Recently it has been shown by exclusive and kinematically complete experiments that the appearance of a narrow resonance structure in double-pionic fusion reactions is strictly correlated with the appearance of the so-called ABC effect, which denotes a pronounced low-mass enhancement in the $pipi$-invariant mass spectrum. Whereas the resonance structure got its explanation by the $d^*(2380)$ dibaryonic resonance, a satisfactory explanation for the ABC effect is still pending. In this paper we discuss possible explanations of the ABC effect and their consequences for the internal structure of the $d^*$ dibaryon.
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