The generating functional for hadronic weak interactions and its quenched approximation

Abstract

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.

44 pages, Latex, uses epsfig.sty, 2 postscript figures

References in corpus (1)

• $K^{+}\to {\pi }^{+}{\pi }^0$ Decay Amplitude with the Wilson Quark Action in Quenched Lattice QCD

Cited by in corpus (15)

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• Final State Interactions in Kaon Decays
• Effects of Quenching and Partial Quenching on Penguin Matrix Elements
• K^+ -> pi^+ pi^0 Decays on Finite Volumes and at Next-to-Leading Order in the Chiral Expansion
• Correlators of left charges and weak operators in finite volume chiral perturbation theory
• On the Determination of Nonleptonic Kaon Decays from $K\to \pi$ Matrix Elements
• On $K\to \pi \pi$ Decays in Quenched and Unquenched Chiral Perturbation Theory
• Probing the chiral weak Hamiltonian at finite volumes
• Charm mass dependence of the weak Hamiltonian in chiral perturbation theory
• Final State Interactions and eps'/eps
• Theoretical status of epsilon'/epsilon
• The quenched generating functional for hadronic weak interactions
• Chiral loop corrections and isospin violation effects in epsilon'/epsilon