Analysis of the strong vertices of hadronic molecules $DK$, $D^*K$, $DK^*$ and their bottom analogs

TL;DR

This work computes the strong couplings of hadronic molecules formed by open-charm and bottom systems—$DK$, $D^*K$, $DK^*$ and their bottom analogs—using three-point QCD sum rules. The authors construct the three-point correlators on both the hadronic and QCD sides, including vacuum condensates up to dimension 6, and employ two continuum-treatment schemes to stabilize the sum rules. They extract the couplings $G_{T_{DK}DK}$, $G_{T_{D^*K}D^*K}$, $G_{T_{DK^*}DK^*}$, $G_{T_{BK}BK}$, $G_{T_{B^*K}B^*K}$, and related channels, then compute partial decay widths for $T_{DK}$ and $T_{D^*K}$ decays via $ ext{eta}- ext{pi}^0$ mixing and standard two-body kinematics. The results show that the predicted widths for the charm sector align with experimental data for $D_{s0}^*(2317)$ and $D_{s1}(2460)$, supporting the interpretation of these states as $DK$ and $D^*K$ hadronic molecules, while providing predictions for the bottom-sector states to aid future searches.

Abstract

In this work, we analyze the strong vertices of hadronic molecules $DK$, $D^*K$, $DK^*$ and their bottom analogs within the framework of three-point QCD sum rules. The coupling between interpolating currents and low spin particles is considered in the phenomenological side, and the vacuum condensates $\left\langle \bar qq \right\rangle ,\left\langle g_s^2GG \right\rangle ,\left\langle \bar qg_sσGq \right\rangle ,\left\langle g_s^3GGG \right\rangle ,{\left\langle \bar qq \right\rangle ^2}$ are included in the QCD side. As an application of strong coupling constants, we also obtain the partial decay widths of these states, where $Γ_{T_{DK}\rightarrow D_sπ}=10.3_{-2.9}^{+3.0}\mathrm{KeV}$, $Γ_{T_{D^*K}\rightarrow D_s^*π}=24.8_{-5.4}^{+5.5}\mathrm{KeV}$, $Γ_{T_{BK}\rightarrow BK}=101_{-21}^{+36}\mathrm{MeV}$ and $Γ_{T_{B^*K}\rightarrow B^*K}=142_{-25}^{+52}\mathrm{MeV}$. It is shown that the results of $Γ_{T_{DK}\rightarrow D_sπ}$ and $Γ_{T_{D^*K}\rightarrow D_s^*π}$ are compatible with the experimental data of $D_{s0}^*(2317)$ and $D_{s1}(2460)$.

Figures (5)

• Figure 1: The production processes of $D_{s0}^*(2317)$, $D_{s1}(2460)$ and $D_{s1}(2536)$
• Figure 2: The Feynman diagram for the perturbative part, The dashed lines denote the Cutkosky's cuts.
• Figure 3: The Feynman diagrams of vacuum condensates for molecule states $D[B]K,D^*[B^*]K,D[B]K^*$, where black and red line represent light and heavy quark respectively, and T denotes the hadronic molecule.
• Figure 4: The central values of hadronic coupling constants $G_{T_{DK}DK}$ and $G_{T_{D^*K}D^*K}$ with variations of the Borel parameters $T^2$ in the Borel platform.
• Figure 8: The coupling constants $G_{T_{DK}DK}$, $G_{T_{D^*K}D^*K}$ and $G_{T_{DK^*}DK^*}$ with the variations of ${P'}^2$.