Four sets of data determining parameters of $a_0(1450)$ and $a_0(980)$ are reanalyzed. These are Crystal Barrel data for $\overline{p}p$ annihilation at rest to $\eta {\pi }^0{\pi }^0$ in (i) liquid hydrogen and (ii) gas, and to (iii) $K_L^0{\pi }^{\pm }{K}^{\mp }$ and (iv) $\omega {\pi }^{+}{\pi }^{-}{\pi }^0$ (mostly $\omega \rho \pi$). Dispersive corrections due to opening of inelastic thresholds are treated fully. This stabilizes parameters of $a_0(1450)$ substantially. The mass of its peak is $1448\pm 13(\mathrm{stat})\pm 25(\mathrm{syst})\mathrm{MeV}$ and its mean full width at half maximum is $192\pm 9\pm 9\mathrm{MeV}$. The pole position is $M-i\Gamma /2=1432\pm 13\pm 25-i(98\pm 5\pm 5)\mathrm{MeV}$. At the peak, $\eta \pi$, $\omega \rho$ and $a_0(980)\sigma$ decay intensities are in the ratios $1:9.2\pm 0.8\pm 1.3:3.1\pm 0.2\pm 0.9$. There is no evidence for a separate $a_0$ near 1300 MeV claimed by Obelix. Parameters of $a_0(980)$ are updated to $M=987.4\pm 1.0\pm 3.0\mathrm{MeV}$, $g^2(\eta \pi )=0.164\pm 0.007\pm 0.010{\mathrm{GeV}}^2$, $g^2(KK)/g^2(\eta \pi )=1.05\pm 0.07\pm 0.05$. Its dominant second-sheet pole in the $KK$ channel is at $(989\pm 1\pm 5)-i(40\pm 2\pm 4)\mathrm{MeV}$. Finally, the nature of the prominent $J^{PC}=0^{-+}\to \omega \rho$ signal in $\omega \rho \pi$ data is also clarified.

• Received 20 August 2008

DOI:https://doi.org/10.1103/PhysRevD.78.074023