On K ->pi pi decays in quenched and unquenched chiral perturbation theory

We calculate the logarithmic corrections to the matrix elements for K+ --> pi(+) and K --> vacuum (which are used on the lattice to determine K --> pi pi amplitudes), in one-loop quenched and unquenched Chiral Perturbation Th eory. We find that these corrections can be large. We also discuss, and pre sent some results for, the direct determination of K --> pi pi amplitudes. In particular, we address effects from choosing m(s) = m(d) and vanishing e xternal spatial momenta, finite volume and quenching. In the quenched octet case, we find enhanced finite-volume contributions which may make numerica l estimates of this matrix element unreliable for large volumes.