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

## TL;DR

This paper investigates non-derivative CP-odd axion-nucleon couplings using effective field theory, Skyrme model, and holographic QCD, providing model-independent expressions and quantitative estimates relevant for phenomenology.

## Contribution

It introduces a comprehensive analysis of axion-nucleon couplings across three theoretical frameworks, deriving model-independent formulas and detailed quantitative estimates.

## Key findings

- Derived expressions for CP-odd axion-nucleon couplings in various models.
- Provided quantitative estimates for these couplings.
- Connected couplings to low-lying mesons and the $ ext{η'}$.

## 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 $\eta'$. 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 $\eta'$ 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.