arXiv subjects

Shi-Dong Liu

Publications and source records attributed to Shi-Dong Liu.

18 recordsLinked to original sources

arXiv2026

Radiative decays of the predicted P-wave $D\bar{D}^*$ molecular state: the $0^{-+}$ case

In the present work, we study the radiative decays of the P-wave $D\bar{D}^*$ molecular state $G_0$ with $I^G(J^{PC})=0^+(0^{-+})$ using a phenomenological Lagrangian approach. The molecular coupling is fixed by the compositeness condition with a Gaussian form factor. The partial widths for $G_0\to γγ$, $γJ/ψ$, $γψ(2S)$, $γh_c$, $γρ$, and $γω$ are evaluated. Our results show that the two-photon and $γh_c$ channels are highly suppressed, while $γJ/ψ$, $γψ(2S)$, and $γρ$ are of the order of a few keV, and $γω$ reaches several tens of keV, making it the dominant radiative mode. The ratios $Γ(G_0 \to γψ(2S))/Γ(G_0 \to γJ/ψ)$ and $Γ(G_0 \to γω)/Γ(G_0 \to γρ)$ are predicted to be 1-2.6 and 3.4-5.4, respectively, with mild parameter dependence. We also compare with hadronic decays and find that the total radiative decay width is lower than the hadronic decay widths by about one order of magnitude. We propose searching for $G_0$ in the sequential decay $Y(4230)\to γG_0 \to γωJ/ψ$, which is accessible to further experimental measurements by the BESIII, Belle II and LHCb Collaborations.

hep-ph↗

arXiv2026

Radiative decays of the isoscalar $S$-wave $D\bar D$ molecule

In the hadronic molecular picture, an isoscalar $S$-wave $D\bar{D}$ molecule is naturally expected as the spin-0 partner of $X(3872)$. Assuming this state, denoted by $X_0$, to be a pure $D\bar D$ molecule with quantum numbers $J^{PC}=0^{++}$, we investigate its radiative decays $X_0\toγV (V=ρ^0,ω)$ within an effective Lagrangian framework. The decay amplitudes are generated by intermediate charmed-meson loops, with electromagnetic gauge invariance consistently maintained throughout the calculation. We evaluate the partial decay widths and examine their dependence on the $X_0$ mass and the cutoff. Although the individual decay widths exhibit a sizable dependence on the cutoff, their ratio is remarkably stable. In particular, we obtain that the ratio for the decays $X_0\toγρ^0$ and $X_0\toγω$ is approximately 2.26, which is insensitive to the variation of the cutoff. This robust ratio provides a useful model-insensitive signature of the molecular structure of $X_0$.

hep-ph↗

arXiv2026

Production of hidden-charm molecular candidates in $ψ(4660)$ decays

We investigate the production of several hidden-charm exotic candidates, including $Z_c(3900)$, $Z_c(4020)$, $Z_{cs}(3985)$, and $Z_2(4250)$, in $ψ(4660)$ decays under the assumption that these states are predominantly hadronic molecules. Treating $ψ(4660)$ as a conventional $ψ(5S)$ charmonium state, the production mechanisms are described through intermediate charmed-meson triangle loops, with its couplings to charmed-meson pairs estimated within the quark model. A systematic analysis of the processes $ψ(4660)\to Z_c(3900)π$, $ψ(4660)\to Z_c(4020)π$, $ψ(4660)\to Z_{cs}(3985)K$, and $ψ(4660)\to Z_2(4250)π$ is performed within a unified framework. The predicted branching fractions are found to be of the order of $10^{-2}$, $10^{-4}$, $10^{-3}$, and $10^{-6}$, respectively, exhibiting only a mild dependence on the cutoff parameter. We further find that the contributions from the $SHH$ intermediate loops dominate over those from the $THH$ and $HHH$ loops in most channels. The sizable production rates obtained in this work indicate that $ψ(4660)$ decays provide a promising platform for probing the molecular nature of charged hidden-charm exotic states and testing their underlying production mechanisms.

hep-ph↗

arXiv2026

Radiative decays of $X(3872)$ within $D{\bar D}^*$ molecular framework

Within the framework of nonrelativistic effective field theory, we calculate the radiative decay width of the process $X(3872) \to \bar{D} D γ$ while taking into account the $D\bar{D}$ final-state interactions. In this work, the $X(3872)$, with the spin-parity quantum numbers $J^{PC}=1^{++}$, is treated as a $D^*\bar{D} +\rm c.c.$ bound state comprising equal proportions of neutral and charged components. Our numerical calculations predict the tree-level partial decay width of approximately $11.0$ keV for the decay process $X(3872) \to \bar{D}^0 D^0γ$, while the partial width for $X(3872) \to D^- D^+γ$ is less than $1.0$ keV. It is found that the $D\bar{D}$ rescattering effect enhances the tree-level width of $X(3872) \to \bar{D}^0 D^0γ$ by $6\%$. In contrast, the rescattering effect makes a suppression to the charged channel $X(3872)\to D^- D^+γ$ by roughly $38\%$. We expect that the present predictions based on the molecular picture of the $X(3872)$ can be tested by future experiments.

hep-ph↗

arXiv2026

Hunting for $B\bar B$ molecular state $X_{b0}$ via radiative transition of $Υ(10753)$

We investigate the radiative decay $Υ(10753) \to γX_{b0}$ within the framework of nonrelativistic effective field theory (NREFT). The $Υ(10753)$ is treated as an $S$-$D$ mixed state of the $Υ(4S)$ and $\YD$, while the $X_{b0}$ is interpreted as a weakly bound $B\bar{B}$ molecule with $J^{PC}=0^{++}$. The decay process was assumed to occur via the intermediate meson loops involving the $S$-wave $B^{(*)}$ and $P$-wave $B_1^{(\prime)}$ mesons. Our calculated results indicate that the decay $Υ(10753) \to γX_{b0}$ is dominated by the $B_1^{(\prime)}$ meson loops. The partial decay width is predicted to be $0.2-1.5~\mathrm{keV}$ for a binding energy range of $ε_X=0-10~\mathrm{MeV}$, corresponding to a branching fraction of $10^{-6}-10^{-5}$. The decay width is found to be insensitive to the full width of the $B_1^{\prime}$ meson. Our study suggests that the radiative decay of the $Υ(10753)$ is a promising channel to search for the $X_{b0}$ state, which is crucial for testing heavy-quark symmetries and understanding the exotic hadron spectrum in the bottom sector.

hep-ph↗

arXiv2026

Study of $χ_{cJ}\to ηηη^\prime$ via intermediate charmed meson loop mechanisms and its implications for non-observation of $η_1(1855)$ in $χ_{cJ}$ decays

Recently, the BESIII Collaboration reported the first observation of the decays $χ_{cJ} \to ηηη^\prime$ in order to search for the $1^{-+}$ exotic state $η_1(1855)$. A partial wave analysis of the $ηη^\prime$ invariant mass spectrum shows no significant signal for the $η_1(1855)$. In this work, we, using an effective Lagrangian approach, investigate the processes $χ_{cJ} \to ηηη^\prime$ via the box and triangle loops involving charmed mesons and the scalar meson $f_0(1500)$. Our calculations reproduce well the experimental branching fractions of $χ_{cJ} \to ηηη^\prime$. Furthermore, we present the predictions of the relevant invariant mass spectra of $ηη^\prime$ and $ηη$ produced in the $χ_{c1}$ decay, which seem overall consistent with the BESIII measurements. In the present model, the decay $χ_{c1} \to ηηη^\prime$ is dominated by the triangle and box loop contributions. The consistency between our theoretical results and the BESIII measurements sheds light on the underlying decay mechanism of the $χ_{cJ}$ decaying into light mesons and might be helpful to understand the absence of the $η_1(1855)$ signal in the decay channels $χ_{cJ} \to ηηη^\prime$.

hep-ph↗

arXiv2026

Dipion transitions from $X(3872)$ to $χ_{cJ}\ (J=0,1,2)$

In this work, we investigate the dipion transition processes $X(3872)\to ππχ_{cJ} (J=0,1,2)$ within the framework of heavy hadron chiral perturbation theory, treating $X(3872)$ as a molecular state composed of $D\bar{D}^*$+ H.c. components. By analyzing the box and triangle loop diagrams with the nonrelativistic effective field theory power-counting rule, we demonstrate that box diagrams dominate these dipion transition processes. Branching ratios are calculated as functions of the mixing angle $θ$, which parametrizes the neutral and charged meson compositions of the $X(3872)$. Our results indicate that the branching fractions for $X(3872)\toππχ_{c0}$, $X(3872)\to ππχ_{c1}$, and $X(3872)\to ππχ_{c2}$ are of the orders of $10^{-4}$, $10^{-3}$, and $10^{-5}$, respectively. We also predict the ratios ${\mathcal{B}[X(3872)\rightarrow ππχ_{c0/2}]}/{\mathcal{B}[X(3872)\rightarrow ππχ_{c1}]}$ and ${\mathcal{B}[X(3872)\rightarrow π^+π^-χ_{cJ}]}/{\mathcal{B}[X(3872)\rightarrow π^0π^0χ_{cJ}]}$. The latter deviates from isospin-symmetry expectations, revealing various degrees of isospin violation. By studying the $π^+π^-$ and $π^+χ_{cJ}$ invariant mass spectra, we find a double-bump structure in the $π^ + π^-$ invariant mass distributions of the process $X(3872)\to π^+π^-χ_{c1}$ and $π^+χ_{c0}$ invariant mass distribution of the process $X(3872)\to π^+π^-χ_{c0}$, which could be tested by future experimental measurements.

hep-ph↗

arXiv2025

Hadronic decays of possible pseudoscalar $P$-wave $D\bar{D}^\ast/\bar{D}D^\ast$ molecular state

Recently, the new structure $G(3900)$ observed by the BESIII Collaboration in the $e^+e^-\to D\bar{D}$ was identified to be the $P$-wave $D\bar{D}^\ast/\bar{D}D^\ast$ vector molecular resonance using a unified meson exchange model. Apart from the vector $P$-wave state, a possible pseudoscalar $P$-wave molecular state of the $D\bar{D}^\ast/\bar{D}D^\ast$ [called $G_0(3900)$ for short] was also predicted, which is likely to be observed in future experiments. Within the molecular framework, we calculated the partial decay widths for a series of hadronic decays of the $G_0$, including $G_0\to ω(ρ^0) J/ψ$, $π^+π^- η_c (1S)$, $π^+π^- χ_{c1} (1P)$, and $D^0\bar{D}^0π^0$. Under present model parameters, the hidden-charm decay modes are dominated by the $G_0\toωJ/ψ$ and $G_0\toπ^+π^-η_c (1S)$, and the partial widths can reach 1 MeV and 0.1 MeV, respectively. The open-charm channel $G_0\to D^0\bar{D}^0π^0$ exhibits a rather small decay rate ($\sim 0.1~\mathrm{keV}$). In terms of our present predictions, we suggest BESIII and Belle II to search for the pseudoscalar $P$-wave $D\bar{D}^\ast / \bar{D}D^\ast$ molecular state with $J^{PC} = 0^{-+}$ in the hidden-charm processes $G_0 \to ωJ/ψ$ or $G_0 \to π^+π^-η_c(1S)$.

hep-ph↗

arXiv2025

Light hadronic decays of spin-0 partner of $X(3872)$

The $X(3872)$ is theoretically predicted to have a spin-0 partner state denoted as $X_0$. Assuming the $X_0$ as a $D\bar{D}$ molecular bound state, we calculate the decay widths of $X_0\to VV$ and $X_0 \to PP$ ($V$ and $P$ stand for light vector and pseudoscalar mesons, respectively) via intermediate charmed meson loops. Three different configurations of the $X_0$, i.e., pure neutral components ($θ= 0$), isospin singlet ($θ= π/4$) and pure charged components ($θ= π/2$), are investigated. Within a commonly accepted range of the model parameter $α$, the predicted decay widths of $X_0 \to VV$ are on the order of a few hundred $\mathrm{keV}$, while the decay widths of $X_0 \to PP$ can reach several $\mathrm{MeV}$. The $X_0 \to ρρ$ and $ππ$ have larger decay rates. The relative width ratios between the channels are nearly model-independent. Moreover, among those channels only with isovector or isoscalar mesons, the relevant ratios are also independent of the phase angle. The predicted ratios are helpful for searching the $X_0$ in the future experiments at BESIII and Belle II.

hep-ph↗

arXiv2025

Hidden charmed decays of $X(3872)$ within the $D{\bar D}^*$ molecular framework

The dipionic transition of the $X(3872)$ to the $η_c$ was investigated using an effective Lagrangian approach. In this study, the $X(3872)$ was assumed to be a $D\bar{D}^\ast + \text{c.c.}$ bound state with the quantum numbers $J^{PC}=1^{++}$ and to decay via triangle and box loops. It is found that the partial decay widths arising from the box loops are one order of magnitude greater than those from the triangle ones. The decay widths are model-dependent, as characterized by the cutoff parameter introduced in the form factor. Moreover, the charged and neutral $D\bar{D}^\ast$ configurations of the $X(3872)$ and its mass also influence the decay widths. With our model parameters, the decay widths for the $X(3872)\toπ^+π^-η_c$ can reach up to several tens of keV. We hope that the current calculations within the molecular interpretation will be helpful for the future experiments.

hep-ph↗

arXiv2025

Investigation of box diagrams for the peak of $Z_{cs}(3985)$ in $e^+e^- \to D^-_s D^{0} K^+$ and $ D^{-}_s D^0 K^+$

The BESIII collaboration recently observed a charged hidden-charm structure with strangeness in the recoil mass spectrum of $K^+$ in the processes $e^+e^- \to D^-_s D^{*0} K^+$ or $D^{*-}_s D^0 K^+$, named as $Z_{cs}(3985)^-$. Within the energy region around the peak of $Z_{cs}(3985)$, various box diagrams are present. A systematic study of these box diagrams reveals the existence of a box singularity. Dalitz plots and invariant mass distributions of two charmed mesons from the box diagram for the processes $e^+e^- \to D^-_s D^{*0} K^+$ and $D^{*-}_s D^0 K^+$ are presented at five energy points $\sqrt s = 4.628,\,4.641,\,4.661,\,4.681$, and $4.698$ GeV. It is found that these box diagrams can generate peaks similar to those observed in experiments, suggesting that the peak of $Z_{cs}(3985)$ may be attributed to the box singularity contribution. Additionally, slight differences in the invariant mass spectra of $D^-_s D^{*0}$ and $D^{*-}_s D^0 K^+$ are identified based on the box diagrams, needing further experimental validation.

hep-ph↗

arXiv2025

Radiative decays of $X(3872)$ in $D{\bar D}^*$ molecule scenario

We investigate the radiative decays of the $X(3872)$ to $γV~(V=ρ^0,\, ω)$ in the molecule scenario, where the $X(3872)$ is regarded as a pure hadronic molecule of the $D\bar{D}^*+c.c$ in an $S$-wave with the quantum numbers $J^{PC}=1^{++}$. The radiative processes were assumed to occur via the triangle hadronic loops, and the relevant calculations were conducted using an effective Lagrangian approach. It is found that the absolute decay widths are model-dependent, but the relative width ratio is rather independent of the model parameter. Moreover, the calculated results indicate that the radiative decays of the $X(3872)$ are strongly influenced by the molecular configuration characterized by the proportion of the charged and neutral constituents. We hope that the present calculations could be tested by the experimental measurements.

hep-ph↗

arXiv2025

Production and decay of anticharmed pentaquark state with quark content $\bar{c}sudd$

We used an effective Lagrangian approach to investigate the production of the anticharmed pentaquark state $P_{\bar{c}s}^{(*)-}$ with the minimal quark content $\bar{c}sudd$ in the $Λ_b^0$ decay and its decay into the $ΛD^{(\ast)-}$ and $ΣD^{(\ast)-}$. In our calculation, the $P_{\bar{c}s}^{(*)-}$ is considered as the molecule state of the $nD_{s0(s1)}^{-}$ in an $S$ wave, and its production and decay occur via triangle loops at the hadron level. The predicted branching fractions for the processes $Λ_b^0\to P_{\bar{c}s}^{(*)-} D^+ $ are around $10^{-4}\sim 10^{-3}$. The partial decay widths of the $ P_{\bar{c}s}^{(*)-} \to ΛD^{(\ast)-}$ are between $0.1$ and $\sim 10~\mathrm{MeV}$, whereas the decay widths of the $ P_{\bar{c}s}^{(*)-} \to ΣD^{(\ast)-}$ are about one order of magnitude smaller. It is found that the width ratios for the $P_{\bar{c}s}^{(*)-}$ decays are nearly independent of the model parameter $α$. It is hoped that these predictions could be helpful in searching for the anticharmed-strange pentaquark candidates in future LHCb experiments.

hep-ph↗

arXiv2024

Pionic transitions of the spin-2 partner of $X(3872)$ to $χ_{cJ}$

We investigated the pionic transitions between the $X_2$ [spin-2 partner of the $X(3872)$] and $χ_{c1,2}$ using a nonrelativistic effective field theory. The $X_2$ is assumed to be a bound state of the $D^{*}$ and $\bar{D}^*$ mesons and to decay through several kinds of loops, including the bubble, triangle and box loops. Within the present model, the widths for the single-pion decays $X_2\toπ^0χ_{cJ}$ are predicted to be about $3$--$30$ keV. For the dipion decays, the widths are a few keVs. These widths yield a branching fraction of $10^{-3}$--$10^{-2}$. The ratio $R_{\mathrm{c}0}=Γ(X_2\toπ^+π^-χ_{cJ})/Γ(X_2\toπ^0π^0χ_{cJ}) \simeq 1.6$, which is a bit smaller than the expected value of $2$, and $R_{21}=Γ(X_2\toππχ_{c2})/Γ(X_2\toππχ_{c1}) \simeq 0.85$. These ratios are nearly independent of the $X_2$ mass and the coupling constants, which might be a good quantity for the experiments. Moreover, the invariant mass spectra of the $π^0χ_{cJ}$ final state for the dipion processes are presented, showing a cusp structure at the $D {\bar D}^*$ threshold enhanced and narrowed by the nearby triangle singularity.

hep-ph↗

arXiv2024

Charmless decays of the spin-2 partner of $X(3872)$

The Belle collaboration recently reported a promising candidate for the spin-2 $D^*\bar{D}^*$ partner of the $X(3872)$, called the $X_2$ for short, having a mass of $(4014.3 \pm 4.0 \pm 1.5)~\mathrm{MeV}$ and a width of $(4 \pm 11 \pm 6)~\mathrm{MeV} $. In present work, we assume the $X_2$ as a pure molecule of the $D^*\bar{D}^*$ under three cases, i.e., pure neutral components ($θ= 0$), isospin singlet ($θ= π/4$) and neutral components dominant ($θ= π/6$), where $θ$ is a phase angle describing the proportion of neutral and charged constituents. Using an effective Lagrangian approach, we calculated the partial widths of $X_2\to VV$ and $X_2 \to PP$ ($V$ and $P$ stand for light vector and pseudoscalar mesons, respectively). The predicted decay widths of $X_2 \to VV$ can reach a few hundreds of $\mathrm{keV}$, while the decay widths of $X_2 \to PP$ are about several tens of $\mathrm{keV}$. In addition, the effects from the proportion of neutral and charged constituent on the decay widths of $X_2\to VV$ and $PP$ are also investigated. We hope that the present calculations will be checked experimentally in the future.

hep-ph↗

arXiv2024

Production of $X_b$ via radiative transition of $Υ(10753)$

We studied the radiative transitions between the $Υ(10753)$, the $S$-$D$ mixed state of the $Υ(4S)$ and $Υ_1(3\,{}^3D_1)$, and the $X_b$, the heavy quark flavor symmetry counterpart of the $X(3782)$ in the bottomonium sector. The radiative transition was assumed to occur through the intermediate bottom mesons, including $P$-wave $B_1^{(\prime)}$ mesons as well as the $S$-wave $B^{(*)}$ ones. The consideration of the $B_1^{(\prime)}$ mesons leads to the couplings to be in $S$-wave, and hence enhances the contributions of the intermediate meson loops. The radiative decay width for the $Υ(10753)\toγX_b$ is predicted to be order of $10~\mathrm{keV}$, corresponding to a branching fraction of $10^{-4}$. Based on the theoretical results, we strongly suggest to search for the $X_b$ in the $e^+e^-\toγX_b$ with $X_b\toππχ_{b1}$ near $\sqrt{s}=10.754~\mathrm{GeV}$, and it is hoped that the calculations here could be tested by the future Belle II experiments.

hep-ph↗

arXiv2023

Hunting for the hidden-charm molecular states with strange quark in $B$ and $B_s$ decays

In the present work, we investigate the productions of the molecular states composed of $D^{(*)}_s \bar{D}^{(*)}$ and $D^{(*)}_s \bar{D}^{(*)}_s$ in the $B$ and $B_s$ decays by using an effective Lagrangian approach. The branching ratios in terms of the model parameter $α$ and the binding energy $ΔE$ are estimated. Our estimations indicate that the branching fractions are of the order of $10^{-4}$ and the relative ratios are very weakly dependent on the model parameter $α$ and the binding energy $ΔE$. The predicted ratios are helpful for searching the hidden-charm molecular states with strange quark in the future experiments at Belle II and LHCb.

hep-ph↗

arXiv2023

Production of $X_b$ via $Υ(5S, 6S)$ radiative decays

We investigate the production of $X_b$ in the process $Υ(5S,6S)\to γX_b$, where $X_b$ is assumed to be a $B {\bar B}^*$ molecular state. Two kinds of meson loops of $B^{(*)}{\bar B}^{(*)}$ and $B_1^{\prime}{\bar B}^{(*)}$ were considered. To explore the rescattering mechanism, we calculated the relevant branching ratios using the effective Lagrangian based on the heavy quark symmetry. The branching ratios for the $Υ(5S\,,6S) \to γX_b$ were found to be at the orders of $10^{-7} \sim 10^{-6}$. Such sizeable branching ratios might be accessible at BelleII, which would provide important clues to the inner structures of the exotic state $X_b$.

hep-ph↗