Many-body Fock sectors in Wick-Cutkosky model

TL;DR

This paper analyzes the contributions of various Fock sectors in the Wick-Cutkosky model using light-front dynamics, revealing that the two-body sector dominates the normalization and form factor, especially at small coupling.

Contribution

It provides a detailed quantitative analysis of Fock sector contributions in the Wick-Cutkosky model, highlighting the dominance of the two-body sector across coupling regimes.

Findings

Two-body sector dominates the normalization integral.

At small coupling, two-body contribution is nearly 100%.

At maximal coupling, two-body contributes 64%, three-body 26%, higher sectors 10%.

Abstract

In the model where two massive scalar particles interact by the ladder exchanges of massless scalar particles (Wick-Cutkosky model), we study in light-front dynamics the contributions of different Fock sectors (with increasing number of exchanged particles) to full normalization integral and electromagnetic form factor. It turns out that two-body sector always dominates. At small coupling constant $\alpha\ll 1$, its contribution is close to 100%. It decreases with increase of $\alpha$. For maximal value $\alpha=2\pi$, corresponding to the zero bound state mass, two-body sector contributes to the normalization integral 64%, whereas the three-body contribution is 26% and the sum of all higher contributions from four- to infinite-body sectors is 10%. Contributions to the form factor from different Fock sectors fall off faster for asymptotically large $Q^2$, when the number of particles in the Fock sectors becomes larger. So, asymptotic behavior of the form factor is determined by the two-body Fock sector.