Three-boson bound states in Minkowski space with contact interactions

TL;DR

This paper develops a numerical method to solve the three-boson bound state problem in Minkowski space with contact interactions, comparing results with Euclidean space solutions and analyzing the complex singularity structure.

Contribution

It introduces a novel numerical approach for Minkowski space Bethe-Salpeter equations and investigates the singularity structure of three-boson systems with contact interactions.

Findings

Minkowski and Euclidean solutions show fair agreement for key quantities.

The complex singularity structure of the Bethe-Salpeter vertex function is characterized.

Power-law behavior of two-body correlations is confirmed at high relative momenta.

Abstract

The structure of the three-boson bound state in Minkowski space is studied for a model with contact interaction. The Faddeev-Bethe-Salpeter equation is solved both in Minkowski and Euclidean spaces. The results are in fair agreement for comparable quantities, like the transverse amplitude obtained when the longitudinal constituent momenta of the light-front valence wave function are integrated out. The Minkowski space solution is obtained numerically by using a recently proposed method based on the direct integration over the singularities of the propagators and interaction kernel of the four-dimensional integral equation. The complex singular structure of the Faddeev components of the Bethe-Salpeter vertex function for space and time-like momenta in an example of a Borromean system is investigated in detail. Furthermore, the transverse amplitude is studied as a mean to access the double-parton transverse momentum distribution. Following that, we show that the two-body short-range correlation contained in the valence wave function is evidenced when the pair has a large relative momentum in a back-to-back configuration, where one of the Faddeev components of the Bethe-Salpeter amplitude dominates over the others. In this situation a power-law behavior is derived and confirmed numerically.