General Analysis of Nucleon-Nucleon Scattering: Critical Tests for Regge-Pole Theory

Using analyticity and crossing, one can express the experimental quantities for the physical channel in terms of the crossed-channel amplitudes. For $N-N$ scattering, a new set of $t$-channel amplitudes $\left\{g_i\right\}$ are introduced for which the $s$-channel experimental quantities $I_0$, $D$, $D_t$, $C_{\mathrm{NN}}$, $C_{\mathrm{KP}}$, $P$, $R$, $A$, $R^{\prime }$, and $A^{\prime }$ are very simple in form. By use of these it is shown that the measurement of certain spin-dependent parameters in $N-N$ scattering can provide critical tests of the validity of the Regge-pole model of high-energy scattering. In particular it is possible to test the factorization theorem, which is an immediate consequence of the simple-pole Regge theory. the relationship of the new amplitudes $g_i$ to the Wolfenstein parameters is given.