Relativistic bound states in Yukawa model

TL;DR

This paper investigates relativistic bound states of two fermions interacting via scalar exchange using covariant light-front dynamics, analyzing stability, wave function behavior, and divergence issues across different angular momentum states.

Contribution

It provides a detailed analysis of bound state stability, wave function asymptotics, and divergence behavior in the Yukawa model within a covariant light-front framework, highlighting critical coupling and cutoff effects.

Findings

Stable for J^π=0^+ below critical coupling α_c≈3.72

Wave functions follow a 1/k^{2+β} decay asymptotically

J^π=1^+ states' binding energies diverge logarithmically with cutoff

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.