Compatibility between current algebra and unitarity constraints in a low-energy πK model

Abstract

An attempt is made to describe the πK scattering amplitude, on and off mass-shell, in the low-energy region, using the requirements of analyticity and unitarity.A three variables crossing symmetric expansion at third order is considered, allowing for the unitarity cuts and allowing one particles to go off its mass-shell. Threshold unitarity is required on-shell and off-shell for one pion or one kaon extrapolated between its physical mass and the Adler's point, thus fixing all the parameters of our model in terms of the two S-wave scattering lengths a O 1 2 and a O 3 2 . Then elastic unitarity is enforced on-shell by a minimization procedure, giving the domains of best unitarity in the (a O 1 2 , a O 3 2 ) plane. Finally some current algebra constraints or a dynamical input provided by the existence of the K ∗ are used to restrict those domains. In the π-extrapolation approach, selected solutions are in agreement with the Adler's condition, give a reasonable value of the π-decay constant f π and satisfy conveniently unitarity and positivity. Moreover their scattering lengths are close to the current algebra results. The predicted phase shifts agree well with the experimental data. Conclusions from the K-extrapolation study, though less accurate are in agreement with the pion extrapolation ones.