One-loop corrections to ALP couplings

We derive the one-loop contributions to ALP-SM effective couplings, including all finite corrections. The complete leading-order -- dimension five -- effective linear Lagrangian is considered. The ALP is left off-shell, which is of particular impact on LHC and accelerator searches of ALP couplings to $\gamma\gamma$, $ZZ$, $Z\gamma$, $WW$, gluons and fermions. All results are obtained in the covariant $R_\xi$ gauge. A few phenomenological consequences are also explored as illustration, with flavour diagonal channels in the case of fermions: in particular, we explore constraints on the coupling of the ALP to top quarks, that can be extracted from LHC data, from astrophysical sources and from Dark Matter direct detection experiments such as PandaX, LUX and XENON1T.