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Relativistic bound states in Yukawa model

M. Mangin-Brinet·J. Carbonell·V. A. Karmanov
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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$^π$=$0^+$ and J$^π$=$1^+$ states is studied. The solutions for J$^π$=$0^+$ are found to be stable for coupling constants $α={g^2\over4π}$ below the critical value $α_c\approx 3.72$ and unstable above it. The asymptotic behavior of the wave functions is found to follow a ${1\over k^{2+β}}$ law. The coefficient $β$ and the critical coupling constant $α_c$ are calculated from an eigenvalue equation. The binding energies for the J$^π$=$1^+$ 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.

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M. Mangin-Brinet, J. Carbonell, V. A. Karmanov. 2001-07-27. Relativistic bound states in Yukawa model. https://doi.org/10.1103/physrevd.64.125005

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