Relativistic bound states in Yukawa model

Abstract

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 $\alpha =\frac{g^2}{4\pi }$ 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 $\frac{1}{k^{2+\beta }}$ 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.

Comments: 22 pages, 13 figures, .tar.gz file