  It is illustrated by the fitted Regge trajectories for a large majority of
mesons that both the radial and orbital Regge trajectories for mesons prefer
being concave. The concavity of the meson Regge trajectories is
model-independent. If the convex Regge trajectories or the Regge trajectories
having the inflection points do not exist, the concavity can act as a criterion
to choose a newly observed meson or to assign a particle to the
unwell-established state. The curvature of the meson Regge trajectories can be
taken as a guide in constructing models. The appropriate models should yield
the spectra which can produce the concave Regge trajectories according to the
concavity of the meson Regge trajectories. If the large majority of the meson
Regge trajectories are concave while a few meson Regge trajectories are convex
which neither have been confirmed nor have been completely excluded at present,
many existing models should be corrected or even be reconstructed, which will
lead to the further understanding of the meson dynamics.
