Two Pomeranchuk-Regge Trajectories

The existence of two Pomeranchuk-Regge trajectories is conjectured. It then follows, with a single numerical coincidence, that at high energies the scattering in each angular momentum state is dominated by inelastic processes. This reinstitutes the physical plausible semiclassical explanation of the origin of diffraction scattering. The width of the diffraction peak still shrinks with energy. It also follows that both total and elastic cross sections increase logarithmically, with a limiting ratio of approximately four. The real part of each phase shift approaches an integral multiple of $\pi$, providing a basis for a general Levinson's theorem; the approach is from above as ${\left(\ln E\right)}^{-1\mathrm{}}$ for increasing energy $E$. The inelastic scattering in each partial wave approaches its maximum value only as ${\left(\ln E\right)}^{-2\mathrm{}}$. Rough quantitative estimates indicate that the typical contribution of two Pomeranchuk trajectories to a total cross section might be quite large (of the order of 66 mb) at 20 BeV.