Regge trajectories for the light diquarks

TL;DR

This paper develops a simplified Regge trajectory approach to describe light meson and diquark spectra, addressing limitations of linear models by fitting experimental data and considering quark masses, providing a new tool for hadron spectroscopy.

Contribution

It introduces a provisional Regge trajectory formula for light diquarks that accounts for quark masses and offers a simple method to estimate their spectra and excitations.

Findings

The linear Regge trajectory formula fails for light mesons and baryons.

Fitted Regge trajectories agree with other theoretical results.

The approach can be used to investigate baryon and multiquark excitations.

Abstract

We attempt to present an unified description of the light meson spectra and the light diquark spectra by applying the Regge trajectory approach. However, we find that the direct application of the linear Regge trajectory formula for the light mesons and baryons fails. To address this issue, we fit the experimental data of light meson spectra and the light diquark spectra obtained by other theoretical approaches. By considering the light quark mass and the parameter $C$ in the Cornell potential, we provide a provisional Regge trajectory formula. We also crudely estimate the masses of the light diquarks $(ud)$, $(us)$, and $(ss)$, and find that they agree with other theoretical results. The diquark Regge trajectory not only becomes a new and very simple approach for estimating the spectra of the light diquarks, but also can explicitly show the behavior of the masses with respect to $l$ or $n_r$. Moreover, it is expected that the diquark Regge trajectory can provide a simple method for investigating the $\rho$-mode excitations of baryons, tetraquarks and pentaquarks containing diquarks.