Partial wave analysis of the ${\pi }^0{\pi }^0$ system produced in ${\pi }^{-}p$ charge exchange collisions

A partial wave analysis of the ${\pi }^0{\pi }^0$ system produced in the charge exchange reaction ${\pi }^{-}\overrightarrow{p}{\pi }^0{\pi }^{0}n$ at an incident momentum of 18.3 $\mathrm{GeV}/c$ is presented as a function of the ${\pi }^0{\pi }^0$ invariant mass $m_{{\pi }^0{\pi }^0}$ and momentum transfer squared $|t|$ from the incident ${\pi }^{-}$ to the outgoing ${\pi }^0{\pi }^0$ system. For small values of $|t|,$ the S-wave intensity shows a broad enhancement at low $m_{{\pi }^0{\pi }^0}$ with a sharp dip in the vicinity of the $f_0\mathrm{}\left(980\right).$ A dip is also observed in the vicinity of the $f_0\mathrm{}\left(1500\right).$ There is a rapid variation of the S to $D_0$ relative phase difference in these mass regions. For large values of $|t|,$ the $f_0\mathrm{}\left(980\right)\mathrm{}$ appears as a bump. The $f_2\mathrm{}\left(1270\right),$ observed in D waves, is produced dominantly by $\pi$ exchange at low values of $|t|$ and $a_2$ exchange at higher values of $|t|.$