Commentary on rainbow-ladder truncation for excited states and exotics

TL;DR

This paper evaluates the rainbow-ladder truncation in studying meson states, confirming its limitations for excited and exotic states, while also providing insights to improve beyond this approximation.

Contribution

It confirms the limitations of rainbow-ladder truncation for excited and exotic mesons and offers guidance for developing better computational techniques and interaction models.

Findings

Rainbow-ladder truncation fails to predict realistic masses for excited and exotic mesons.

The approach offers qualitative insights into hadron observables independent of detailed dynamics.

Provides constraints on the interaction kernel's long-range behavior.

Abstract

Ground-state, radially-excited and exotic scalar-, vector- and flavoured-pseudoscalar-mesons are studied in rainbow-ladder truncation using an interaction kernel that is consonant with modern DSE- and lattice-QCD results. The inability of this truncation to provide realistic predictions for the masses of excited- and exotic-states is confirmed and explained. On the other hand, its application does provide information that is potentially useful in proceeding beyond this leading-order truncation, e.g.: assisting with development of projection techniques that ease the computation of excited state properties; placing qualitative constraints on the long-range behaviour of the interaction kernel; and highlighting and illustrating some features of hadron observables that do not depend on details of the dynamics.