Abstract
We provide model-independent bounds on the rates of rare decays $\eta (\eta^\prime) \to \pi\pi$ based on experimental limits on the neutron electric dipole moment (nEDM). Starting from phenomenological $\eta(\eta^\prime) \pi\pi$ couplings, the nEDM arises at two loop level. The leading-order relativistic ChPT calculation with the minimal photon coupling to charged pions and a proton inside the loops leads to a finite, counter term-free result. This is an improvement upon previous estimates which used approximations in evaluating the two loop contribution and were plagued by divergences. While constraints on the $\eta(\eta^\prime) \pi\pi$ couplings in our phenomenological approach are somewhat milder than in the picture with the QCD $\theta$-term, our calculation means that whatever the origin of these couplings, The decays $\eta (\eta') \to 2 \pi$ will remain unobservable in the near future.
Highlights
The observed matter-antimatter asymmetry in the Universe indicates that at some early stage in the evolution of the Universe the CP symmetry, an exact balance of the rates for processes that involve particles and antiparticles, should have been broken [1]
III, we present the calculation of the neutron electric dipole moment (nEDM) at two loops with the leading-order chiral perturbation theory (ChPT) meson-nucleon interaction
Upon evaluating the two-loop diagrams we obtain an expression for the nEDM induced by the CPV ηðη0Þππ couplings via meson loops and minimal coupling to the electromagnetic field, dEn gηNN mη m2N
Summary
The observed matter-antimatter asymmetry in the Universe indicates that at some early stage in the evolution of the Universe the CP symmetry, an exact balance of the rates for processes that involve particles and antiparticles, should have been broken [1]. Given the experimental constraints on the nEDM it is informative to ask how large a CPV ηð0Þππ interaction generated by an unspecified new physics mechanism could be We are able to derive very robust constraints on the CPV ηð0Þ → ππ decay branching ratios from the tight experimental bounds on the nEDM, Brðη → πþπ−Þ < 5.3 × 10−17; Brðη → π0π0Þ < 2.7 × 10−17; Brðη0 → πþπ−Þ < 5.0 × 10−19; Brðη0 → π0π0Þ < 2.5 × 10−19: ð4Þ It makes the observation of these decay channels hardly possible, independent of the particular mechanism that may lead to the generation of such an interaction. IV, we derive the upper bounds for the η → 2π and η0 → 2π decay rates
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