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

We investigate the pion scalar form factor in the Meiman-Okubo framework, implementing the phase below the inelastic KK¯ threshold, where it is known from the ππ scalar isoscalar phase shift δ00 by Watson theorem. State-of-the-art knowledge of the perturbative QCD expansion of the scalar correlator and the phase shift δ00 is used as input. No assumptions about the phase above the inelastic threshold or the possible zeros of the form factor in the complex plane are necessary. We obtain a model-independent constraint relating the sum of the light quark masses to the slope and the curvature of the pion scalar form factor at the origin. The recent lattice results for the light quark masses and the pion scalar radius are found to satisfy this constraint. We obtain also a strong correlation between the pion scalar radius and the curvature of the form factor, with rather high values predicted for the curvature.