Residual correlations between decay products of $\pi^0\pi^0$ and $p\Sigma^0$ systems

Residual correlations between decay products due to a combination of both correlations between parents at small relative velocities and small decay momenta are discussed. Residual correlations between photons from pion decays are considered as a new possible source of information on direct photon fraction. Residual correlations in $p\gamma$ and $p\Lambda$ systems due to $p\Sigma^0$ interaction in final state are predicted based on the $p\Sigma^0$ low energy scattering parameters deduced from the spin-flavour SU$_6$ model by Fujiwara et al. including effective meson exchange potentials and explicit flavour symmetry breaking to reproduce the properties of the two-nucleon system and the low-energy hyperon-nucleon cross section data. The $p\gamma_{\Sigma^0}$ residual correlation is concentrated at $k^* \approx 70$ Mev/$c$ and its shape and intensity appears to be sensitive to the scattering parameters and space-time dimensions of the source. The $p\Lambda_{\Sigma^0}$ residual correlation recovers the negative parent $p\Sigma^0$ correlation for $k^* > 70$ Mev/$c$. The neglect of this negative residual correlation would lead to the underestimation of the parent $p\Lambda$ correlation effect and to an overestimation of the source size.