Form factors of the isovector scalar current and the ηπ scattering phase shifts

الأصل · EN

A model for S-wave ηπ scattering is proposed which could be realistic in an energy range from threshold up to above one GeV, where inelasticity is dominated by the KK channel. The T-matrix, satisfying two-channel unitarity, is given in a form which matches the chiral expansion results at order p⁴ exactly for the ηπ→ηπ, ηπ→ KK amplitudes and approximately for KK→ KK. It contains six phenomenological parameters. Asymptotic conditions are imposed which ensure a minimal solution of the Muskhelishvili-Omnès problem, thus allowing to compute the ηπ and KK form factor matrix elements of the I=1 scalar current from the T-matrix. The phenomenological parameters are determined such as to reproduce the experimental properties of the a₀(980), a₀(1450) resonances, as well as the chiral results of the ηπ and KK scalar radii which are predicted to be remarkably small at O(p⁴). This T-matrix model could be used for a unified treatment of the ηπ final-state interaction problem in processes such as η'→ ηππ, ϕ→ηπγ, or the ηπ initial-state interaction in η→3π.