The quenched generating functional for hadronic weak interactions

Abstract

The ultraviolet behaviour of the generating functional for hadronic weak interactions with $|\Delta S| =1, 2$ is investigated to one loop for a generic number of flavours and in the quenched approximation. New quenched chiral logarithms generated by the weak interactions can be accounted for via a redefinition of the weak mass term in the $\Delta S=\pm 1$ weak effective Lagrangian at leading order. Finally, we illustrate how chiral logarithms are modified by the quenched approximation in $K\to\pi\pi$ matrix elements with $\Delta I=1/2$ and 3/2.