Efimov Effect in Relativistic Three Body Integral Equations

Relativistic three-body integral equations have important applications in connecting finite volume (Lattice QCD) observables to infinite volume physical observables. In this work, we numerically solve the relativistic three-body integral equations for a system of three identical scalar bosons. The two-body sub-channel of the underlying three-body system is defined by the leading order effective range expansion, i.e. scattering length, and can form two-body bound states. We determine the three-body bound states by solving the integral equations for energies below three particle threshold. In the large scattering length limit, we find a series of three-body bound states. In this limit, the ratio of the binding energies of two consecutive bound states follows Efimov's prediction. Although these binding energies are model dependent, we show that their ratios are not, hence a universal property of the defined three-body system. We also calculate the three-body bound state wavefunctions and compare them to non-relativistic quantum mechanical predictions.