Non-derivative Axionic Couplings to Nucleons at large and small N

Abstract

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 ${\eta }^{\prime }$. 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 $N_c$ and flavors $N_f$. Then, we compute the CP-odd couplings to nucleons of the axion, the ${\eta }^{\prime }$ and the pseudo-Goldstone mesons in both the Skyrme and the holographic QCD model with $N_f=2,3$. 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.

Comments: v1: 45 pages + appendices, 1 figure; v2: typos corrected, references added; v3: 38 pages + appendices, 1 figure, section 4 added containing model-independent IR relations for the couplings, sections 3,5,6 re-edited, table 1 added and discussion section improved, review material moved to the appendices, comments and references added, typos corrected