Determine the asymptotic isospin-zero pion-to-kaon scattering phase

Determine experimentally the asymptotic value of the isospin-zero S-wave phase shift for the inelastic scattering process \(\pi\pi\to KK\), \(\psi^0_0(+\infty)\), which is required to fix the large-energy behavior of the two-channel Muskhelishvili–Omnès determinant and associated form factors.

Background

The two-channel dispersive treatment uses the phase shift $\psi^0_0(s)$ for isospin-zero $\pi\pi\to KK$ scattering to construct the determinant of the Muskhelishvili–Omnès matrix. Its asymptotic value controls the power-law damping of that determinant and constrains the asymptotic behavior of the individual pion- and kaon-pair form factors.

Experimental information reaches only approximately 2 GeV, where the phase is estimated to lie between $250^\circ$ and $290^\circ$. The analysis therefore extrapolates it to $360^\circ$, while noting that alternative asymptotic values would modify the damping and could jeopardize the expected asymptotic behavior. Establishing the asymptotic phase experimentally would reduce this dispersive uncertainty.