Relativistic bound states in Yukawa model

The bound state solutions of two fermions interacting by a scalar exchange are obtained in the framework of the explicitly covariant light-front dynamics. The stability with respect to cutoff of the J$^{\pi}$=$0^+$ and J$^{\pi}$=$1^+$ states is studied. The solutions for J$^{\pi}$=$0^+$ are found to be stable for coupling constants $\alpha={g^2\over4\pi}$ below the critical value $\alpha_c\approx 3.72$ and unstable above it. The asymptotic behavior of the wave functions is found to follow a ${1\over k^{2+\beta}}$ law. The coefficient $\beta$ and the critical coupling constant $\alpha_c$ are calculated from an eigenvalue equation. The binding energies for the J$^{\pi}$=$1^+$ solutions diverge logarithmically with the cutoff for any value of the coupling constant. For a wide range of cutoff, the states with different angular momentum projections are weakly split.