Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1998-08-17
JHEP 9901 (1999) 012
Physics
High Energy Physics
High Energy Physics - Lattice
44 pages, Latex, uses epsfig.sty, 2 postscript figures
Scientific paper
10.1088/1126-6708/1999/01/012
We derive the generating functional of $|\Delta S| =1, 2$ hadronic weak interactions at one loop for a generic number of flavours and its counterpart in the quenched approximation. A systematic analysis of the ultraviolet divergences in the full theory (with and without a singlet dynamical field) and in the quenched case is performed. We show that the quenched chiral logarithms in the presence of weak interactions amount to a redefinition of the weak mass term in the $\Delta S=\pm 1$ weak effective Lagrangian at leading order. Finally, we apply the results to $B_K$ and $K\to\pi\pi$ matrix elements with $\Delta I=1/2,3/2$ to analyze the modifications induced by quenching on the coefficients of chiral logarithms in the one-loop corrections.
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