Method of Extending the Blankenbecler-Sugar-Logunov-Tavkhelidze Approximation to the Bethe-Salpeter Equation

Abstract

We propose a systematic method of obtaining accurate solutions to the Bethe-Salpeter (BS) equation, starting with the Blankenbecler-Sugar-Logunov-Tavkhelidze (BSLT) equation as the lowest-order approximation. For the equal-mass scattering problem, where the difference between the BS and the BSLT amplitudes is the most marked, the first-order correction we evaluate gives good agreement with the BS amplitude. We have also applied the method to the unequal-mass scattering problem, when the mass ratio is the pion-nucleon mass ratio. Here we find that the BSLT amplitude itself is a good approximation to the BS amplitude.