On the stability of three-body bound states on the light front

Beyer, M, Mattiello, S, Frederico, T, Weber, H J

Published Feb 8, 2003• 5 citations

Abstract

We investigate the stability of the relativistic three-boson system with a zero range force in the light front form. In particular we study the dependence of the system on an invariant cut-off. We discuss the conditions for the relativistic Thomas collapse. Finally, we fix the parameters of the model introducing a scale.

Related papers

Three-body collapse for Tabakin potentials and the Thomas effect

A. Delfino, Sadhan K. Adhikari, Lauro Tomio +1 more

A system constituted of three bosons interacting via two-body separable potentials with fixed two-boson binding is known to lead to bound-state collapse in the case where the potential parameters allow two-boson S-matrix poles close to (resonance) and on (continuum bound state) the real momentum axis. The collapse is shown to be accompanied by an increase in the average kinetic energy of the two-body bound state, which signals a decrease in the range of the two-body interaction for fixed two-body binding. The collapse is claimed to be a manifestation of the well-known Thomas effect which leads to a collapse of the three-body system when the range of the two-body interaction goes to zero for a fixed two-body binding.

Physical Review CAug 1, 199213 citations

Critical stability of three-body relativistic bound states with zero-range interaction

Vladimir A. Karmanov, Jaume Carbonell

For zero-range interaction providing a given mass M_2 of the two-body bound state, the mass M_3 of the relativistic three-body bound state is calculated. We have found that the three-body system exists only when M_2 is greater than a critical value M_c (approx. 1.43m for bosons and approx. 1.35m for fermions, m is the constituent mass). For M_2=M_c the mass M_3 turns into zero and for M_2

Sep 1, 20031 citation

Three-body bound states with zero-range interaction in the Bethe–Salpeter approach

E. Ydrefors, J. H. Alvarenga Nogueira, Vitor Gigante +2 more

The Bethe–Salpeter equation for three bosons with zero-range interaction is solved for the first time. For comparison the light-front equation is also solved. The input is the two-body scattering length and the outputs are the three-body binding energies, Bethe–Salpeter amplitudes and light-front wave functions. Three different regimes are analyzed: ( i ) For weak enough two-body interaction the three-body system is unbound. ( ii ) For stronger two-body interaction a three-body bound state appears. It provides an interesting example of a deeply bound Borromean system. ( iii ) For even stronger two-body interaction this state becomes unphysical with a negative mass squared. However, another physical (excited) state appears, found previously in light-front calculations. The Bethe–Salpeter approach implicitly incorporates three-body forces of relativistic origin, which are attractive and increase the binding energy.

arXiv:1703.07981Physics Letters BApr 20, 201714 citations

Relativistic Bound States in 2+1 and 1+1 Dimensions in the Null-Plane

J. P. B. C. de Melo, Antonio Eduardo Assis Amorim, Lauro Tomio +1 more

The Relativistic formulation of the three-boson model interacting via a zero-range two-body force in the null-plane is given in 2+1 and 1+1 space-time dimension. The bound state energy is calculed as function of the two-body boson binding energy.

arXiv:hep-ph/9806508Jun 27, 19980 citations

Recent developments in light-front dynamics

Vladimir A. Karmanov

Recent results on relativistic few body systems, obtained in the framework of light‐front dynamics, are briefly reviewed. The following subjects are discussed: two scalar bosons with ladder and cross ladder kernel; two fermions with OBE kernel; relativistic scattering (elastic and inelastic); three bosons and fermions with zero‐range interaction; many‐body contributions.

arXiv:nucl-th/0410033AIP conference proceedingsJan 1, 20050 citations

Recent developments in light-front dynamics

Vladimir A. Karmanov

Abstract. Recent results on relativistic few body systems, obtained in the framework of light-front dynamics, are briefly reviewed. The following subjects are discussed: two scalar bosons with ladder and cross ladder kernel; two fermions with OBE kernel; relativistic scattering (elastic and inelastic); three bosons and fermions with zero-range interaction; many-body contributions.

Jan 1, 20040 citations