  The Effective Field Theory (EFT) Lagrangian for a generic axion-like particle
(ALP) has many free parameters, and leaves quite some freedom for the expected
phenomenology. In this work, we set up more constrained EFTs by enforcing true
axion-like properties for the ALP. Indeed, though the Peccei-Quinn symmetry of
the QCD axion is anomalous, it is so in specific ways, and this shows up as
consistency conditions between the gauge boson and fermion couplings. We
propose to enforce such conditions, as inspired from the DFSZ and KSVZ
scenarios, on the generic ALP EFTs. These truly axion-like ALP EFTs are then
particularly well-suited as benchmark scenarios, to be used in the search for
ALPs both at colliders and at low-energy experiments.
