Abstract
We report about the calculation of the branching ratios of the yet unmeasured eta' decays into four pions, based on a combination of chiral perturbation theory and vector-meson dominance [1]. The decays eta' -> 2(pi^+pi^-) and eta' -> pi^+pi^-2pi^0 are P-wave dominated and can largely be thought to proceed via two rho resonances. Branching fractions of (1.0 +- 0.3) x 10^-4 and (2.4 +- 0.7) x 10^-4, respectively, are calculated which are not much lower than the current experimental upper limits. The decays eta' -> 4pi^0 and eta -> 4pi^0, 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 eta -> 4pi^0 could almost certainly be interpreted as a signal of CP violation. The CP-violating amplitudes for eta', eta -> 4pi^0, induced by the QCD theta-term, are given as well.
Highlights
The following report about the four-pion decays of the η and η′ mesons is based on a joint project with Feng-Kun Guo and Bastian Kubis (Bonn University) [1] which was initiated by Andrzej Kupsc [2]
We have found only one previous calculation, performed in the framework of a quark model [4], whose partial width predictions, have in the meantime been ruled out by the experimental upper limit of the channel η′ → 2(π+π−) [3, 5]
The leading contributions to the η′ decay amplitudes with charged pions in the final state, where CP symmetry forbids the pions to be in relative S-waves, are of O(p6) according to chiral power-counting rules
Summary
The following report about the four-pion decays of the η and η′ mesons is based on a joint project with Feng-Kun Guo and Bastian Kubis (Bonn University) [1] which was initiated by Andrzej Kupsc [2].Very little is known about the four-pion decays of the η and η′. 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].
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