Interference phenomena in the decay $D_s^{+}\to \eta {\pi }^0{\pi }^{+}$ induced by the $a_0^0(980)-f_0(980)$ mixing

Abstract

Using the data on the decay $D_s^{+}\to f_0(980){\pi }^{+}\to K^{+}{K}^{-}{\pi }^{+}$, we estimate the amplitude of the process $D_s^{+}\to \left[f_0(980)\to (K^{+}{K}^{-}+K^0{\bar{K}}^0)\to a_0^0(980)\right]{\pi }^{+}\to \eta {\pi }^0{\pi }^{+}$, caused by the mixing of $a_0^0(980)$ and $f_0(980)$ resonances that breaks the isotopic invariance due to the $K^{+}$ and $K^0$ meson mass difference. Effects of the interference of this amplitude with the amplitudes of the main mechanisms responsible for the decay $D_s^{+}\to \eta {\pi }^0{\pi }^{+}$ are analyzed. As such mechanisms, we examine the transition $D_s^{+}\to \eta {\rho }^{+}\to \eta {\pi }^0{\pi }^{+}$, which is observed in experiment, and the possible transition $D_s^{+}\to \left(a_0^0(980){\pi }^{+}+a_0^{+}(980){\pi }^0\right)\to \eta {\pi }^0{\pi }^{+}$. It is shown that the rapidly varying phase of the $a_0^0(980)-f_0(980)$ transition amplitude strongly influences on the interference curves.

7 pages, 7 figures; v2, replaced with the published version; typos corrected, clarifications and reference added

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Cited by in corpus (9)

• Resonant $a_0(980)$ state in triangle rescattering $D_s^{+}\to {\pi }^{+}{\pi }^0\eta$ decays
• Theoretical study of the process $D_s^{+}\to {\pi }^{+}{K}_S^0{K}_S^0$ and the isovector partner of $f_0(1710)$
• Strong isospin symmetry breaking in light scalar meson production
• Study of the Decay $D_s^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}\eta$ and Observation of the W-annihilation Decay $D_s^{+}\to a_0(980{)}^{+}{\rho }^0$
• Observation of $D^{+}\to K_S^0{a}_0(980{)}^{+}$ in the amplitude analysis of $D^{+}\to K_S^0{\pi }^{+}\eta$
• $a_0(980)-f_0(980)$ mixing in ${\chi }_{c1}\to {\pi }^0{f}_0(980)\to {\pi }^0{\pi }^{+}{\pi }^{-}$ and ${\chi }_{c1}\to {\pi }^0{a}_0(980)\to {\pi }^0{\pi }^0\eta$
• Study of the isospin breaking decay $\mathbf{Y}(2175)\to \mathbf{\varphi }{\mathbf{f}}_0(980)\to \mathbf{\varphi \eta }{\mathbf{\pi }}^0$ at BESIII
• Observation of the isospin breaking decay ${\rm Y}(10860)\to {\rm Y}(1S)f_0(980)\to {\rm Y}(1S)\eta {\pi }^0$ with the Belle II detector
• Study of $a_0^0(980)$-$f_0(980)$ mixing from $a_0(1450)\to a_0^0(980)f_0(500)\to {\pi }^{+}{\pi }^{-}{f}_0(500)$