Under chiral effective field theory, we study the S-wave DD^* interactions up to second chiral order at one-loop level, which contain full contact, one-pion-exchange (OPE) and two-pion-exchange (TPE) contributions. Here, we adopt a new subtraction scheme of the two-particle-reducible contributions, and introduce three regularization schemes uniquely for the TPE contributions since they are highly divergent on the momentum transfer. These different schemes all lead to same conclusions: In the I=0 channel, the TPE contribution is repulsive, then the competition between this powerful repulsing TPE and the other two (contact and OPE) results in a quite weak attraction. This explains why T₂₂ has a extremely small binding energy if treated as the I=0 DD^* bound state. This feature resembles that of hidden charm DD^* as we investigated in previous work 1, which also interpreted the extremely near-threshold phenomenon of X (3872). In addition, we also solve the Bethe-Salpeter equation with the chiral interactions for a consistency check.
Xu et al. (Sun,) studied this question.