Stability of the three-fermion bound state on the light front

We derive and solve a set of coupled equations of a relativistic three fermion system subject to an effective scalar zero-range interaction in the 1S0 channel on the light front. In the computation of the three- and two-fermion bound states as functions of the coupling constant λ we have introduced an invariant cut-off Λ. The invariant cut-off allows us to investigate the stability of the three-fermion bound state, i.e. the dependence on the coupling strength also for cases where the two-fermion system is unbound. Analogous to the three-boson system we find the relativistic Thomas collapse. Furthermore, we explicitly investigate the ground state mass of the three-fermion system and compare to previous simplifying calculations.