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

Abstract

In this work, we systematically study the interactions of the $S$-wave $D^{(\ast )}{\bar{B}}^{(\ast )}$ systems within the framework of chiral effective field theory in heavy hadron formalism. We calculate the $D^{(\ast )}{\bar{B}}^{(\ast )}$ effective potentials up to next-to-leading order, explore the bound state formations, and investigate the $D^{(\ast )}{\bar{B}}^{(\ast )}$ scattering properties such as scattering rate, scattering length, and effective range. Our results show that all $I=1$ $D^{(\ast )}{\bar{B}}^{(\ast )}$ 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 $D{\bar{B}}^{\ast }[I(J^P)=0(1^{+})]$ system; second, $D^{\ast }{\bar{B}}^{\ast }[I(J^P)=0(0^{+})]$ and $D^{\ast }{\bar{B}}^{\ast }[I(J^P)=0(1^{+})]$ systems possess relatively large binding energies and positive scattering lengths, which suggests strong bound state formations in these channels. So the attractions in the $D^{\ast }{\bar{B}}^{\ast }[I=0]$ systems are deeper than those in the $D{\bar{B}}^{(\ast )}[I=0]$ systems, thus we strongly recommend the future experiment to search for the $D^{\ast }{\bar{B}}^{\ast }[I=0]$ 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 $D{\bar{B}}^{(\ast )}$ binding energies on the contact low-energy coupling constants.

35 pages, 16 figures, 24 tables

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Cited by in corpus (1)

• Investigating the two-pion exchange of the double charm $D{D}^{\ast }$ chiral interactions and $T_{cc}$