Effects of quenching and partial quenching on penguin matrix elements

In the calculation of non-leptonic weak decay rates, a "mismatch" arises whenthe QCD evolution of the relevant weak hamiltonian down to hadronic scales isperformed in unquenched QCD, but the hadronic matrix elements are then computedin (partially) quenched lattice QCD. This mismatch arises because thetransformation properties of penguin operators under chiral symmetry change inthe transition from unquenched to (partially) quenched QCD. Here we discussQCD-penguin contributions to $\Delta S=1$ matrix elements, and show that newlow-energy constants contribute at leading order in chiral perturbation theoryin this case. In the partially quenched case (in which sea quarks are present),these low-energy constants are related to electro-magnetic penguins, while inthe quenched case (with no sea quarks) no such relation exists. As a simpleexample, we give explicit results for $K^+\to\pi^+$ and $K^0\to vacuum$ matrixelements, and discuss the implications for lattice determinations of$K\to\pi\pi$ amplitudes from these matrix elements.Comment: 10 pages, minor corrections, ref. added, to appear in JHE