arXiv subjects

Ming-Zhu Liu

Publications and source records attributed to Ming-Zhu Liu.

At least 19 recordsLinked to original sources

arXiv2026

Probing direct $CP$ violation in $Λ_b^0 \to P_c^+ h^-$ $(h=π,K)$ with final-state rescattering

The LHCb Collaboration recently reported a measurement of the difference in direct CP asymmetries for the decays $Λ_b^0 \to J/ψ\, p \, h^-$ (with $h = K, π$), offering new experimental constraints on the decay dynamics of heavy baryons into charmonium final states. Inspired by these findings, we explore the branching ratios and direct CP violations for the decays $Λ_b^0 \to P_c^+(4312, 4440, 4457)\,h^-$ within the framework of final-state rescattering. Our analysis indicates that the branching fractions for $Λ_b^0 \to P_c^+ π^-$ lie around the $10^{-6}$ level, with the corresponding direct CP asymmetries approaching approximately $1\%$. In contrast, the direct CP violation for the decay $Λ_b^0 \to P_c^+ K^-$ is found to be very small, while its branching ratios show a strong dependence on the spin assignments of the $P_c$ states. These predictions may provide useful guidance for more precise CP measurements and amplitude analyses in the $P_c$ region in future experiments.

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arXiv2026

Decay constants of the two-pole $D_0^*(2300)$

The nature of the scalar charmed meson $D_0^*(2300)$ remains one of the most intriguing states in hadron spectroscopy. A prominent interpretation is a two-pole structure generated by the coupled channels $Dπ$, $Dη$, $D_s\bar K$, and $Dη'$, in which the lower pole couples mainly to $Dπ$ and the higher pole to $D_s\bar K$. Following this picture, we calculate the decay constants of these two poles using the effective Lagrangian approach. The resulting values, $f_{D_0^*}^{(\mathrm{lower})}=64.6^{+0.9}_{-1.0}\,\mathrm{MeV}$ and $f_{D_0^*}^{(\mathrm{higher})}=80.8^{+9.6}_{-5.3}\,\mathrm{MeV}$, are substantially smaller than those predicted by conventional $c\bar q$ excited-state scenarios. This difference suggests that decay constants can serve as a sensitive probe to discriminate between different internal structures of the $D_0^*(2300)$. As a phenomenological application, we further predict the branching fractions for the Cabibbo-favored decays $B_s \to D_s D_0^*$, $Λ_b \to Λ_c D_0^*$, and $Ξ_b \to Ξ_c D_0^*$ within the factorization approach. These predictions provide crucial tests to validate the two-pole interpretation of the $D_0^*(2300)$.

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arXiv2026

Probing the structure of the $D_{s 0}^*(2317)$ and $X(3872)$ states through correlation functions

Over the past 20 years, many new hadron states have been discovered, but understanding their nature remains a key experimental and theoretical challenge. Recent studies have established that hadron-hadron interactions primarily govern the generation of new hadronic states, with their spectroscopy serving as a powerful tool for probing these interactions and determining the corresponding compositeness. In this work, we study four scenarios to determine the $DK$ interaction by reproducing the mass of the $D_{s0}^*(2317)$, i.e., assuming the $D_{s0}^*(2317)$ as a $DK$ molecule, a mixture of a $DK$ molecule and a bare state, a $DK-D_sη$ molecule, and a mixture of a $DK-D_sη$ molecule and a bare state. Using the $D^{0}K^{+}$ interactions derived from these scenarios, we predict the $D^{0}K^{+}$ correlation functions. Our results demonstrate that the lineshape of the $D^{0}K^{+}$ correlation function is sensitive to the admixture effects from the coupled-channel $D^+K^0$ and the bare state. Furthermore, we find that the $D^{0}K^{+}$ correlation function can probe the position of the bare state, if such a QCD bare state exists. Using the shallow-bound state candidate $X(3872)$ as input, we study the $D^0\bar{D}^{*0}$ correlation functions. These functions are highly sensitive to short-range dynamics and bare-state admixtures, resulting in clearly distinguishable correlation-function line shapes across different values of compositeness.

hep-ph↗

arXiv2026

Solving the Inverse Source Problem in Femtoscopy with a Toy Model

Hadron-hadron interactions, as a non-perturbative effect, play a significant role in understanding phenomenological problems in particle physics. Femtoscopy is a powerful tool in heavy-ion collision experiments, enabling the extraction of hadron-hadron interactions via momentum-correlation functions (CFs). These CFs are generally factorized into a convolution of source functions and hadron-hadron wave functions, with the latter encoding information about hadron-hadron interactions. However, source functions remain ambiguous and are commonly approximated by a Gaussian form. Reconstructing source functions from experimental correlation data constitutes an ``inverse problem." To address it, we propose a toy model based on the Tikhonov regularization. Employing a square potential well of four distinct potential strengths, we calculate the CFs for inputs of a Gaussian source function and its hybrid form. The obtained CFs are subsequently used to reconstruct the source functions via the Tikhonov regularization. Our results demonstrate that the Gaussian source function can be successfully reconstructed, indicating the potential of this approach for extracting realistic source functions of hadron pairs of interest in the future.

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arXiv2026

Probing the three-body force in hadronic systems with specific charge parity

Three-body forces, a type of non-perturbative strong interaction, are widely studied in nuclear physics. However, whether their inclusion is necessary in nuclear systems remains a topic of intense debate. In this letter, we propose that the existence of three-body forces in certain three-body hadronic systems with definite $C$-parity is certain. Such systems consist of two components whose interactions are mediated by three-body forces--a mechanism not easily realized in conventional three-nucleon systems. We investigate two specific three-body hadronic systems, $\bar{D}_sDK$ and $\bar{D}^*Dη$, using contact-range potentials. The two-body hadron-hadron interactions are constrained by reproducing their scattering lengths, while the three-body couplings are constrained by charge symmetry. Our results indicate that three-body forces play a minor role in binding the $I(J^{PC})=0(0^{--})$ $\bar{D}_sDK$ system, but a crucial one in binding the $I(J^{PC})=0(1^{-+})$ $\bar{D}^*Dη$ system. In fact, three-body forces determine whether $\bar{D} ^*Dη$ forms a bound state, making this system a promising candidate for exploring three-body forces in hadronic physics.

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arXiv2025

$J/ψΛ$ femtoscopy and the nature of $P_{ψs}^Λ(4338)$

Over the past two decades, numerous exotic hadron states have been discovered, yet their underlying nature remains unclear. It is widely acknowledged that understanding hadron-hadron interactions is essential to unraveling their properties. Hadron spectroscopy is a powerful tool for this endeavor, providing rich experimental data that can shed light on exotic systems. Recently, the LHCb experiment analyzed the process $B^{-} \rightarrow J/ψΛ\bar{p}$ and observed a narrow peak in the $J/ψΛ$ invariant mass spectrum, regarding it as a candidate for a pentaquark. In this work, we extract the coupled-channel $J / ψΛ-\bar{D} Ξ_c-\bar{D}_s Λ_c$ potential based on the $J/ψΛ$ invariant mass spectrum. Our results indicate the existence of a bound state below the $\bar{D} Ξ_c$ mass threshold, corresponding to the experimentally measured state $P_{cs}(4338)$. Furthermore, we predict the scattering lengths and momentum correlation functions for the $J/ψΛ$ and $\bar{D}Ξ_c$ channels, which serve as theoretical references for future femtoscopy experiments.

hep-ph↗

arXiv2025

Femtoscopy can tell whether $Z_c(3900)$ and $Z_{cs}(3985)$ are resonances or virtual states

There have been extended and heated discussions on the nature of the two exotic states, $Z_c(3900)$ and $Z_{cs}(3985)$, particularly whether they are near-threshold resonances, virtual states, or bound states. In this work, we demonstrate for the first time that the femtoscopic technique can be employed to distinguish between these three scenarios. More concretely, based on the Koonin-Pratt formula with a Gaussian source, we show that the low-momentum $D^0D^{*-}$/$D^0D_s^{*-}$ correlation functions significantly differ in the three scenarios. The high-momentum results exhibit distinct characteristics in the resonant and virtual state scenarios, especially in small collision systems of 1 fm, as produced in $pp$ collisions at the LHC. We hope that these discoveries will stimulate further experimental studies and help clarify the nature of the many exotic states that have been discovered.

hep-ph↗

arXiv2025

Productions of $T_{cc}$ and its SU(3)-flavor symmetry and heavy quark spin symmetry partners in $B_c$ decays

Inspired by the observation of the doubly charmed tetraquark state $T_{cc}$ at $pp$ collisions in the inclusive processes, we systematically investigate the production of doubly charmed tetraquark states in exclusive $B_c$ decays. In this work, we assume the $T_{cc}$ as a $DD^*$ bound state, and then predict the masses of its heavy quark spin symmetry partner $D^*D^*$ (denoted by $T_{cc}^{*}$) as well as their SU(3)-flavor symmetry partners, i.g., $D_sD^*/D_s^*D$ (denoted by $T_{ccs}^{+}$ and $T_{ccs}^{++}$) and $D^*D_s^*$ (denoted by $T_{ccs}^{*+}$ and $T_{ccs}^{*++}$), using the contact range effective field theory. Within the molecular picture, we compute their partial decays and production rates in $B_c$ meson decays. We identify the decays $B_c \to D^0D^0π^+\bar{D}^0 $ and $B_c \to D_s^+ D^{0} π^+{D}^{-}$ as promising channels to observe the tetraquark states $T_{cc}^{(*)}$ and $T_{ccs}^{(*)++}$, respectively. Finally, by combining these results with $B_c$ production cross sections, we estimate the expected event yields for these states in the upcoming LHC Run 3 and 4. Our results indicate that the $T_{ccs}^{+}$ and $T_{ccs}^{*++}$ states are likely to be observed in $B_c$ decays, while it is quite difficult for the $T_{cc}$ and $T_{cc}^{*}$ states.

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arXiv2025

Charmonium-nucleon femtoscopic correlation function

This study investigates the femtoscopic correlation functions of charmonium-nucleon pairs, utilizing the lattice QCD phase shifts provided by the HAL QCD Collaboration. A ``model-independent'' formalism is employed to transform scattering phase shifts directly into momentum correlation functions, thereby circumventing the approximations inherent in traditional methods, such as the Lednický-Lyuboshits model. The $J/ψ$-$p$ correlation functions, including spin-averaged and partial-wave results, are predicted using near-physical pion mass lattice results. The $η_c$-$p$ correlation function is calculated for the first time. The derived correlation functions provide critical references for future experiments, such as those at the LHC, where high-precision measurements of charmonium-nucleon correlations could unveil valuable insights into non-perturbative QCD dynamics.

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arXiv2025

Implication of the existence of $J^{PC}=0^{--}$ $\bar{D}_sDK$ bound state on nature of $D_{s0}^*(2317)$ and new configuration of exotic state

The discovery of numerous new hadrons over the past two decades has provided unprecedented opportunities to understand the non-perturbative QCD and hadron structure. Hadronic molecule picture plays an important role in explaining these new hadrons and enriching the configurations of exotic hadronic states. In this letter, using the model-independent $DK$ potential extracted from the relevant experimental data, a $J^{PC}=0^{--}$ $\bar{D}_sDK$ three-body hadronic molecule is predicted with a mass of $4310^{+14}_{-24}$ MeV. This state shows decoupling to conventional $c\bar{c}$ charmonia or the $\bar{D}_s D_{s0}^*(2317)$ two-body molecular state. It can be regarded as a compelling three-body hadronic molecular candidate. We further demonstrate that the $B^+ \to {D}^{*\pm}D^\mp K^+$ decays could be promising channels for searching for the predicted state in future high-luminosity LHCb runs.

hep-ph↗

arXiv2025

$B$ meson decays to vector charmonium(like) states and a $K$ meson: the role of final-state interactions

A series of vector charmonium(like) states, accompanied by a $K$ meson, have been observed in the decays of $B$ meson. These processes are color-suppressed at the quark level, as inferred from topological diagram analysis. In this work, we calculate the branching fractions of the decays $B \to ψK$, where $ψ$ denotes the charmonium(like) states $ψ(1S)$, $ψ(2S)$, $ψ(4040)$, $ψ(3770)$, and $ψ(4160)$. Our analysis incorporates both short-distance (naive factorization approach) and long-distance (final-state interactions) contributions. Within reasonable parameters, our results align with experimental data except for the $ ψ(4160)$, suggesting its possible exotic nature. Furthermore, we find that long-distance contributions dominate these decay processes, highlighting the crucial role of final-state interactions in the productions of charmonium(like) states in $B$ decays.

hep-ph↗

arXiv2025

Exploring the nature of $Y(4230)$ and $Y(4360)$ in B decays

Vector charmonium states can be directly produced in the $e^+e^{-}$ annihilation process. Among them, $Y(4230)$ and $Y(4360)$ splitting from the previously discovered $Y(4260)$ are not easily arranged into the conventional charmonium spectrum, while recent studies have indicated that they have strong couplings to $D\bar{D}_1$ and $D^*\bar{D}_1$. In this work, we investigate the production of $Y(4230)$ and $Y(4360)$ as the heavy-quark spin symmetry doublet hadronic molecules of $D\bar{D}_1$ and $D^*\bar{D}_1$ in $B$ decays via the triangle diagram mechanism. In particular, we propose that the decay constants of $Y(4230)$ and $Y(4360)$ extracted in $B$ decays are useful for clarifying their nature.

hep-ph↗

arXiv2024

Three ways to decipher the nature of exotic hadrons: multiplets, three-body hadronic molecules, and correlation functions

In the past two decades, a plethora of hadronic states beyond the conventional quark model of $q\bar{q}$ mesons and $qqq$ baryons have been observed experimentally, which motivated extensive studies to understand their nature and the non-perturbative strong interaction. Since most of these exotic states are near the mass thresholds of a pair of conventional hadrons, the prevailing picture is that they are primarily hadronic molecules. In principle, one can verify the molecular nature of these states by thoroughly comparing their masses, decay widths, and production rates in a particular picture with experimental data. However, this is difficult or impossible. First, quantum mechanics allows for the mixing of configurations allowed by symmetries and quantum numbers. Second, data are relatively scarce because of their small production rates and the many difficulties in the experimental measurements. As a result, other alternatives need to be explored. This review summarizes three such approaches that can help disentangle the nature of the many exotic hadrons discovered. In the first approach, based on the molecular interpretations for some exotic states, we study the likely existence of multiplets of hadronic molecules related by various symmetries, such as isospin symmetry, SU(3)-flavor symmetry, heavy quark spin/flavor symmetry, and heavy antiquark diquark symmetry. In the second approach, starting from some hadronic molecular candidates, one can derive the underlying hadron-hadron interactions. With these interactions, one can study related three-body systems and check whether three-body bound states/resonances exist. In the third approach, one can turn to the femtoscopy technique to derive the hadron-hadron interactions, hence inaccessible. This technique provided an unprecedented opportunity to understand the interactions between unstable hadrons.

hep-ph↗

arXiv2024

Studying the heavy quark spin symmetry multiplet of hadronic molecules $\bar{D}^{()}Σ_c^{()}$ in the three-body decays of $\bar{D}^{(*)}Λ_c π$

The decay behavior of an exotic state can be used to probe its internal structure. We note that the hidden-charm pentaquark states, $P_ψ^{N}(4312)$, $P_ψ^{N}(4440)$, and $P_ψ^{N}(4457)$, have only been observed in the $J/ψp$ channel. In this work, we employ the effective Lagrangian approach to systematically investigate the two-body and three-body decays of the heavy quark spin symmetry multiplet of hadronic molecules $\bar{D}^{(*)}Σ_c^{(*)}$. Our results show that the partial decay widths of the hidden-charm pentaquark molecules into $\bar{D}^{(*)}Λ_c π$ are sizable so that $\bar{D}^{(*)}Λ_c π$ are promising channels to search for them, which can help clarify their molecular nature.

hep-ph↗

arXiv2024

Productions of $X(3872)$/$Z_c(3900)$ and $X_2(4013)$/$Z_c(4020)$ in $Y(4220)$ and $Y(4360)$ decays

The two excited vector charmonium states $Y(4220)$ and $Y(4360)$ are difficult to be understood as pure $c\bar{c}$ charmonium states. Since they are located close to the mass thresholds of $\bar{D}D_{1}$ and $\bar{D}^*D_{1}$, they can be viewed as $\bar{D}D_{1}$ and $\bar{D}^*D_{1}$ molecules. Furthermore, recent studies indicated that the exotic states $X(3872)$/$Z_c(3900)$ and $X_2(4013)$/$Z_c(4020)$ are the isoscalar/isovector $\bar{D}D^{*}$ and isoscalar/isovector $\bar{D}^*D^{*}$ molecules, respectively. In this work, in the molecular picture, we employ the triangle diagram mechanism to study the productions of $ Z_{c}(3900) $ and $X(3872)$ in the pionic and radiative decays of $Y(4220)$, as well as their heavy-quark spin symmetry (HQSS) partners, i.e., the productions of $Z_{c}(4020)$ and $X_2(4013)$ in the pionic and radiative decays of $Y(4360)$. Using the effective Lagrangian approach, we obtain the ratios of the branching fractions $\mathcal{B}[Y(4360) \to Z_c(4020)π]/\mathcal{B}[Y(4220)\to Z_c(3900)π]=1.2$ and $\mathcal{B}[Y(4360)\to X_2(4013) γ]/\mathcal{B}[Y(4220)\to X(3872)γ]=0.5$, almost independent of model parameters, which indicate that the productions of $X_2(4013)$ and $Z_c(4020)$ in the radiative and pionic decays of $Y(4360)$ are likely to be measured in the future. The experimental studies of the predicted decay modes will help verify the molecular nature of $X(3872)$, $Z_c(3900)$, and $Y(4220)$. We hope the present work can stimulate experimental and further theoretical studies on these decay modes.

hep-ph↗

arXiv2024

Implication of a negative effective range on the $D\bar{D}^*$ interaction and the nature of $X(3872)$

A recent analysis of the LHCb data [Phys. Rev. D 105 (2022) L031503] obtained a sizable negative effective range for the $X(3872)$. This has attracted intensive discussions on whether $X(3872)$ can be deemed as a $D\bar{D}^*$ molecular state. This work explicitly demonstrates that the negative effective range of the $X(3872)$ does not contradict the molecular picture, adopting an effective field theory formulation of the $D\bar{D}^*$ interaction that can simultaneously reproduce the binding energy and effective range of the $X(3872)$. We elaborate on the implications of the large negative effective range of $X(3872)$ and the small binding energy on the underlying $D\bar{D}^*$ interaction. Such results are relevant for a better understanding of hadronic molecules and their binding mechanism.

hep-ph↗

arXiv2024

Investigations on the weak decays of $D\bar{B}$ molecules

The decays of exotic states discovered experimentally always proceed via the strong and electromagnetic interactions. Recently, a tetraquark state with the quark content $bc\bar{q}\bar{q}$ was predicted by Lattice QCD simulations. It is below the mass threshold of $D\bar{B}$, which can only decay via the weak interaction. In this work, based on the decay mechanism of $T_{cc}$ as a $DD^*$ molecule, we propose that the decays of the $bc\bar{q}\bar{q}$ tertaquark state as a $D\bar{B}$ molecule proceed via the Cabibbo-favored weak decays of the $\bar{B}$ or $D$ meson, accompanied by the tree-level decay modes and the triangle decay modes. Our results indicate that the branching fraction of the $D\bar{B}$ molecule decaying into $π^+ K^{-} \bar{B}^0$ is sizable, which is a good channel to observe the $D\bar{B}$ molecule in future experiments.

hep-ph↗

arXiv2024

Productions of $D^*_{s0}(2317)$ and $D_{s1}(2460)$ in $B_{(s)}$ and $Λ_b(Ξ_b)$ decays

Recent studies show that $D_{s0}^{\ast}(2317)$ and $D_{s1}(2460)$ contain large molecular components. In this work, we employ the naive factorization approach to calculate the production rates of $D_{s0}^{\ast}(2317)$ and $D_{s1}(2460)$ as hadronic molecules in $B_{(s)}$ and $Λ_b(Ξ_b)$ decays, where their decay constants are estimated in the effective Lagrangian approach. With the so-obtained decay constants $f_{D_{s0}^{\ast}(2317)}$ and $f_{D_{s1}(2460)}$, we calculate the branching fractions of the $b$-meson decays $B_{(s)}\to \bar{D}_{(s)}^{(*)}D_{s0}^*$ and $B_{(s)}\to \bar{D}_{(s)}^{(*)}D_{s1}$ and the $b$-baryon decays $Λ_b(Ξ_{b}) \to Λ_c(Ξ_{c}) D_{s0}^*$ and $Λ_b(Ξ_{b}) \to Λ_c(Ξ_c) D_{s1}$. Our results show that the production rates of $D_{s0}^{\ast}(2317)$ and $D_{s1}(2460)$ in the $B_s$, $Λ_b$ and $Ξ_b$ decays are rather large that future experiments could observe them. In particular, we demonstrate that one can extract the decay constants of hadronic molecules via the triangle mechanism because of the equivalence of the triangle mechanism to the tree diagram established in calculating the decays $B \to \bar{D}^{(*)}D_{s0}^{\ast}(2317)$ and $B \to \bar{D}^{(*)}D_{s1}(2460)$.

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