Unitarity restrictions on meson-nucleon helicity-flip amplitudes and slope of the diffraction peak

Abstract

We generalize the MacDowell-Martin bound on the slope parameter b^A for the spinless case to the case of spin-0-spin-½ elastic scattering with parity conservation. We give the optimal answer for all energies as well as the simpler (slightly weaker) bound b^A≥σ²_tot/36πσ_el[√1+9πσ_el/4k²σ²_tot+1]−1/4k² (k=c.m. momentum). Here the superscript A refers to the absorptive-part contribution. We also obtain unitarity restrictions on the helicity-flip amplitude ƒ^A_+- (t)/√ −t|_t=0 in terms of σ_tot, σ_el, and b^A(s).