In search of the $\sigma$ resonance in $\pi^0\pi^0$ production by $\pi^-$ and $K^-$

The identification of the light scalar mesons, in particular the $\sigma$ state also called the $f_0(600)$ with $I^G(J^{PC}) = 0^+(0^{++})$, is a long-standing puzzle. The main $\sigma$ decay mode is to two pions. The study of the process $K^-p \to \pi^0\pi^0\Lambda$ is especially attractive because the $\pi^0\pi^0$ pair is a pure $I=0$ state. This is in contrast to $\pi^+\pi^-$, which features $I=0$ and 1. Extensive new data have become available recently from the Crystal Ball at the AGS [1] on $\pi^-p \to \pi^0\pi^0n$, $K^-p\to\pi^0\pi^0\Lambda$, and $K^-p\to\pi^0\pi^0\Sigma^{0}$, which cast doubts on the picture of the $\sigma$ being a simple $2\pi^0$ state with $m\sim600$~MeV, as recommended in recent editions of the Review of Particle Physics. The latest experimental data have fully measured kinematics, so the four-dimensional variable space has been determined in its entirety; there is major structure in the $\pi^0\pi^0$ invariant mass which varies with the $\pi^0\pi^0$ angle and the incident energy.\\ Reference: S. Prakhov \emph{et al.}\ (Crystal Ball Collaboration), Phys.\ Rev.\ C \textbf{69}, 042202 (2004); S. Prakhov \emph{et al.}\ (Crystal Ball Collaboration), Phys.\ Rev.C \textbf{69}, 045202 (2004); S. Prakhov \emph{et al.}\ (Crystal Ball Collaboration), Phys.\ Rev.\ C \textbf{70}, 034605 (2004).