Empirical Systematics ofπNAmplitudes

The structure of $\pi N$ $s$-channel helicity amplitudes as a function of momentum transfer and energy is examined in FESR (finite-energy sum rule) Regge fits, direct amplitude analysis of data, and phase-shift analyses. Information on the separated amplitudes from these various sources is found to agree. The value of helicity correlation measurements in testing the zero structure of helicity amplitudes is demonstrated. The approximation of $s$-channel helicity conservation for the $I_t=0\mathrm{}$ amplitude above 5 GeV/c is justified from polarization data. The partial-wave and impact-parameter decompositions of the FESR Regge results are presented.