Structure of the meson Regge trajectories

TL;DR

This paper analyzes meson Regge trajectories using a quadratic spinless Salpeter-type equation, highlighting their energy dependence, parameter limitations, and variations across different mesons.

Contribution

It introduces a detailed analysis of meson Regge trajectories considering energy dependence and constituent masses, revealing limitations of current fitting formulas.

Findings

Regge trajectories depend on energy regions.

Fitted parameters lack explicit physical meaning.

Masses of constituents influence trajectory slopes.

Abstract

We investigate the structure of the meson Regge trajectories based on the quadratic form of the spinless Salpeter-type equation. It is found that the forms of the Regge trajectories depend on the energy region. As the employed Regge trajectory formula does not match the energy region, the fitted parameters neither have explicit physical meanings nor obey the constraints although the fitted Regge trajectory can give the satisfactory predictions if the employed formula is appropriate mathematically. Moreover, the consistency of the Regge trajectories obtained from different approaches is discussed. And the Regge trajectories for different mesons are presented. Finally, we show that the masses of the constituents will come into the slope and explain why the slopes of the fitted linear Regge trajectories vary with different kinds of mesons.