Manifestations of the $a_0^0(980)-f_0(980)$ mixing in $D^0\to K_S^0{\pi }^{+}{\pi }^{-}$ and $D^0\to K_S^0\eta {\pi }^0$ decays

Abstract

Possible manifestations of the isospin-breaking mixing of the $a_0^0(980)$ and $f_0(980)$ resonances are analyzed in the $D^0\to K_S^0{\pi }^{+}{\pi }^{-}$ and $D^0\to K_S^0\eta {\pi }^0$ decays. It is shown that the $a_0^0(980)-f_0(980)$ mixing has the most influence on the ${\pi }^{+}{\pi }^{-}$ mass spectrum in the decay $D^0\to K_S^0{\pi }^{+}{\pi }^{-}$. Owing to the $a_0^0(980)-f_0(980)$ mixing, the $f_0(980)$ peak in $D^0\to K_S^0{f}_0(980)\to K_S^0{\pi }^{+}{\pi }^{-}$ can experience distortions comparable with its size. The effect essentially depends on the relative phase between the amplitudes of the $D^0\to K_S^0{f}_0(980)$ and $D^0\to K_S^0{a}_0^0(980)$ transitions.

7 pages, 2 figures; v2: replaced with the published version; typos corrected, clarifications and reference added

References in corpus (2)

• Measurement of $D^0$-$\overline{D}{}^0$ Mixing and Search for Indirect $CP$ Violation Using $D^0\to K_S^0{\pi }^{+}{\pi }^{-}$ Decays
• Mechanisms of the isospin-breaking decay $f_1(1285)\to f_0(980){\pi }^0\to {\pi }^{+}{\pi }^{-}{\pi }^0$

Cited by in corpus (7)

• Strong isospin symmetry breaking in light scalar meson production
• $a_0(980)-f_0(980)$ 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 $a_0(1450)\to a_0^0(980)f_0(500)\to {\pi }^{+}{\pi }^{-}{f}_0(500)$
• Direct CP violation in multi-body $B$ decays with the $a_0^0(980)$--$f_0(980)$ mixing
• The impact of $a_0^0(980)-f_0(980)$ mixing on the localized $CP$ violations of the $B^{-}\to K^{-}{\pi }^{+}{\pi }^{-}$ decay