Relativistic bound states in Yukawa model

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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 Jπ=0+ and Jπ=1+ states is studied. The solutions for Jπ=0+ are found to be stable for coupling constants α=g²4π below the critical value αc≈ 3.72 and unstable above it. The asymptotic behavior of the wave functions is found to follow a 1 k²⁺β law. The coefficient β and the critical coupling constant αc are calculated from an eigenvalue equation. The binding energies for the Jπ=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.