Updated limits on the CP violating $\eta \pi \pi$ and ${\eta }^{\prime }\pi \pi$ couplings derived from the neutron EDM

Abstract

We complete our derivation of upper limits on the CP violating $\eta \pi \pi$ and ${\eta }^{\prime }\pi \pi$ 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 $\eta ({\eta }^{\prime })$ 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 ${\eta }^{\prime }\pi \pi$ couplings $|f_{\eta \pi \pi }(M_{\eta }^2)|<4.4\times 10^{-11}$ and $|f_{{\eta }^{\prime }\pi \pi }(M_{{\eta }^{\prime }}^2)|<3.8\times 10^{-11}$ 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 $\bar{\theta }<4.7\times 10^{-10}$.

arXiv comment6 pages, 2 figures

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• Patterns of $C$- and $CP$-violation in hadronic $\eta$ and ${\eta }^{\prime }$ three-body decays
• Deuteron EDM induced by CP violating couplings of pseudoscalar mesons
• Static electric dipole moment of the francium atom induced by axionlike particle exchange
• Dark SU(2) Stueckelberg portal