Non-derivative axionic couplings to nucleons at large and small N

Among the possible CP-odd couplings of the axion to ordinary matter, the most relevant ones for phenomenology are the Yukawa couplings to nucleons. We analyze such non-derivative couplings within three different approaches: standard effective field theory, the Skyrme model and holographic QCD. In all the cases, the couplings can be related to the CP-odd non-derivative couplings to nucleons of the low-lying mesons and the η′. Using the effective field theory approach we discuss how to derive the expressions for the CP-odd interaction terms as functions of the parameters of the effective Lagrangian at generic number of colors Nc and flavors Nf. Then, we compute the CP-odd couplings to nucleons of the axion, the η′ and the pseudo-Goldstone mesons in both the Skyrme and the holographic QCD model with Nf = 2, 3. We present model-independent expressions for the coefficients of the non-derivative axion-nucleon couplings. This allows us to provide quantitative estimates of these couplings.