Three-boson relativistic bound states with zero-range two-body interaction

A relation between the mass $M_3$ of the relativistic three-body bound state and the mass $M_2$ of the two-body one is obtained for the zero-range interaction $({\phi }^4$ theory), using light-front dynamics. It is found that the three-body system exists only when $M_2$ is greater than a critical value $M_c\approx 1.43m$ $(m$ is the constituent mass). For $M_2{=M}_c,$ the mass $M_3$ turns into zero and for $M_2<M_c,$ there is no solution with real value of $M_3.$