Revisiting K → πa decays

The theoretical calculation for pseudo-scalars hadronic decays K → πa is reviewed. While one-loop penguin contributions are usually considered, tree-level processes have most often been overlooked in literature. Following the Lepage-Brodsky approach the tree-level contribution to the charged and neutral pseudo-scalar decay in ALP is estimated. Assuming generic ALP couplings to SM fermions, the latest NA62/E949 results for the K${}^{+}$ → π${}^{+}$a decay and the present/future KOTO results for the K${}_L^0$ → π${}^0$a decay are used to provide updated bounds on the ALP-fermion Lagrangian sector. Finally, the interplay between the tree-level and one-loop contributions is investigated.