Model of the Pion-Pomeranchon Cut Based on the Mandelstam Diagram

The pion-Pomeranchon Regge cut is calculated from the Mandelstam diagram, using Gribov's approach. Explicit calculations are made for three representative $\pi$-exchange processes: $\mathrm{np}\to \mathrm{pn}$, ${\pi }^{-}p\to {\rho }^{0}n$, and ${\pi }^{+}p\to {\rho }^0{\Delta }^{++}$. Pomeranchon exchange is assumed to be mediated by an isoscalar scalar σ meson. Convergence of the loop integrals is ensured by inserting form factors to relate the off-shell pion-exchange amplitudes to known on-shell behavior. Parameters in the model are the mass of the σ meson, its coupling constants, and cutoff masses in the form factors. Excellent agreement with the data is obtained over a fairly wide range of energy. The model extrapolates well to $t=-1.0\mathrm{}$ ${\mathrm{GeV}}^2$ although the parameters are obtained from a fit to much smaller values of $t$ ($\mathrm{}\left|t\right|<0.1\mathrm{}$ ${\mathrm{GeV}}^2$). Some characteristics of the $\pi P$ cut can be deduced from the results. It is self-conspiratory, a feature which is essential to account for the sharp forward spike in $\mathrm{np}\to \mathrm{pn}$. It does not contribute to amplitudes with unnatural parity and unnatural charge-conjugation parity in the $t$ channel. Furthermore, the cut contribution to amplitudes with natural parity in the $t$ channel are strong only if the amplitudes have double helicity flip in the $s$ channel.