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.

arXiv comment7 pages, 6 figures. Formalism revised, new figures, new references

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Cited by in corpus (21)

• Amplitude analysis of the ${\chi }_{c1}\to \eta {\pi }^{+}{\pi }^{-}$ decays
• Theoretical interpretation of the $D_s^{+}\to {\pi }^{+}{\pi }^0\eta$ decay and the nature of $a_0(980)$
• Role of scalar $a_0(980)$ in the single Cabibbo Suppressed process $D^{+}\to {\pi }^{+}{\pi }^0\eta$
• Can the nature of $a_0(980)$ be tested in the $D_s^{+}\to {\pi }^{+}{\pi }^0\eta$ decay?
• Abnormal isospin violation and $a_0-f_0$ mixing in the $D_s^{+}\to {\pi }^{+}{\pi }^0{a}_0(980)(f_0(980))$ reactions
• Theoretical study of the $D^0\to K^{-}{\pi }^{+}\eta$ reaction
• Repercussion of the $a_0(1710)$ [$a_0(1817)$] resonance and future developments
• The $a_0(980)$ in the single Cabibbo-suppressed process ${\Lambda }_c\to {\pi }^0\eta p$
• Combined theoretical study of the $D^{+}\to {\pi }^{+}\eta \eta$ and $D^{+}\to {\pi }^{+}{\pi }^0\eta$ reactions
• 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
• The ${\chi }_{cJ}$ decay to $\varphi K^{\ast }\bar{K},\varphi h_1(1380)$ testing the nature of axial vector meson resonances
• 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
• $J/\psi \to \gamma \pi \pi$, $\gamma {\pi }^0\eta$ reactions and the $f_0(980)$ and $a_0(980)$ resonances
• 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 $D_s^{+}\to {\pi }^{+}{\pi }^0{\pi }^0$
• Roles of $a_0(980)$ and $a_0(1710)$ in Cabibbo-suppressed process $D^{+}\to {\pi }^0{\pi }^{+}\eta$
• Role of $a_0(1710)$ in the $J/\psi \to {\rho }^{+}{\rho }^{-}\omega$ and $J/\psi \to \gamma {\rho }^0\omega$ reactions