Dispersive calculation of complex Regge trajectories for the lightest $f_2$ resonances

TL;DR

This paper uses a dispersive formalism to calculate the Regge trajectories of lightest $f_2$ mesons directly from resonance data, revealing nearly real, linear trajectories consistent with universal slopes.

Contribution

It introduces a dispersive method to compute Regge trajectories from resonance pole data without fitting to resonance families.

Findings

Trajectories are nearly real and linear.

Slopes agree with the universal value of about 1 GeV$^{-2}$.

Method applies to elastic approximation of resonances.

Abstract

We apply a recently developed dispersive formalism to calculate the Regge trajectories of the $f_2(1270)$ and $f_2'(1525)$ mesons. Trajectories are calculated, not fitted to a family of resonances. Assuming that these spin-2 resonances can be treated in the elastic approximation the only input are the pole position and residue of the resonances. In both cases, the predicted Regge trajectories are almost real and linear, with slopes in agreement with the universal value of order 1 GeV$^{-2}$.