Proton-antiproton annihilation at 900 MeV/c into $\pi^{0}\pi^{0}\pi^{0}, \pi^{0}\pi^{0}\eta$ and $\pi^{0}\eta\eta$

The three reactions $\overline{p}p \rightarrow \pi^0\pi^0\pi^0$ , $\pi^0\pi^0\eta$ and $\pi^0\eta\eta$ in proton-antiproton annihilation in flight at 900 MeV/c are used to search for isoscalar $0^{++}$ and $2^{++}$ mesons in the mass range 1000–2000 MeV, in particular the $f_0(1710)$ . The description of both $\pi^0\pi^0\pi^0$ and $\pi^0\eta\eta$ data sets requires an isoscalar tensor resonance decaying into $\pi^0\pi^0$ and $\eta\eta$ with a mass of $(1867\pm46)$ MeV and a width of $(385\pm58)$ MeV. The ratio of partial widths $\Gamma(\eta\eta)/\Gamma(\pi\pi)$ is $0.27 \pm 0.10$ . The analyses of both $\pi^0\pi^0\pi^0$ and $\pi^0\eta\eta$ show no signal for the $f_0(1710)$ . The $\pi^0\eta\eta$ data set shows a strong signal of the $f_2^{\prime}(1525)$ suggesting a large OZI rule violation for tensor meson production in $\overline{p}p$ annihilation. The $\pi^0\pi^0\pi^0$ data set also requires the $f_2(1565)$ . The signal for the $f_2(1810)$ reported by earlier experiments is confirmed neither in $\pi^0\pi^0\pi^0$ nor in $\pi^0\eta\eta$ . The analysis of $\pi^0\pi^0\eta$ leads to an isovector tensor state decaying into $\pi^0\eta$ with a mass of $(1698\pm44)$ MeV and a width of $(265\pm55)$ MeV.