Elastic scattering of hadrons without optical theorem

TL;DR

This paper challenges the widespread use of the optical theorem in modeling elastic hadronic scattering, arguing it is based on assumptions incompatible with actual collision physics, especially for short-range interactions.

Contribution

It demonstrates that the derivation of the optical theorem from unitary S-matrix theory relies on assumptions not valid for real particle collisions, proposing a new approach based on impact parameter analysis.

Findings

Optical theorem derivation depends on unrealistic assumptions.

Short-range interactions invalidate the optical theorem.

Progress requires impact parameter-based collision probability analysis.

Abstract

All contemporary phenomenological models of elastic hadronic scattering have been based on the assumption of validity of optical theorem that was overtaken from optics. It has been stated that it may be proven in particle physics. However, it will be shown that its derivation in the framework of unitary S-matrix theory (which is supposed to be the most general approach in this case) has been based on several requirements that do not correspond to the actual collision characteristics of two particles. It will be shown that especially in the case of short-ranged interaction (for which the theorem is used most frequently) it cannot be applied to. The analysis of corresponding collision experiments is to be done under new basic physical assumptions. The actual progress in the description of hadronic collision processes may exist only if the distribution of different initial states will be specified on the basis of impact parameter values of colliding particles and the dependence of collision probability on this parameter will be established, without limiting corresponding conclusions by the assumption of optical theorem validity from the very beginning.