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 = β (c l l + π n r + c 0 )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.

Nonlinear Regge trajectories with AdS/QCD

“…By introducing the ν exponent in the radial Regge trajectory we can explore the effect of the quark mass. As it was pointed out in [16][17][18], increasing the quark mass should deviate the trajectory from the linear case. In this holographic approach, such behavior was observed.…”

“…The relation between hadronic squared mass and radial (and orbital) quantum number is considered usually as linear. This affirmation in general, accepted due to experimental evidence, is especially true in the light sector, but when quark masses are increased, a nonlinear Regge trajectory seems better to describe hadron spectra [16][17][18][19][20].…”

“…But, on the other hand, it was possible to fit heavy light vector mesons and to test, at holographic level, possible candidates to be non-qq states, just by considering how the hadronic operators at the boundary change their conformal dimension, that has information about the meson constituent indirectly, altogether with the holographic thresholdm, that parametrizes the structure of the state at hand. The change in the conformal dimension is translated into a modification of the bulk mass term that appears in the holographic potential (17), whilem fixes in the calibration curves (13) and (12) the values for κ and α. The same methodology was used to do the holographic fit for the heavy-light mesons and the K Ã vector states.…”

“…If we want to consider the case when the constituent quarks are massive, we must extend to nonlinear Regge trajectories [16][17][18][19][20]. As we mentioned early, we consider nonlinearity connected with the quark constituent mass.…”

“…Linear Regge trajectories are a good description of the mesonic mass spectra in the light sector, and this has been used traditionally as a guideline in order to catch hadron properties in the AdS side of AdS/QCD models. But if hadrons contain s or heavy quarks, linearity in trajectory is lost [16][17][18][19][20]. Moreover, starting from the quadratic form of Bethe Salpeter equation [19,21], it is possible to infer that mesons consisting of heavier quarks have Regge trajectories deviated from the linearity.…”