“…While the ISI factor with pp → ppη reaction near threshold is relatively simple with 3 P 0 pp initial state dominant, it becomes technically more complicated for pp → NNπ with several important initial partial waves even at energies very close to the threshold. In practice, for the pion production reactions, the ISI dumping effect is not included explicitly in previous calculations [22,23] and is done by adjusting the vertex form factors to reproduce the total cross sections. Since how to treat this dumping factor does not influence our main conclusion here, we follow the simple practical approach as these previous calculations [22,23] on the same reaction, although the ISI could be taken into account by some more complicated approaches, such as by including the partial wave ISI factors [42,43] or distortions of wave functions [44,45,46].…”