Analysis of the pion-kaon sigma term and related topics

Abstract.

We calculate the one-loop contributions to the difference $\Delta_\pi K$ between the isoscalar on-shell pion-kaon scattering amplitude at the Cheng-Dashen point and the scalar form factor $\Gamma_K (2M_\pi_2)$ in the framework of three flavor chiral perturbation theory. These corrections turn out to be small. This is further sharpened by treating the kaons as heavy fields (two flavor chiral perturbation theory). We also analyze the two-loop corrections to the kaon scalar form factor based on a dispersive technique. We find that these corrections are smaller than in the comparable case of the scalar form factor of the pion. This is related to the weaker final state interactions in the pion-kaon channel.