Relativistic Faddeev 3D equations for three-body bound states without two-body t-matrices

Abstract

This paper explores a novel revision of the Faddeev equation for three-body (3B) bound states, as initially proposed in Ref. [1]. This innovative approach, referred to as t −matrix-free in this paper, directly incorporates two-body (2B) interactions and completely avoids the 2B transition matrices. We extend this formalism to relativistic 3B bound states using a three-dimensional (3D) approach without using partial wave decomposition. To validate the proposed formulation, we perform a numerical study using spin-independent Malfliet-Tjon and Yamaguchi interactions. Our results demonstrate that the relativistic t −matrix-free Faddeev equation, which directly implements boosted interactions, accurately reproduces the 3B mass eigenvalues obtained from the conventional form of Faddeev equation, referred to as t −matrix-dependent in this paper, with boosted 2B t −matrices. Moreover, the proposed formulation provides a simpler alternative to the standard approach, avoiding the computational complexity of calculating boosted 2B t −matrices and leading to significant computational time savings.