Scalar radius of the pion and zeros in the form factor

The quadratic pion scalar radius, 〈r2〉sπ, plays an important role for present precise determinations of ππ scattering. Recently, Ynduráin, using an Omnès representation of the null isospin (I) non-strange pion scalar form factor, obtains 〈r2〉sπ=0.75±0.07fm2. This value is larger than the one calculated by solving the corresponding Muskhelishvili-Omnès equations, 〈r2〉sπ=0.61±0.04fm2. A large discrepancy between both values, given the precision, then results. We follow Ynduráin's method and show that by requiring continuity of the resulting pion scalar form factor under tiny changes in the input ππ phase shifts, the form factor obtained has a zero for some S-wave I=0T-matrices. Once this is accounted for, the resulting value is 〈r2〉sπ=0.63±0.05fm2. The main source of error in our determination is present experimental uncertainties in low energy S-wave I=0ππ phase shifts. Another important contribution to our error is the not yet settled asymptotic behaviour of the phase of the scalar form factor from QCD.