First Radial Excitations of Mesons and Diquarks in a Contact Interaction

TL;DR

This paper calculates the masses of the first radially excited states of various mesons and diquarks across different quark flavors using a symmetry-preserving contact interaction, providing predictions consistent with existing data and extending to unobserved states.

Contribution

It introduces a unified approach employing Bethe-Salpeter and Schwinger-Dyson equations with a contact interaction to predict excited meson and diquark masses across multiple flavors.

Findings

Results agree with experimental data and lattice QCD predictions.

Provides mass predictions for many unobserved radial excitations.

Satisfies Gell-Mann Okubo mass relations.

Abstract

We present a calculation for the masses of the first radially excited states of forty mesons and diquarks made up of $u,d,s,c$ and $b$ quarks, including states that contain one or both heavy quarks. To this end, we employ a combined analysis of the Bethe-Salpeter and Schwinger-Dyson equations within a self-consistent and symmetry preserving vector-vector contact interaction. The same set of parameters describe ground and excited states of mesons and their diquark partners. The wave-function of the first radial excitation contains a zero whose location is correlated with an additional parameter $d_F$ which is a function of dressed quark masses. Our results satisfy the equal spacing rules given by the Gell-Mann Okubo mass relations. Wherever possible, we make comparisons of our findings with known experimental observations as well as theoretical predictions of several other models and approaches including lattice quantum chromodynamics, finding a very good agreement. We report predictions for a multitude of radial excitations not yet observed in experiments.