Combined theoretical study of the $D^{+}\to {\pi }^{+}\eta \eta$ and $D^{+}\to {\pi }^{+}{\pi }^0\eta$ reactions

Abstract

We study the $D^{+}\to {\pi }^{+}\eta \eta$ and $D^{+}\to {\pi }^{+}{\pi }^0\eta$ reactions, which are single Cabibbo suppressed and can proceed both through internal and external emission. The primary mechanisms at quark level are considered, followed by hadronization to produce three mesons in the $D^{+}$ decay, and after that the final state interaction of these mesons leads to the production of the $a_0(980)$ resonance, seen in the ${\pi }^{+}\eta$, ${\pi }^0\eta$ mass distributions. The theory has three unknown parameters to determine the shape of the distributions and the ratio between the $D^{+}\to {\pi }^{+}\eta \eta$ and $D^{+}\to {\pi }^{+}{\pi }^0\eta$ rates. This ratio restricts much the sets of parameters but there is still much freedom leading to different shapes in the mass distributions. We call for a measurement of these mass distributions that will settle the reaction mechanism, while at the same time provide relevant information on the way that the $a_0(980)$ resonance is produced in the reactions.

11 pages, 12 figures

References in corpus (9)

• The low lying scalar resonances in the $D^0$ decays into $K_s^0$ and $f_0(500)$, $f_0(980)$, $a_0(980)$
• Role of scalar $a_0(980)$ in the single Cabibbo Suppressed process $D^{+}\to {\pi }^{+}{\pi }^0\eta$
• Predictions for ${\eta }_c\to \eta {\pi }^{+}{\pi }^{-}$ producing $f_0(500)$, $f_0(980)$ and $a_0(980)$
• The scalar $f_0(500)$ and $f_0(980)$ resonances and vector mesons in the single Cabibbo-suppressed decays ${\Lambda }_c\to p{K}^{+}{K}^{-}$ and $p{\pi }^{+}{\pi }^{-}$
• Theoretical study of the $D^0\to K^{-}{\pi }^{+}\eta$ reaction
• Isospin analysis of D0 decay to three pions
• Scalar resonances in the $D^{+}\to K^{-}{K}^{+}{K}^{+}$ decay
• Signatures of the two $K_1(1270)$ poles in $D^{+}\to \nu e^{+}VP$ decay
• Further study of $D_s^{+}$ decays into ${\pi }^{-}{\pi }^{+}{\pi }^{+}$

Cited by in corpus (4)

• Hadronic decay $D^{+}\to {\pi }^{+}\eta \eta$ and the $a_0(980)$ and $f_0(1370)$ contributions
• The $D_s^{+}\to K^{+}{\pi }^{+}{\pi }^{-}$ reaction and the scalar $f_0(500)$, $f_0(980)$ and $K_0^{\ast }(700)$ resonances
• 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 $D^{+}\to {\pi }^0{\pi }^{+}\eta$