Pion-Pion and Pion-Kaon Scattering

An easier derivation of Chew-Mandelstam's effective-range formula for pion-pion scattering is given using the conventional Feynman method with the interaction Hamiltonian $H_1=4\mathrm{}\pi \lambda {\phi }^4$ in an approximation where only the chain diagrams are included. Furthermore, we have calculated a correction term to this formula due to the cross-diagram, both for $S$ waves as well as for $P$ waves. The method has been applied to pion-kaon scattering.