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

Abstract

The $D{D}^{\ast }$ potentials are studied within the framework of heavy meson chiral effective field theory. We obtain the effective potentials of the $D{D}^{\ast }$ system up to $O({ϵ}^2)$ 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 Schrödinger 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.

Comments: 18 pages, 12 figures. Published in Phys. Rev. D. We correct three typos in which $I=1$ and $I=0$ were mistaken for each other