Investigating the two-pion exchange of the double charm $DD^*$ chiral interactions and $T_{cc}$ (2509.11234v1)

Abstract: 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 $T_{cc}$ has a extremely small binding energy if treated as the $I=0$ $DD^*$ bound state. This feature resembles that of hidden charm $D\bar{D}^*$ 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.