Abstract
The radially excited pseudoscalar state $\eta(1295)$ is still poorly understood [as well as its $SU(3)$ partners $\pi(1300)$ and $K(1460 )$] and we want to attract attention experimenters to its comprehensive study. As for the main three-body decay $\eta(1295)\to \eta\pi\pi$, here the main interest is the measurements of the shapes of the $\eta\pi $ and $\pi\pi$ mass spectra in which the contributions from the $a_0(980)$ resonance and the large $\pi\pi$ $S$ wave ($\sigma$) should manifest themselves. To describe these mass spectra, we propose to use a simple isobar model with a single fitting parameter characterizing the relative intensity of the $a_0 (980)$ and $\sigma$ state production. Our main goal is to discuss the dynamics of the isospin-breaking decays $\eta(1295)\to\pi^+ \pi^-\pi^0$ and $\eta(1295)\to3\pi^0$, whose experimental studies could continue the impressive story of isospin violations in the decays of light isoscalar mesons $\omega\to2\pi$, $\eta\to3 \pi$, $\eta'\to3\pi$, $\eta(1405)\to3\pi$, and $f_1(1285)\to3\pi$. We estimate the widths of the isospin-breaking decays $\eta(1295)\to 3\pi$ produced via the mixing of the $\pi^0-\eta$ and $a^0_0(980) -f_0(980)$ states and also due to the $\pi^0(1300)-\eta(1295)$ mixing. Processes that have the potential for detecting $\eta(1295) \to3\pi$ decays are discussed.
Highlights
Note that when estimating the widths of the direct decays ηð1295Þ → 3π caused by π0 − η and a00ð980Þ − f0ð980Þ mixing, we did not take into account the rescattering effects of pions in the final state
Studies of radial excitations of light pseudoscalar mesons are of physical interest
In the series of pseudoscalar isoscalar mesons η, η0, ηð1295Þ, and ηð1405Þ [1] the ηð1295Þ remained the last one that has not yet presented unexpected surprises associated with the violation of isotopic invariance in its decays into π0πþπ− and 3π0
Summary
Mechanisms of the isospin-breaking decays of light mesons are highly diverse. For instance, the decay of ω → πþπ− [1] occurs mainly due to the ρ0 − ω mixing [2,3]. III we use the above model for ηð1295Þ → ηππ to estimate the widths of the direct decays ηð1295Þ → 3π caused by the π0 − η and a00ð980Þ − f0ð980Þ mixing These sources of the isospin breaking lead to very different shapes of the twopion mass spectra. Note that when estimating the widths of the direct decays ηð1295Þ → 3π caused by π0 − η and a00ð980Þ − f0ð980Þ mixing, we did not take into account the rescattering effects of pions in the final state Such approach utilizing a minimum number of free parameters presents a quite reasonable guide for the primary treatment of future data.
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