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 confining parameter $1\mathrm{/}a$ up to a factor depending on the strong coupling ${\alpha }_s$ when the orbital quantum number $L$ is large. The result is tested against the experimental data of the spectra of the meson families $\pi \mathrm{/}b$,$\rho \mathrm{/}a$,$\eta \mathrm{/}h$ and $\omega \mathrm{/}f$ in the ($L$,$M^2$) planes, with the fitted parameters consistent with that in the literatures.