Physical-Region Constraints on Low-Energy Partial-Wave Amplitudes

On the basis of analyticity, crossing, and positivity of the imaginary parts of the partial-wave amplitudes, we derive inequalities on integrals involving the low partial waves of elastic ${\pi }^0{\pi }^0$ scattering in the physical region. The integrals are sensitive only to the low-energy region, and can therefore be tested once a phase-shift analysis is given. The relations can be used to discriminate between various proposed ${\pi }^0{\pi }^0$ phase shifts.