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

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 1/a when the orbital angular momentum L is large. The result is tested against the experimental data of the spectra of the meson families pi/b, rho/a,eta/h and omega/f in the (L, M-2) planes, with the fitted parameters consistent with that in the literatures.