Novel correlated ${{{D}^{0}}{\overline{{D}}{}^{0}}}$ systems for ${c/b}$ physics and tests of ${T/CPT}$

Decays of charmonia(-like) particles with definite $J^{PC}$ (e.g. ${{\chi_{c{\rm 1}}}(3872)}$) to a ${{D}^{0}}{\overline{{D}}{}^{0}}$ system and any combination of $C$-definite decay particles, are sources of quantum-correlated ${{D}^{0}}{\overline{{D}}{}^{0}}$ systems with $C = P = \pm 1$. Several $b$-hadron decays also produce quantum-correlated ${{D}^{0}}{\overline{{D}}{}^{0}}$ systems. Advantages of isolating these systems in their $C = +1$ components for amplitude analyses and studies of lineshapes are discussed. Methods to separate the $C = \pm 1$ ${{D}^{0}}{\overline{{D}}{}^{0}}$ components from ${{\chi_{c{\rm 1}}}(3872)}$ decay samples are presented. Studies of $T$ and $CPT$ conservation in $C = +1$ ${{D}^{0}}{\overline{{D}}{}^{0}}$ systems can be performed with more easily reconstructible final states, when compared to $C = -1$ ${{D}^{0}}{\overline{{D}}{}^{0}}$ systems. Experimental mechanisms that can produce $C = \pm 1$ ${{D}^{0}}{\overline{{D}}{}^{0}}$ systems are described in an appendix.