Alejandro Celis On SU(2) Chiral Perturbation Theory for K -> pi pi Decay Amplitudes Abstract We study the CP conserving decays $K \rightarrow \pi \pi$ using $SU(2)_L \times SU(2)_R$ Chiral Perturbation Theory (SU(2) ChPT) at next-to-leading order. The external pions in $K \rightarrow \pi \pi$ are hard, thus complicating the power counting of the theory. However we provide arguments about the possibility of calculating the pion chiral logarithms, i.e. the corrections of $O(M^2 \mathrm{log}(M^2))$, for the nonleptonic decay $K \rightarrow \pi \pi$. A comparison with SU(3) ChPT is done to check our results. LU TP 09-12