# Relativistic bound states in the 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 $\alpha={g^2\over4\pi}$ 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.
Document type :
Journal articles

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Submitted on : Tuesday, December 4, 2001 - 4:19:09 PM
Last modification on : Thursday, November 19, 2020 - 12:58:34 PM

### Citation

M. Mangin-Brinet, J. Carbonell, V.A. Karmanov. Relativistic bound states in the Yukawa model. Physical Review D, American Physical Society, 2001, 64, 125005-(17 p.). ⟨in2p3-00010610⟩

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