# Updated limits on the CP violating $\eta\pi\pi$ and $\eta'\pi\pi$ couplings derived from the neutron EDM

## TL;DR

This paper refines the upper limits on CP violating eta-pi-pi couplings and the neutron EDM using a phenomenological hadronic model, including nonminimal photon couplings, providing constraints relevant for upcoming experiments.

## Contribution

It extends previous analyses by incorporating nonminimal photon couplings into the model, leading to more accurate upper limits on CP violating couplings and the theta parameter.

## Key findings

- Upper limits on eta-pi-pi couplings: |f_eta pi pi|<4.4e-11 and |f_eta' pi pi|<3.8e-11.
- Derived upper limit on the CP violating theta parameter: <4.7e-10.
- Results are relevant for planned experiments at JLab Eta Factory.

## Abstract

We complete our derivation of upper limits on the CP violating $\eta\pi\pi$ and $\eta'\pi\pi$ couplings from an analysis of their two-loop contributions to the neutron electric dipole moment (nEDM). We use a phenomenological Lagrangian approach which is formulated in terms of hadronic degrees of freedom - nucleons and pseudoscalar mesons. The essential part of the Lagrangian contains the CP violating couplings between $\eta(\eta')$ and pions. Previously, we included photons using minimal substitution in case of the proton and charged pions. Now we extend our Lagrangian by adding the nonminimal couplings, i.e. anomalous magnetic couplings of nucleons with the photon. The obtained numerical upper limits for the $\eta\pi\pi$ and $\eta'\pi\pi$ couplings $|f_{\eta\pi\pi}(M_\eta^2)|<4.4 \times10^{-11}$ and $|f_{\eta^\prime\pi\pi}(M_{\eta'}^2)|<3.8 \times10^{-11}$ can be useful for the related, planned experiments at the JLab Eta Factory. Using present experimental limits on the nEDM, we derive upper limits on the CP violating $\bar\theta$ parameter of $\bar{\mathrm{\theta}}<4.7 \times 10^{-10}$.