Study of $a_0^0(980)$-$f_0(980)$ mixing from $a_0(1450)\to a_0^0(980)f_0(500)\to {\pi }^{+}{\pi }^{-}{f}_0(500)$

Abstract

The $a_0^0(980)-f_0(980)$ mixing is one of the most potential tools to learn about the nature of $a_0^0(980)$ and $f_0(980)$. Using the $f_0(980)$-$a_0^0(980)$ mixing intensity ${\xi }_{af}$ measured recently at BESIII, we calculate the the branching ratio of the the isospin violation decay $J/\psi \to \gamma {\eta }_c\to \gamma {\pi }^0{a}_0^0(1450)\to \gamma {\pi }^0{a}_0^0(980)f_0(500)\to \gamma {\pi }^0{f}_0(980)f_0(500)\to \gamma {\pi }^0{\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$. The value of the branching ratio is found to be $O(10^{-6})$, which can be observed with $10^{10}$ $J/\psi$ events collected at BESIII. The narrow peak from the $f_0(980)$-$a_0^0(980)$ mixing in the ${\pi }^{+}{\pi }^{-}$ mass square spectrum can also be observed. In addition, we study the non-resonant decay $a_0^0(1450)\to f_0(980){\pi }^{+}{\pi }^{-}(\text{non-resonant})$, which is dominated by the $a_0^0(980)$-$f_0(980)$ mixing. We find that the non-resonant decay $a_0^0(1450)\to f_0(980){\pi }^{+}{\pi }^{-}$ and the decay $a_0^0(1450)\to f_0(980)f_0(500)$ can be combined to measure the mixing intensity ${\xi }_{af}$ in experiment. These decays are the perfect complement to the decay ${\chi }_{c1}\to f_0(980){\pi }^0\to {\pi }^{+}{\pi }^{-}{\pi }^0$ which had been observed at BESIII, the observations of them will make the measurement of the mixing intensity ${\xi }_{af}$ more precisely.

References in corpus (17)

• Future Physics Programme of BESIII
• Scalar Mesons a0(1450) and sigma(600) from Lattice QCD
• $f_1(1285)$ decays into $a_0(980){\pi }^0$, $f_0(980){\pi }^0$ and isospin breaking
• Possibility of measuring a0(980)-f0(980) mixing from J/psi -> phi a0
• Study of J/psi->eta phi pi+pi- at BESIII
• Investigation of a0-f0 mixing
• Amplitude analysis of the ${\chi }_{c1}\to \eta {\pi }^{+}{\pi }^{-}$ decays
• Re-analysis of data on a0(1450) and a0(980)
• Study a0(980)-f0(980) mixing from a0(980) -> f0(980) transition
• Triangle singularity in the $J/\psi \to K^{+}{K}^{-}{f}_0(980)(a_0(980))$ decays
• Abnormal isospin violation and $a_0-f_0$ mixing in the $D_s^{+}\to {\pi }^{+}{\pi }^0{a}_0(980)(f_0(980))$ reactions
• Semileptonic decays $D\to {\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e$ and $D_s\to {\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e$ as the probe of constituent quark-antiquark pairs in the light scalar mesons
• $\eta$ and ${\eta }^{\prime }$ Physics at BES-III
• pi-pi Scattering in Twisted Mass Chiral Perturbation Theory
• $a_0(980)-f_0(980)$ mixing in ${\chi }_{c1}\to {\pi }^0{f}_0(980)\to {\pi }^0{\pi }^{+}{\pi }^{-}$ and ${\chi }_{c1}\to {\pi }^0{a}_0(980)\to {\pi }^0{\pi }^0\eta$
• Investigation of the tetraquark candidate $a_0(980)$: technical aspects and preliminary results
• 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

Cited by in corpus (3)

• The $D_s^{+}\to a_0(980)e^{+}{\nu }_e$ reaction and the $a_0(980)-f_0(980)$ mixing
• The ${\bar{B}}_s^0\to J/\psi {\pi }^0\eta$ decay and the $a_0(980)-f_0(980)$ 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