Scalar radius of the pion and zeros in the form factor

Abstract

The quadratic pion scalar radius, \la r^2\ra^π_s, plays an important role for present precise determinations of ππscattering. Recently, Ynduráin, using an Omnès representation of the null isospin(I) non-strange pion scalar form factor, obtains \la r^2\ra^π_s=0.75\pm 0.07 fm^2. This value is larger than the one calculated by solving the corresponding Muskhelishvili-Omnès equations, \la r^2\ra^π_s=0.61\pm 0.04 fm^2. A large discrepancy between both values, given the precision, then results. We reanalyze Ynduráin's method and show that by imposing continuity of the resulting pion scalar form factor under tiny changes in the input ππphase shifts, a zero in the form factor for some S-wave I=0 T-matrices is then required. Once this is accounted for, the resulting value is \la r^2\ra_s^π=0.65\pm 0.05 fm^2. The main source of error in our determination is present experimental uncertainties in low energy S-wave I=0 ππphase shifts. Another important contribution to our error is the not yet settled asymptotic behaviour of the phase of the scalar form factor from QCD.