Connection between the Wigner Inequalities and Analyticity and Unitarity

Abstract

A lower bound on the momentum derivative of the phase shifts, $\frac{d{\ensuremath{\delta}}_{l}}{\mathrm{dk}}$, is derived from the combination of unitarity, crossing, and analyticity (in the domain resulting from axiomatic field theory). As an application, a lower bound for the ${\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ scattering length is deduced.