$D D^{*}$ potentials in chiral perturbation theory and possible molecular states

TL;DR

This paper investigates the $DD^{*}$ interaction potentials using heavy meson chiral effective field theory, identifying conditions under which bound molecular states may form, especially in the isospin zero channel.

Contribution

The study provides a detailed calculation of $DD^{*}$ potentials up to $O(psilon^2)$, including one-pion, two-pion exchange, and contact interactions, and explores their implications for molecular state formation.

Findings

Bound state in the $I=0$ channel near $m_ ho$ cutoff.

No bound state found in the $I=1$ channel across cutoff range.

Contact and two-pion exchange are crucial for binding.

Abstract

The $DD^{*}$ potentials are studied within the framework of heavy meson chiral effective field theory. We obtain the effective potentials of the $DD^{*}$ system up to $O(\epsilon^2)$ at the one-loop level. In addition to the one-pion exchange contribution, the contact and two-pion exchange interactions are also investigated in detail. Furthermore, we search for the possible molecular states by solving the Schr\"odinger equation with the potentials. We notice that the contact and two-pion exchange potentials are numerically non-negligible and important for the existence of a bound state. In our results, no bound state is found in the $I=1$ channel within a wide range of cutoff parameter, while there exists a bound state in the $I=0$ channel as the cutoff is near $m_\rho$ in our approach.