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

Understand

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.