Description of the πK system with allowance for baryon and quark loops

The scattering lengths of the πK and ππ systems are calculated in chiral models with quark and baryon loops. A procedure is proposed for the correct inclusion, in accordance with the low-energy theorems of current algebra, of the meson masses in diagrams with baryon and quark loops. It is shown that the single-loop approximation of the quantum chiral theory makes it possible to give a qualitatively correct description of the values of the lowest scattering lengths of the πK system