A novel Faddeev approach for relativistic three-body bound state calculations with direct utilizing 2B boosted interactions

This presentation introduces an innovative implementation of relativistic Faddeev equations for three-body (3B) bound states without relying on two-body (2B) boosted t-matrices. This approach advances the original non-relativistic Faddeev equation from Ref. [1], incorporating relativistic corrections by directly integrating boosted 2B potentials into the Faddeev equations. Consequently, it eliminates the need for fully-off-shell 2B t-matrices [2]. We conducted a numerical assessment of this new formulation in a three-dimensional framework, using spin-independent Malfliet-Tjon and Yamaguchi interactions. Our findings demonstrate that this t-matrix-independent form of the relativistic Faddeev equation effectively reproduces the 3B mass eigenvalues previously calculated using the traditional Faddeev equation with boosted 2B t-matrices. This development offers a streamlined and less complex alternative to the traditional approach, removing the demanding task of calculating boosted 2B t-matrices via the relativistic Lippmann-Schwinger equation, thus significantly simplifying computational coding and saving computational time.

[1] J. Golak, K. Topolnicki, R. Skibiński, W. Gloeckle, H. Kamada, and A. Nogga, Few-Body Systems, 54, 2427–2446 (2013). https://doi.org/10.1007/s00601-012-0472-5

[2] M. Mohammadzadeh, M. Radin, M. R. Hadizadeh, Progress of Theoretical and Experimental Physics 2024.1 (2024): 013D03, https://doi.org/10.1093/ptep/ptad153