Three-boson relativistic bound states with zero-range interaction

Abstract

For the zero-range interaction providing a given mass M_2 of the two-body bound state, the mass M_3 of the relativistic three-boson state is calculated. We have found that the three-body system exists only when M_2 is greater than a critical value M_c approximately 1.43 m (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.

Comments: 7 pages, 4 figures