Revisiting the $DD^\ast$ chiral interactions with the local momentum-space regularization up to the third order and the nature of $T_{cc}^+$

TL;DR

This paper revisits $DD^*$ interactions using chiral effective field theory up to third order, focusing on long-range behaviors and supporting the molecular interpretation of $T_{cc}^+$.

Contribution

It introduces a detailed third-order chiral interaction analysis with local momentum-space regularization for $DD^*$ systems, highlighting differences from nucleon interactions and clarifying the nature of $T_{cc}^+$.

Findings

Long-range two-pion exchange interactions are similar to HAL QCD results but occur at longer distances.

Binding solutions are only found in the isoscalar channel.

Subleading pion-charmed meson couplings are weaker than in pion-nucleon systems.

Abstract

We revisit the $DD^\ast$ interactions in chiral effective field theory up to the third order for the first time. We deal with the pion-exchanged interactions via local momentum-space regularization, in which we focus on their long-range behaviors through demanding their contributions vanish at the origin in the coordinate space. The short-range contact interactions and subleading pion-charmed meson couplings are estimated with the phenomenological resonance saturation model. The subleading pion-charmed meson couplings are much weaker than those in the pion-nucleon system, thus the $DD^\ast$ binding mechanism is very different with that of the $NN$ system. We also obtain the analytic structure of the two-pion exchange interactions in the coordinate space, and we find that its asymptotic behavior at long distance is similar to but slightly different with the $NN$ interactions. We get the same asymptotic behavior of the two-pion exchange interaction with that from HAL QCD method but appearing in the longer distance rather than $1 <r<2\text{ fm}$. The binding solution only exists in the isoscalar channel. Our calculation supports the molecular interpretation of $T_{cc}^+$.