Cross-ladder effects in Bethe-Salpeter and Light-Front equations

TL;DR

This paper compares Bethe-Salpeter and Light-Front equations for scalar particles, revealing significant cross-ladder effects and negligible stretched box contributions, with both methods producing consistent results.

Contribution

It provides the first detailed comparison of cross-ladder effects in Bethe-Salpeter and Light-Front equations for scalar particles.

Findings

Cross-ladder effects are large and attractive.

Stretched box contributions are negligible.

BS and LF approaches yield very similar results.

Abstract

Bethe-Salpeter (BS) equation in Minkowski space for scalar particles is solved for a kernel given by a sum of ladder and cross-ladder exchanges. The solution of corresponding Light-Front (LF) equation, where we add the time-ordered stretched boxes, is also obtained. Cross-ladder contributions are found to be very large and attractive, whereas the influence of stretched boxes is negligible. Both approaches -- BS and LF -- give very close results.