Anomalous decays of η′ and η into four pions

¹ Institut für Kernphysik (Theorie), Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany
² Institute for Advanced Simulation, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany
³ Jülich Center for Hadron Physics, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany

^a e-mail: a.wirzba@fz-juelich.de

Abstract

We report about the calculation of the branching ratios of the yet unmeasured η′ decays into four pions, based on a combination of chiral perturbation theory and vector-meson dominance [1]. The decays η′ → 2(π⁺π⁻) and η′ → π⁺π⁻2π⁰ are P-wave dominated and can largely be thought to proceed via two ρ resonances. Branching fractions of (1.0 ± 0.3) × 10⁻⁴ and (2.4 ± 0.7) × 10⁻⁴, respectively, are calculated which are not much lower than the current experimental upper limits. The decays η′ → 4π⁰ and η → 4π⁰, in contrast, are D-wave driven [2] as long as conservation of CP symmetry is assumed, and are significantly further suppressed. Any experimental evidence for the decay η → 4π⁰ could almost certainly be interpreted as a signal of CP violation. The CP-violating amplitudes for η′, η → 4π⁰, induced by the QCD θ-term, are given as well.