Form factors of the isovector scalar current and the ... formula ... scattering phase shifts

摘要

A model for S-wave ηπ scattering is proposed which could be realistic in an energy range from threshold up to above 1 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 one 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, id="IEq19">ϕ → ηπγ, or the id="IEq20">ηπ initial-state interaction in id="IEq21">η → 3π.