Form factors of the isovector scalar current and the $\eta\pi$ scattering phase shifts

Understand

A model for S-wave $\eta\pi$ scattering is proposed which could be realistic in an energy range from threshold up to above one GeV, where inelasticity is dominated by the $K\bar{K}$ channel.

• The $T$-matrix, satisfying two-channel unitarity, is given in a form which matches the chiral expansion results at order $p^4$ exactly for the $\eta\pi\to\eta\pi$, $\eta\pi\to K\bar{K}$ amplitudes and approximately for $K\bar{K}\to K\bar{K}$.
• It contains six phenomenological parameters.
• Asymptotic conditions are imposed which ensure a minimal solution of the Muskhelishvili-Omn\`es problem, thus allowing to compute the $\eta\pi$ and $K\bar{K}$ form factor matrix elements of the $I=1$ scalar current from the $T$-matrix.