Observation of $a_0^0(980)$-$f_0(980)$ Mixing

We report the first observation of $a_0^0(980)$-$f_0(980)$ mixing in the decays of $J/\psi\to\phi f_{0}(980)\to\phi a^{0}{0}(980)\to\phi\eta\pi^{0}$and$\chi{c1}\to a^{0}{0}(980)\pi^{0}\to f{0}(980)\pi^{0}\to\pi^{+}\pi^{-}\pi^{0}$,usingdatasamplesof$1.31\times10^{9}$ $J\mathrm{/}\psi$ events and $4.48\times {10}^8$ $\psi (3686)$ events accumulated with the BESIII detector. The signals of $f_{0}(980)\to a^{0}{0}(980)$and$a^{0}{0}(980)\to f_{0}(980)$ mixing are observed at levels of statistical significance of $7.4\sigma$ and $5.5\sigma$, respectively. The corresponding branching fractions and mixing intensities are measured and the constraint regions on the coupling constants, $g_{a_0{K}^{+}{K}^{-}}$ and $g_{f_0{K}^{+}{K}^{-}}$, are estimated. The results improve the understanding of the nature of $a_0^0(980)$ and $f_0(980)$.