Color-suppression of non-planar diagrams in bosonic bound states

Abstract

We study the suppression of non-planar diagrams in a scalar QCD model of a meson system in $3+1$ space-time dimensions due to the inclusion of the color degrees of freedom. As a prototype of the color-singlet meson, we consider a flavor-nonsinglet system consisting of a scalar-quark and a scalar-antiquark with equal masses exchanging a scalar-gluon of a different mass, which is investigated within the framework of the homogeneous Bethe-Salpeter equation. The equation is solved by using the Nakanishi representation for the manifestly covariant bound-state amplitude and its light-front projection. The resulting non-singular integral equation is solved numerically. The damping of the impact of the cross-ladder kernel on the binding energies are studied in detail. The color-suppression of the cross-ladder effects on the light-front wave function and the elastic electromagnetic form factor are also discussed. As our results show, the suppression appears significantly large for $N_c=3$, which supports the use of rainbow-ladder truncations in practical nonperturbative calculations within QCD.

12 pages, 7 figures. To appear in Physics Letters B

References in corpus (3)

• Solving Bethe-Salpeter equation for two fermions in Minkowski space
• Advances in solving the two-fermion homogeneous Bethe-Salpeter equation in Minkowski space
• Bound state structure and electromagnetic form factor beyond the ladder approximation

Cited by in corpus (1)

• Observing the Minkowskian dynamics of the pion on the null-plane