Strong decays of the $DK^\ast$ and $\bar{D}K^{\ast}$ molecular states

TL;DR

This study investigates strong decays of potential near-threshold hadronic molecules formed from DK^* and bar{D}K^* with isospin 0/1 and positive parity. Using an effective Lagrangian framework and Weinberg's compositeness condition to fix couplings, the authors compute two-body and three-body decay widths for the DK^* and bar{D}K^* molecular states and their charge conjugates. Key results show that D^*K tends to dominate for the f-state while D_s^*π dominates for the a-state in the DK^* and that the two-body widths for bar{D}K^* states can reach tens of MeV with total widths around tens to about one hundred MeV, depending on model parameters. The distinct ratios of partial widths, especially between D_s^*η and D^*K versus D_s^*π and D^*K, provide a concrete experimental handle to test the molecular interpretation, and the predicted sizable widths offer plausible connections to recent LHCb hints for related threshold structures.

Abstract

Inspired by the abundant structure near the threshold of the $D^{(*)}K^{(*)}/\bar{D}^{(*)}K^{(*)}$, we estimate the strong decay properties of the $T_{c\bar{s}1}^{f/a}$ and $T_{\bar{c}\bar{s}1}^{f/a}$ with $I(J^{P})=0/1(1^{+})$ in $DK^{*}$ and $\bar{D}K^{*}$ molecular scenarios in the present paper. By employing the effective Lagrangian approach, the widths of the processes $T_{c\bar{s}1}^{f}\to D^{*}K, D_{s}^{*}η, DKπ$, $T_{c\bar{s}1}^{a}\to D^{*}K, D_{s}^{*}π, DKπ$, and $T_{\bar{c}\bar{s}1}^{f/a}\to\bar{D}^{*}K, \bar{D}Kπ$ are estimated. Considering the present estimations, we propose to search for $T_{c\bar{s}1}^{f/a}$ states in $D^{*}K$ and $D_{s}^{*}π/D_{s}^{*}η$ mass invariant spectra. Their ratios may serve as an important test of the molecular scenario.

Figures (9)

• Figure 1: The schematic picture of states near the $D^{(\ast)}K^{(\ast)}/\bar{D}^{(\ast)}K^{(\ast)}$ thresholds. Here the solid black lines and solid red lines refer to the observed potential molecular states composed of $D^{(*)}K/D^{*}K^{*}$ and $\bar{D}^{*}K^{*}$, respectively, while the dashed lines indicate possible molecular states that have not yet been reported experimentally.
• Figure 2: The mass operators of $T_{c\bar{s}1}^{f/a}$ and $T_{\bar{c}\bar{s}1}^{f/a}$.
• Figure 3: The typical diagrams contributing to $T_{c\bar{s}1}\to D^{*}K$ (diagrams (a)-(b)), $T_{c\bar{s}1}\to D_{s}^{*}\pi/\eta$ (diagrams (c)-(e)) and $T_{\bar{c}\bar{s}1}\to\bar{D}^{*}K$ (diagrams (f)-(h)).
• Figure 4: The three-body decay of $T_{c\bar{s}1}^{f/a}$ and $T_{\bar{c}\bar{s}1}^{f/a}$ .
• Figure 5: (Color online.) The coupling constants $g_{T_{c\bar{s}1}} /g_{T_{\bar{c}\bar{s}1}}$ depending on model parameter $\Lambda$ with $E_{b}=5~\mathrm{MeV}$, $10~\mathrm{MeV}$ and $15~\mathrm{MeV}$.