Mechanisms of the isospin-breaking decay $f_1(1285)\to f_0(980){\pi }^0\to {\pi }^{+}{\pi }^{-}{\pi }^0$

Abstract

Estimated are the contributions of the following mechanisms responsible for the decay $f_1(1285)\to f_0(980){\pi }^0\to {\pi }^{+}{\pi }^{-}{\pi }^0$: 1) the contribution of the $a_0^0(980)-f_0(980)$ mixing, $f_1(1285)\to a_0(980){\pi }^0\to (K^{+}{K}^{-}+K^0{\bar{K}}^0){\pi }^0\to f_0(980){\pi }^0\to {\pi }^{+}{\pi }^{-}{\pi }^0$, 2) the contribution of the transition $f_1(1285)\to (K^{+}{K}^{-}+K^0{\bar{K}}^0){\pi }^0\to f_0(980){\pi }^0\to {\pi }^{+}{\pi }^{-}{\pi }^0$, arising due to the pointlike decay $f_1(1285)\to K\bar{K}{\pi }^0$, 3) the contribution of the transition $f_1(1285)\to (K^{\ast }\bar{K}+{\bar{K}}^{\ast }K)\to (K^{+}{K}^{-}+K^0{\bar{K}}^0){\pi }^0\to f_0(980){\pi }^0\to {\pi }^{+}{\pi }^{-}{\pi }^0$, where $K^{\ast }=K^{\ast }(892)$, and 4) the contribution of the transition $f_1(1285)\to (K_0^{\ast }\bar{K}+{\bar{K}}_0^{\ast }K)\to (K^{+}{K}^{-}+K^0{\bar{K}}^0){\pi }^0\to f_0(980)\to {\pi }^{+}{\pi }^{-}{\pi }^0$, where $K_0^{\ast }=K_0^{\ast }(800)$ (or $\kappa$) and $K_0^{\ast }(1430)$. These mechanisms break the conservation of the isospin due to the nonzero mass difference of the $K^{+}$ and $K^0$ mesons. They result in the appearance of the narrow resonance structure in the ${\pi }^{+}{\pi }^{-}$ mass spectrum in the region of the $K\bar{K}$ thresholds, with the width $\approx 2m_{K^0}-2m_{K^{+}}\approx 8$ MeV. The observation of such a structure in experiment is the direct indication on the $K\bar{K}$ loop mechanism of the breaking of the isotopic invariance. We point out that existing data should be more precise, and it is difficult to explain them using the single specific mechanism from those listed above. Taking the decay $f_1(1285)\to f_0(980){\pi }^0\to {\pi }^{+}{\pi }^{-}{\pi }^0$ as the example, we discuss the general approach to the description of the $K\bar{K}$ loop mechanism of the breaking of isotopic invariance.

14 pages, 7 figures; v2: matches published version in PRD

References in corpus (6)

• $f_1(1285)$ decays into $a_0(980){\pi }^0$, $f_0(980){\pi }^0$ and isospin breaking
• Isospin breaking decay $\eta (1405)\to f_0(980){\pi }^0\to 3\pi$
• Possibility of measuring a0(980)-f0(980) mixing from J/psi -> phi a0
• Study a0(980)-f0(980) mixing from a0(980) -> f0(980) transition
• Observation of the isospin-violating decay $J/\psi \to \varphi {\pi }^0{f}_0(980)$
• Search for $f_1(1285)\to {\pi }^{+}{\pi }^{-}{\pi }^0$ decay with VES detector

Cited by in corpus (13)

• Observation of $a_0^0(980)$-$f_0(980)$ Mixing
• Interference phenomena in the decay $D_s^{+}\to \eta {\pi }^0{\pi }^{+}$ induced by the $a_0^0(980)-f_0(980)$ mixing
• Comprehensive study of light axial vector mesons with the presence of triangle singularity
• Strong isospin symmetry breaking in light scalar meson production
• 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
• Isotopic Symmetry Breaking in the $\eta (1405)\to f_0(980){\pi }^0\to {\pi }^{+}{\pi }^{-}{\pi }^0$. Decay through a $K\bar{K}$ Loop Diagram and the Role of Anomalous Landau Thresholds
• $a_0(980)-f_0(980)$ 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
• Proposal to look for the anomalous isotopic symmetry breaking in central diffractive production of the $f_1(1285)$ and $a_0^0(980)$ resonances at the LHC
• Study of $a_0^0(980)$-$f_0(980)$ mixing from $a_0(1450)\to a_0^0(980)f_0(500)\to {\pi }^{+}{\pi }^{-}{f}_0(500)$
• The role of triangle singularity in the decay process $D^0\to {\pi }^{+}{\pi }^{-}{f}_0(980),f_0\to {\pi }^{+}{\pi }^{-}$
• $\varphi \varphi$ and $J/\psi \varphi$ mass spectra in decay $B_s^0\to J/\psi \varphi \varphi$