Duality and the Pomeranchuk Singularity

The conjecture on the role played by the Pomeranchuk singularity in finite-energy sum-rule (FESR) calculations and within the duality framework is reviewed and subjected to various experimental tests. It is assumed that in the FESR sense the Pomeranchon is built from nonresonating background contributions, while all other trajectories are constructed from $s$-channel resonances. Previous results based on this conjecture are reviewed first. A detailed model for $\pi N$ elastic scattering is then compared with experiment. All $I=1\mathrm{}$ $t$-channel amplitudes for $\pi N$ scattering are entirely accounted for by the $N^{*}$-resonance contributions, while the $I=0\mathrm{}$ $t$-channel amplitudes require significant nonresonating background. This background is predominantly imaginary, and is presumably associated with the Pomeranchon-exchange term. The residue functions of the $P$ and $P^{\prime }$ trajectories are calculated, using FESR and assuming our conjecture. The calculated functions are then used to predict high-energy differential cross sections and polarizations for $\pi N$ scattering, in reasonable agreement with experiment. The $P^{\prime }$ trajectory seems to favor the Gell-Mann ghost-eliminating mechanism both in $\pi N$ and in $\mathrm{KN}$ elastic scattering. Inelastic processes such as $K^{+}n\to K^{0}p$, $\mathrm{KN}\to K\Delta$, and $\mathrm{KN}\to K^{*}N$ are predicted to have purely real amplitudes at large $s$ and small $t$. Various phenomenological models are shown to be consistent with this prediction. The paper concludes with a few remarks concerning various properties of the Pomeranchon, the connection of the model with multiparticle production and to photon initiated reactions, and the (only) failure of the model in baryon-antibaryon scattering.