will assume that there exist point-like constituents in the sense of quantum field theory which are, however, strongly interacting. It is convenient to refer to these particles as partons.