Investigation of J/ψ→γπ${}^0$η(π${}^{+}$π${}^{-}$, π${}^0$π${}^0$) radiative decays including final-state interactions

We revisit the coupled-channel $K\overline{K}$ interactions and dynamically generate the resonances f${}_0$(980) and a${}_0$(980) within both the isospin and the physical bases. The $f_0$(980)–$a_0$(980) mixing effects are generated in the scattering amplitudes of the coupled channels with the physical basis, which exploits the important role of the $K\overline{K}$ channel in the dynamical nature of these resonances. With the scattering amplitudes obtained, we investigate the $f_0$(980) and $a_0$(980) contributions to the J/ψ→γηπ${}^0$, J/ψ→γπ${}^{+}$π${}^{-}$ and J/ψ→γπ${}^0$π${}^0$ radiative decays through the final-state interactions. We obtain the corresponding branching fractions Br(J/ψ→γ$a_0$(980)→γηπ${}^0$)=(0.48±0.03)×10${}^{-7}$, Br(J/ψ→γ$f_0$(980)→γπ${}^{+}$π${}^{-}$)=(0.52−2.08)×10${}^{-7}$, Br(J/ψ→γ$f_0$(980)→γπ${}^0$π${}^0$)=(0.26−1.04)×10${}^{-7}$, and predict Br(J/ψ→γ$a_0$(980))=(1.24−1.61)×10${}^{-7}$ and Br(J/ψ→γ$f_0$(980))=(0.69−4.00)×10${}^{-7}$. These fractions are within the upper limits of the experimental measurements.