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We investigate the pion scalar form factor in the Meiman-Okubo framework,implementing the phase below the inelastic $K\bar K$ threshold, where it isknown from the $\pi\pi$ scalar isoscalar phase shift $\delta_0^0$ by Watsontheorem. State-of-the-art knowledge of the perturbative QCD expansion of thescalar correlator and the phase shift $\delta_0^0$ is used as input. Noassumptions about the phase above the inelastic threshold or the possible zerosof the form factor in the complex plane are necessary. We obtain amodel-independent constraint relating the sum of the light quark masses to theslope and the curvature of the pion scalar form factor at the origin. Therecent lattice results for the light quark masses and the pion scalar radiusare found to satisfy this constraint. We obtain also a strong correlationbetween the pion scalar radius and the curvature of the form factor, withrather high values predicted for the curvature.

Model-independent constraint on the pion scalar form factor and light quark masses