Structure and EM form factors of purely relativistic systems

TL;DR

This paper investigates the structure and electromagnetic form factors of relativistic two-particle systems using the Bethe-Salpeter equation, revealing differences between normal and abnormal solutions and their particle compositions.

Contribution

It provides a detailed analysis of normal and abnormal solutions of the Bethe-Salpeter equation, including their composition and electromagnetic form factors, highlighting the dominance of different sectors.

Findings

Normal states are dominated by two massive particles.

Abnormal states are dominated by massless particles, even at small binding energies.

Electromagnetic form factors for both states and their transitions are calculated.

Abstract

The Bethe-Salpeter equation for two massive scalar particles interacting by scalar massless exchange has solutions of two types, which differ from each other by their behavior in the non-relativistic limit: the normal solutions which turn into the Coulomb ones and the "abnormal" solutions. The latter ones have no non-relativistic counterparts and disappear in the non-relativistic limit. We studied the composition of all these states. It turns out that the normal states, even for large binding energy, are dominated by two massive particles. Whereas, the contribution of the two-body sector into the abnormal states, even for small binding energy, is of the order of 1% only; they are dominated by an indefinite number of the massless particles. The elastic electromagnetic form factors for both normal and abnormal states, as well as the transition ones between them, are calculated.