$D^{(*)}\bar{B}^{(*)}$ dynamics in chiral effective field theory

Abstract

In this work, we systematically study the interactions of the $S$-wave $D^{(*)}\bar{B}^{(*)}$ systems within the framework of chiral effective field theory in heavy hadron formalism. We calculate the $D^{(*)}\bar{B}^{(*)}$ effective potentials up to next-to-leading order, explore the bound state formations, and investigate the $D^{(*)}\bar{B}^{(*)}$ scattering properties such as scattering rate, scattering length, and effective range. Our results show that all $I=1$ $D^{(*)}\bar{B}^{(*)}$ potentials are repulsive, preventing the formation of bound states, while the $I=0$ potentials are generally attractive. Specifically, we get two important observations: first, the shallow bound state is more likely to exist in the $D\bar{B}[I(J^{P})=0(0^{+})]$ system than in the $D\bar{B}^{*}[I(J^{P})=0(1^{+})]$ system; second, $D^{*}\bar{B}^{*}[I(J^{P})=0(0^{+})]$ and $D^{*}\bar{B}^{*}[I(J^{P})=0(1^{+})]$ systems possess relatively large binding energies and positive scattering lengths, which suggests strong bound state formations in these channels. So the attractions in the $D^{*}\bar{B}^{*}[I=0]$ systems are deeper than those in the $D\bar{B}^{(*)}[I=0]$ systems, thus we strongly recommend the future experiment to search for the $D^{*}\bar{B}^{*}[I=0]$ tetraquark systems. We also investigate the coupled-channel effects on the $J=0, 1$ systems and conclude that the inclusion of the coupled channels introduces small but visible influences. In addition, we also investigate the dependencies of the $D\bar{B}^{(*)}$ binding energies on the contact low-energy coupling constants.