Theoretical Models

Abstract

Since the theory of strong interactions is absent, an attempt to describe a certain characteristic of a reaction, for example, polarization requires the development of various models. Many famous theoreticians were involved in this problem at the initial stage of polarization investigations at accelerators. Their ideas were understandable, because they originated from well established facts. They derived simple analytical formulas for calculating observables, for example, the cross sections or polarizations in a particular reaction. These formulas were used as guiding stars when analyzing experimental data and designing new experiments. As an example, we point to the Fermi model proposed in 1954. As energy increases, theoretical models are painfully complicated. Most of them do not provide analytical dependences of observables on arguments, but express these observables in terms of multiple integrals with numerous fitting parameters. For this reason, any physical picture of a process is lost, and these calculations can likely be performed only by their authors themselves. For example, we point to modern calculations of single-spin asymmetry in the perturbative QCD model. Such complicated numerical calculations of observables, which can be represented by very simple functions in experiments, seem very strange: why all are simple in experiments and are very complicated in theory? In view of such a situation, asymptotic predictions are very attractable. These are the hypothesis of γ ₅ invariance or asymptotic relations between amplitudes in cross channels, which are derived on the basis of the Phragmén–Lindelöf theorem. They are also presented in this section.