Two-pion exchange potential in $D^{(\ast )}{D}^{(\ast )}$ system

Abstract

Motivated by the recent HAL QCD lattice results on the $D$ - $D^{\ast }$ potential at nearly physical point $m_{\pi }=146.4$ MeV, we theoretically examine effects from the two-pion exchange in (semi-)long-range parts of the $D{D}^{\ast }$ system. We employ the framework of heavy-meson chiral perturbation theory with heavy-quark spin symmetry. The pion exchanges up to next-to-next-to-leading order (N${}^2$LO) are taken into account. In order to separate the (semi-)long-range contributions, we apply the dispersion-relation method to one-loop diagrams. As a result, we find that the lattice data on the $D$ - $D^{\ast }$ potential in the regime of $0.5\mathrm{fm}\lesssim r$ is reproduced by adjusting the unknown $O(p^2)$ couplings. In particular, it turns out that contributions from isospin-independent N${}^2$LO triangle diagrams play a central role in reproducing the lattice data of the form $V^{D{D}^{\ast }}\sim {\left({\mathrm{e}}^{-m_{\pi }r}/r\right)}^2$ in $1.0\mathrm{fm}\lesssim r\lesssim 2.0\mathrm{fm}$. We also present predictions of other $D^{(\ast )}$ - $D^{(\ast )}$ potentials, where the similar two-pion exchange tail is predicted. Our findings provide useful information on the (semi-)long-range regime of the $D$ - $D^{\ast }$ potential focusing on two-pion exchanges.

Comments: 19 pages, 10 figures