Will the Resonances on the Leading Trajectories Become Stable to Strong Decay at High Spin?

A heuristic discussion is given of the decay modes of high-spin particles lying on a linearly rising trajectory. Among other things, it is concluded that for particles with masses ≳3500 MeV ($J\gtrsim 12$), the total decay widths decrease with $J$ and go to zero approximately like ${\left(J\mathrm{In}J\right)}^{-0.28\mathrm{}{J}^{\frac{1}{2}}}$ as $J\to \infty$ ($0.28=2m_{\pi }{b}^{\frac{1}{2}}$, where $b\simeq 1$ ${\mathrm{GeV}}^{-1/2\mathrm{}}$ is asymptotic slope of the rising trajectory).