Near-threshold structures in the $D_s^{+}{D}_s^{-}$ mass distribution of the decay $B^{+}\to D_s^{+}{D}_s^{-}{K}^{+}$

Abstract

Two near-threshold peaking structures with spin-parities $J^{\mathrm{PC}}=0^{++}$ were recently discovered by the LHCb Collaboration in the $D_s^{+}{D}_s^{-}$ invariant mass distribution of the decay $B^{+}\to D_s^{+}{D}_s^{-}{K}^{+}$. The first of them is the resonance $X(3960)$, whereas the second one, $X_0(4140)$, is a structure with the mass around $4140\mathrm{MeV}$. To explore their natures and model them, we study the hadronic molecule $\mathcal{M}=D_s^{+}{D}_s^{-}$ and calculate its mass, current coupling, and width. The mass and current coupling of the molecule are extracted from the QCD two-point sum rule analyses by taking into account vacuum condensates up to dimension $10$. To evaluate its full width, we consider the processes $\mathcal{M}\to D_s^{+}{D}_s^{-}$, $\mathcal{M}\to {\eta }_c{\eta }^{(\prime )}$, and $\mathcal{M}\to J/\psi \varphi$. Partial widths of these decays are determined by the strong couplings $g_i,i=1,2,3,4$ at vertices $\mathcal{M}{D}_s^{+}{D}_s^{-}$, $\mathcal{M}{\eta }_c{\eta }^{(\prime )}$, and $\mathcal{M}J/\psi \varphi$. They are computed by means of the three-point sum rule method. Predictions for the mass $m=(4117\pm 85)\mathrm{MeV}$ and width ${\Gamma }_{\mathcal{M}}=(62\pm 12)\mathrm{MeV}$ of the molecule $\mathcal{M}$ are compared with the corresponding LHCb data, and also with our results for the diquark-antidiquark state $X=[cs][\overline{c}\overline{s}]$. We argue that the structure $X_0(4140)$ may be interpreted as the hadronic molecule $D_s^{+}{D}_s^{-}$, whereas the resonance $X(3960)$ can be identified with the tetraquark $X$.

11 Pages, 4 Figures and 1 Table

References in corpus (16)

• Evidence for a Narrow Near-Threshold Structure in the $J/\psi \varphi$ Mass Spectrum in $B^{+}\to J/\psi \varphi K^{+}$ Decays
• The Heavy Quark Spin Symmetry Partners of the X(3872)
• Observation of new resonances decaying to $J/\psi K^{+}$ and $J/\psi \varphi$
• Four-quark exotic mesons
• A global fit to determine the pseudoscalar mixing angle and the gluonium content of the eta' meson
• Transition form factors ${\gamma }^{\ast }\gamma \to \eta$ and ${\gamma }^{\ast }\gamma \to {\eta }^{\prime }$ in QCD
• Mass spectra for $qc\bar{q}\bar{c}$, $sc\bar{s}\bar{c}$, $qb\bar{q}\bar{b}$, $sb\bar{s}\bar{b}$ tetraquark states with $J^{PC}=0^{++}$ and $2^{++}$
• Establishing the heavy quark spin and light flavor molecular multiplets of the $X(3872)$, $Z_c(3900)$ and $X(3960)$
• Analysis of the $X(3960)$ and related tetraquark molecular states via the QCD sum rules
• Predicting the ${\bar{D}}_s^{(\ast )}{D}_s^{(\ast )}$ bound states as the partners of $X(3872)$
• The $X(3960)$ seen in $D_s^{+}{D}_s^{-}$ as the $X(3930)$ state seen in $D^{+}{D}^{-}$
• Decay behaviors of the fully-bottom and fully-charm tetraquark states
• Production rates of $D_s^{+}{D}_s^{-}$ and $D\bar{D}$ molecules in $B$ decays
• Resonance $X(3960)$ as a hidden charm-strange scalar tetraquark
• Connection between near the $D_s^{+}{D}_s^{-}$ threshold enhancement in $B^{+}\to D_s^{+}{D}_s^{-}{K}^{+}$ and conventional charmonium ${\chi }_{c0}(2P)$
• Resonance $X(4630)$

Cited by in corpus (1)

• $X(3960)$, $X_0(4140)$, and other compact $cs\bar{c}\bar{s}$ states