Mass formula for light nonstrange mesons and Regge trajectories in quark model

Abstract

We study the Regge-like spectra of light mesons in a relativized quark model. An analytical mass formula is presented for the light unflavored mesons with the help of auxiliary field method, by which a quasi-linear Regge–Chew–Frautschi plot is predicted for the orbitally excited states. We show that the trajectory slope is proportional to the inverse of the confining parameter [Formula: see text] when the orbital angular momentum [Formula: see text] is large. The result is tested against the experimental data of the spectra of the meson families [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] in the [Formula: see text] planes, with the fitted parameters consistent with that in the literatures.