Leading logs in QCD axion effective field theory

A bstract The axion is much lighter than all other degrees of freedom introduced by the Peccei-Quinn mechanism to solve strong CP problem. It therefore natural use an effective field theory (EFT) describe its interactions. Loop processes calculated in EFT may however explicitly depend on ultraviolet cutoff. In general, UV cutoff not uniquely defined, but dimensionful couplings suggest identify it with symmetry-breaking scale. An example are K + ? ? a decays that will soon be tested improved precision NA62 and KOTO whose amplitude dominated term logarithmically dependent this paper, we critically examine adequacy using such naive approach study loop comparing calculations ones performed complete QCD models. DFSZ models, for example, found set additional Higgs closer electroweak scale fact, there non-trivial requirements models where close scale, result reproduced. This suggests existence suitable embedding impose restrictions EFTs. We provide explicit construction model fermion find promising prospects IAXO.