Form factors of the isovector scalar current and the η π η π scattering phase shifts

A model for S-wave [Formula: see text] scattering is proposed which could be realistic in an energy range from threshold up to above 1 GeV, where inelasticity is dominated by the [Formula: see text] channel. The T-matrix, satisfying two-channel unitarity, is given in a form which matches the chiral expansion results at order [Formula: see text] exactly for the [Formula: see text], [Formula: see text] amplitudes and approximately for [Formula: see text]. It contains six phenomenological parameters. Asymptotic conditions are imposed which ensure a minimal solution of the Muskhelishvili-Omnès problem, thus allowing one to compute the [Formula: see text] and [Formula: see text] form factor matrix elements of the [Formula: see text] scalar current from the T-matrix. The phenomenological parameters are determined such as to reproduce the experimental properties of the [Formula: see text], [Formula: see text] resonances, as well as the chiral results of the [Formula: see text] and [Formula: see text] scalar radii, which are predicted to be remarkably small at [Formula: see text]. This T-matrix model could be used for a unified treatment of the [Formula: see text] final-state interaction problem in processes such as [Formula: see text], [Formula: see text], or the [Formula: see text] initial-state interaction in [Formula: see text].