Regge trajectories for the mesons consisting of different quarks

Abstract

By applying the Bohr–Sommerfeld quantization approach to the quadratic form of the spinless Salpeter-type equation (QSSE), we show that the obtained Regge trajectories for the mesons consisting of unequally massive quarks take the form M^2=beta left( {c_l}l+{pi }n_r+c_0right) ^{2/3}+c_1, which have the same form as the Regge trajectories for charmonia and bottomonia. Then we apply the obtained Regge trajectories to fit the spectra of the strange mesons, the heavy-light mesons (the D, D_s, B and B_s mesons) and the bottom-charmed mesons. The fitted Regge trajectories are in agreement with the experimental data and the theoretical predictions, which demonstrates that the newly proposed Regge trajectories can be applied universally to the light mesons, the heavy-light mesons and the heavy mesons. By fitting the spectra of the mesons composed of different quarks, the concavity of these Regge trajectories are illustrated, which is of cardinal significance for the potential models.