Predictions for ${\eta }_c\to \eta {\pi }^{+}{\pi }^{-}$ producing $f_0(500)$, $f_0(980)$ and $a_0(980)$

Abstract

We perform calculations for the ${\eta }_c\to \eta {\pi }^{+}{\pi }^{-}$ decay using elements of SU(3) symmetry to see the weight of different trios of pseudoscalars produced in this decay, prior to the final state interaction of the mesons. After that, the interaction of pairs of mesons, leading finally to $\eta {\pi }^{+}{\pi }^{-}$, is done using the chiral unitary approach. We evaluate the ${\pi }^{+}{\pi }^{-}$ and $\pi \eta$ mass distributions and find large and clear signals for $f_0(500)$, $f_0(980)$ and $a_0(980)$ excitation. The reaction is similar to the ${\chi }_{c1}\to \eta {\pi }^{+}{\pi }^{-}$, which has been recently measured at BESIII and its implementation and comparison with these predictions will be very valuable to shed light on the nature of the low mass scalar mesons.

7 pages, 6 figures. Formalism revised, new figures, new references

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• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
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• $B^0$ and $B_s^0$ decays into $J/\psi$ $f_0(980)$ and $J/\psi$ $f_0(500)$ and the nature of the scalar resonances
• The low lying scalar resonances in the $D^0$ decays into $K_s^0$ and $f_0(500)$, $f_0(980)$, $a_0(980)$
• $f_0(500)$, $f_0(980)$ and $a_0(980)$ production in the ${\chi }_{c1}\to \eta {\pi }^{+}{\pi }^{-}$ reaction

Cited by in corpus (13)

• Amplitude analysis of the ${\chi }_{c1}\to \eta {\pi }^{+}{\pi }^{-}$ decays
• Abnormal isospin violation and $a_0-f_0$ mixing in the $D_s^{+}\to {\pi }^{+}{\pi }^0{a}_0(980)(f_0(980))$ reactions
• Repercussion of the $a_0(1710)$ [$a_0(1817)$] resonance and future developments
• Exploring kaon induced reactions for unraveling the nature of the scalar meson $a_0(1817)$
• Theoretical description of the $\mathbf{J}/\mathbf{\psi }\to \mathbf{\eta }({\mathbf{\eta }}^{\prime }){\mathbf{h}}_1(1380)$, $\mathbf{J}/\mathbf{\psi }\to \mathbf{\eta }({\mathbf{\eta }}^{\prime }){\mathbf{h}}_1(1170)$ and $\mathbf{J}/\mathbf{\psi }\to {\mathbf{\pi }}^0{\mathbf{b}}_1(1235{)}^0$ reactions
• Unveiling the $a_0(1710)$ nature in the process $J/\psi \to {\bar{K}}^0{K}^{+}{\rho }^{-}$
• $a_0(980)-f_0(980)$ mixing in ${\chi }_{c1}\to {\pi }^0{f}_0(980)\to {\pi }^0{\pi }^{+}{\pi }^{-}$ and ${\chi }_{c1}\to {\pi }^0{a}_0(980)\to {\pi }^0{\pi }^0\eta$
• ${\chi }_{c1}$ decays into a pseudoscalar meson and a vector-vector molecule
• Traces of the new $a_0(1780)$ resonance in the $J/\psi \to \varphi K^{+}{K}^{-}(K^0{\bar{K}}^0)$ reaction
• Roles of the scalar $f_0(500)$ and $f_0(980)$ in the process $D^0\to {\pi }^0{\pi }^0{\bar{K}}^0$
• The theoretical study of $D_s^{+}\to {\pi }^{+}{\pi }^0{\pi }^0$
• Role of $a_0(1710)$ in the $J/\psi \to {\rho }^{+}{\rho }^{-}\omega$ and $J/\psi \to \gamma {\rho }^0\omega$ reactions
• Roles of $a_0(980)$ and $a_0(1710)$ in Cabibbo-suppressed process $D^{+}\to {\pi }^0{\pi }^{+}\eta$