$DK$, $DDK$, and $DDDK$ molecules--understanding the nature of the $D_{s0}^{\ast }(2317)$

Abstract

The $DK$ interaction is strong enough to form a bound state, the $D_{s0}^{\ast }(2317)$. This in turn begs the question of whether there are bound states composed of several charmed mesons and a kaon. Previous calculations indicate that the three-body $DDK$ system is probably bound, where the quantum numbers are $J^P=0^{-}$, $I=\frac{1}{2}$, $S=1$ and $C=2$. The minimum quark content of this state is $cc\bar{q}\bar{s}$ with $q=u,d$, which means that, if discovered, it will be an explicitly exotic tetraquark. In the present work. we apply the Gaussian Expansion Method to study the $DDDK$ system and show that it binds as well. The existence of these three and four body states is rather robust with respect to the $DD$ interaction and subleading (chiral) corrections to the $DK$ interaction. If these states exist, it is quite likely that their heavy quark symmetry counterparts exist as well. These three-body $DDK$ and four-body $DDDK$ molecular states could be viewed as counterparts of atomic nuclei, which are clusters of nucleons bound by the residual strong force, or chemical molecules, which are clusters of atoms bound by the residual electromagnetic interaction.

20 pages, 4 figures

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Cited by in corpus (33)

• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• Can we understand the decay width of the $T_{cc}^{+}$ state?
• Novel coupled channel framework connecting quark model and lattice QCD: an investigation on near-threshold $D_s$ states
• $DDK$ system in finite volume
• Few-body systems consisting of mesons
• Excited $K$ meson, $K_c(4180)$, with hidden charm as a $D\bar{D}K$ bound state
• Production of $D_{s0}^{\ast }(2317)$ and $D_{s1}(2460)$ in $B$ decays as $D^{(\ast )}K$ and $D_s^{(\ast )}\eta$ molecules
• Strong decays of the explicitly exotic doubly charmed $DDK$ bound state
• Triple-charm molecular states composed of $D^{\ast }{D}^{\ast }D$ and $D^{\ast }{D}^{\ast }{D}^{\ast }$
• Double-charm heptaquark states composed of two charmed mesons and one nucleon
• Three-body molecules $\bar{D}{\bar{D}}^{\ast }{\Sigma }_c$- understanding the nature of $T_{cc}$, $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$
• Faddeev fixed-center approximation to the $D\bar{D}K$ system and the hidden charm $K_{c\bar{c}}(4180)$ state
• Two-pole structures in a relativistic Friedrichs-Lee-QPC scheme
• Prediction of possible exotic states in the $\eta \bar{K}{K}^{\ast }$ system
• Remarks on non-perturbative three--body dynamics and its application to the $KK\bar{K}$ system
• Quadruply charmed baryons as heavy quark symmetry partners of the $D_{s0}^{\ast }(2317)$
• Molecular states of $D^{\ast }{D}^{\ast }{\bar{K}}^{\ast }$ nature
• One way to verify the molecular picture of exotic hadrons --from $DK$ to $DDK/D{\bar{D}}^{(\ast )}K$
• Study on the ${\Omega }_c^0$ States Decaying to ${\Xi }_c^{+}{K}^{-}$ in $pp$ collisions at $\sqrt{s}=7$, 13 TeV
• Theoretical investigation of the molecular nature of $D_{s0}^{\ast }(2317)$ and $D_{s1}(2460)$ and the possibility of observing the $D\bar{D}K$ bound state $K_{c\bar{c}}(4180)$ in inclusive $e^{+}{e}^{-}\to c\bar{c}$ collisions
• The study of exotic state $Z_c^{\pm }(3900)$ decaying to $J/\psi {\pi }^{\pm }$ in the $pp$ collisions at $\sqrt{s}$ = 1.96, 7, and 13 TeV
• Binding of the three-hadron $D{D}^{\ast }K$ system from the lattice effective field theory
• Productions of $D_{s0}^{\ast }(2317)$ and $D_{s1}(2460)$ in $B_{(s)}$ and ${\Lambda }_b({\Xi }_b)$ decays
• Search for a doubly-charged $DDK$ bound state in ${\rm Y}(1S,2S)$ inclusive decays and via direct production in $e^{+}{e}^{-}$ collisions at $\sqrt{s}$ = 10.520, 10.580, and 10.867 GeV
• Masses and radiative decay widths of the $D_{s0}^{\ast }(2317)$ and $D_{s1}^{\prime }(2460)$ and their bottom analogs
• Study on triple-hadron bound states with Gaussian expansion method
• Constraining the $DD{D}^{\ast }$ three-body bound state via the $Z_c(3900)$ pole
• Production of the (predicted) $K^{\ast }(4307)$ in $B$ decays
• Investigating $S$-wave bound states composed of two pseudoscalar mesons
• Tri-meson state $\bar{\mathbf{B}}{\bar{\mathbf{B}}}^{\ast }{\bar{\mathbf{B}}}^{\ast }$
• Exotic Heavy Hadrons
• Analysis of the hadronic molecules $DK$, $D^{\ast }K$, $D{K}^{\ast }$ and their bottom analogs with QCD sum rules
• Low-energy $DD$ scattering in lattice QCD