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Register a new userStudy on the possible molecular state composed of $D^*_sbar D_{s1} $ within the Bethe-Salpeter framework
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Recently a vector charmonium-like state $Y(4626)$ was observed in the portal of $D^+_sD_{s1}(2536)^-$. It intrigues an active discussion on the structure of the resonance because it has obvious significance for gaining a better understanding on its hadronic structure with suitable inner constituents. It indeed concerns the general theoretical framework about possible structures of exotic states. Since the mass of $Y(4626)$ is slightly above the production threshold of $D^+_sbar D_{s1}(2536)^-$ whereas below that of $D^*_sbar D_{s1}(2536)$ with the same quark contents as that of $D^+_sbar D_{s1}(2536)^-$, it is natural to conjecture $Y(4626)$ to be a molecular state of $D^{*}_sbar D_{s1}(2536)$, as suggested in literature. Confirming or negating this allegation would shed light on the goal we concern. We calculate the mass spectrum of a system composed of a vector meson and an axial vector i.e. $D^*_sbar D_{s1}(2536)$ within the framework of the Bethe-Salpeter equations. Our numerical results show that the dimensionless parameter $lambda$ in the form factor which is phenomenologically introduced to every vertex, is far beyond the reasonable range for inducing an even very small binding energy $Delta E$. It implies that the $D^*_sbar D_{s1}(2536)$ system cannot exist in the nature as a hadronic molecule in this model, so that we may not think the resonance $Y(4626)$ to be a bound state of $D^*_sbar D_{s1}(2536)$, but something else, for example a tetraquark and etc.
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$P_c(4312)$ observed by the LHCb collaboration is confirmed as a pentaquark and its structure, production, and decay behaviors attract great attention from theorists and experimentalists. Since its mass is very close to sum of $Sigma_c$ and $bar D$ masses, it is naturally tempted to be considered as a molecular state composed of $Sigma_c$ and $bar D$. Moreover, $P_c(4312)$ is observed in the channel with $J/psi p$ final state, requiring that isospin conservation $P_c(4312)$ is an isospin-1/2 eigenstate. In literature, several groups used various models to estimate its spectrum. We systematically study the pentaquarks within the framework of the Bethe-Salpeter equation; thus $P_c(4312)$ is an excellent target because of the available data. We calculate the spectrum of $P_c(4312)$ in terms of the Bethe-Salpter equations and further study its decay modes. Some predictions on other possible pentaquark states that can be tested in future experiments are made.
Recently, a new structure $Y(4626)$ was reported by the Belle Colloboration in the process $e^+e^-to D_s^+D_{s1}(2536)^-$. In this work, we propose an assignment of the $Y(4626)$ as a ${D}^*_sbar{D}_{s1}(2536)$ molecular state, which decays into the $D_s^+D_{s1}(2536)^-$ channel through a coupling between ${D}^*_sbar{D}_{s1}(2536)$ and ${D}_sbar{D}_{s1}(2536)$ channels. With the help of the heavy quark symmetry, the potential of the interaction ${D}^*_sbar{D}_{s1}(2536)-{D}_sbar{D}_{s1}(2536)$ is constructed within the one-boson-exchange model, and inserted into the quasipotential Bethe-Salpeter equation. The pole of obtained scattering amplitude is searched for in the complex plane, which corresponds to a molecular state from the interaction ${D}^*_sbar{D}_{s1}(2536)-{D}_sbar{D}_{s1}(2536)$. The results suggest that a pole is produced near the ${D}^*_sbar{D}_{s1}(2536)$ threshold, which exhibits as a peak in the invariant mass spectrum of the ${D}_sbar{D}_{s1}(2536)$ channel at about 4626 MeV. It obviously favors the $Y(4265)$ as a ${D}^*_sbar{D}_{s1}(2536)$ molecular state. In the same model, other molecular states from the interaction ${D}^*_sbar{D}_{s1}(2536)-{D}_sbar{D}_{s1}(2536)$ are also predicted, which can be checked in future experiments.
We discuss the possibility that the X(3872) can be a $Dbar{D}^*$ molecular bound state in the Bethe-Salpeter equation approach in the ladder and instantaneous approximations. We show that the $Dbar{D}^*$ bound state with quantum numbers $J^{PC}=1^{++}$ exists. We also calculate the decay width of $X(3872) rightarrow gamma J/psi$ channel and compare our result with those from previous calculations.
Using a well-established effective interaction in a rainbow-ladder truncation model of QCD, we fix the remaining model parameter to the bottomonium ground-state spectrum in a covariant Bethe-Salpeter equation approach and find surprisingly good agreement with the available experimental data including the 2^{--} Upsilon(1D) state. Furthermore, we investigate the consequences of such a fit for charmonium and light-quark ground states.
We choose the Reduction Formula, PCAC and Low Energy Theory to reduce the $S$ matrix of a OZI allowed two-body strong decay involving a light pseudoscalar, the covariant transition amplitude formula with relativistic wave functions as input is derived. After confirm this method by the decay $D^*(2010)to Dpi$, we study the state $D^*(2007)$, and the full width $Gamma_{rm{th}}(D^*(2007))=53.8pm0.7$ keV is obtained. Supposing the newly observed $D_{s0}(2590)^{+}$ to be the state $D_s(2^1S_0)^+$, we find its decay width $Gamma$ is highly sensitive to the $D_{s0}(2590)^{+}$ mass, which result in the meaningless comparison of widths by different models with various input masses. Instead of width, we introduce a model independent quantity $X$ and the ratio $Gamma/{|{vec P_f}|^3}$, which are almost mass independent, to give us useful information. The results show that, all the existing theoretical predictions $X_{D_s(2S) to D^*K}=0.25sim 0.41$ and $Gamma/{|{vec P_f}|^3}=0.81sim1.77$ MeV$^{-2}$ are much smaller than experimental data $0.585^{+0.015}_{-0.035}$ and $4.54^{+0.25}_{-0.52}$ MeV$^{-2}$. Further compared with $X^{ex}_{D^*(2010) to Dpi}=0.58$, the current data $X^{ex}_{D_s(2S) to D^*K}=0.585^{+0.015}_{-0.035}$ is too big to be an reasonable value, so to confirm $D_{s0}(2590)^{+}$ as the state $D_s(2^1S_0)^+$, more experimental studies are needed.
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