arXiv subjects

Ming-Zhu Liu

Publications and source records attributed to Ming-Zhu Liu.

At least 37 records · Page 2Linked to original sources

arXiv2024

Productions of $X(3872)$, $Z_c(3900)$, $X_2(4013)$, and $Z_c(4020)$ in $B_{(s)}$ decays offer strong clues on their molecular nature

The exotic states $X(3872)$ and $Z_c(3900)$ have long been conjectured as isoscalar and isovector $\bar{D}^*D$ molecules. In this work, we first propose the triangle diagram mechanism to investigate their productions in $B$ decays as well as their heavy quark spin symmetry partners, $X_2(4013)$ and $Z_c(4020)$. We show that the large isospin breaking of the ratio $\mathcal{B}[B^+ \to X(3872) K^+]/\mathcal{B}[B^0 \to X(3872) K^0] $ can be attributed to the isospin breaking of the neutral and charged $\bar{D}^*D$ components in their wave functions. For the same reason, the branching fractions of $Z_c(3900)$ in $B$ decays are smaller than the corresponding ones of $X(3872)$ by at least one order of magnitude, which naturally explains its non-observation. A hierarchy for the production fractions of $X(3872)$, $Z_c(3900)$, $X_2(4013)$, and $Z_c(4020)$ in $B$ decays, consistent with all existing data, is predicted. Furthermore, with the factorization ansatz we extract the decay constants of $X(3872)$, $Z_c(3900)$, and $Z_c(4020)$ as $\bar{D}^*D^{(*)}$ molecules via the $B$ decays, and then calculate their branching fractions in the relevant $B_{(s)}$ decays, which turn out to agree with all existing experimental data. The mechanism we proposed is useful to elucidate the internal structure of the many exotic hadrons discovered so far and to extract the decay constants of hadronic molecules,which can be used to predict their production in related processes.

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arXiv2023

Systematic studies of $DDKK$ and $D\bar{D}K\bar{K}$ four-hadron molecules

Assuming that $D_{s0}^{*}(2317)$ is a $DK$ molecular state with a binding energy of 45 MeV, we investigate the existence of four-hadron molecules, $DDKK$ and $D\Bar{D}K\Bar{K}$, with the Gaussian expansion method. Their binding energies are $138\sim155$ MeV and $123\sim163$ MeV below the mass thresholds of $DDKK$ and $D\Bar{D}K\Bar{K}$. The $D\Bar{D}K\Bar{K}$ state has a decay width of $36\sim54$ MeV due to the complex $K\Bar{K}$ interaction. Further theoretical studies of and experimental searches for such four-hadron molecules can help deepen the understanding of the nonperturbative strong interaction in a nontrivial way.

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arXiv2023

Stripping triangle loops: Discussion of $D_s^+\to ρ^+η\to π^+π^0η$ in $a_0(980)$ production

We address a general problem in the evaluation of triangle loops stemming from the consideration of the range of the interaction involved in some of the vertices, as well as the energy dependence of the width of some unstable particles in the loop. We find sizeable corrections from both effects. We apply that to a loop relevant to the $D_s^+ \to π^+ π^0 η$ decay, and find reductions of about a factor of $4$ in the mass distribution of invariant mass of the $πη$ in the region of the $a_0(980)$. The method used is based on the explicit analytical evaluation of the $q^0$ integration in the $d^4q$ loop integration, using Cauchy's residues method, which at the same time offers an insight on the convergence of the integrals and the effect of form factors and cutoffs.

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arXiv2023

Tribaryons with lattice QCD and one-boson exchange potentials

Motivated by the existence of two-body hadronic molecules composed of $ΩΩ$, $Ω_{ccc}Ω_{ccc}$ and $Ω_{bbb}Ω_{bbb}$ predicted by lattice QCD simulations, we use the Gaussian expansion method to investigate whether three-body systems composed of $ΩΩΩ$, $Ω_{ccc}Ω_{ccc}Ω_{ccc}$ and $Ω_{bbb}Ω_{bbb}Ω_{bbb}$ can bind with the two-body $^1S_0$ interactions provided by lattice QCD. Our results show that none of the three-body systems bind. On the other hand, we find that with the one-boson exchange potentials the $ΩΩΩ$ system develops a bound state, for which the $^5S_2$ interaction plays an important role. Our studies support the existence of the $\frac{3}{2}^+$ $ΩΩΩ$ bound state and the nonexistence of the $\frac{3}{2}^+$ $Ω_{ccc}Ω_{ccc}Ω_{ccc}$ and $Ω_{bbb}Ω_{bbb}Ω_{bbb}$ bound states, due to the suppressed $^5S_2$ interactions in heavier systems.

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arXiv2023

Production rates of hidden-charm pentaquark molecules in $Λ_b$ decays

The partial decay widths and production mechanism of the three pentaquark states, $P_ψ^{N}(4312)$, $P_ψ^{N}(4440)$, and $P_ψ^{N}(4457)$, discovered by the LHCb Collaboration in 2019, are still under debate. In this work, we employ the contact-range effective field theory approach to construct the $\bar{D}^{(*)}Σ_{c}^{(*)}$, $\bar{D}^{*}Λ_c$, $\bar{D}Λ_c$, $J/ψp$, and $η_c p$ coupled-channel interactions to dynamically generate the multiplet of hidde-charm pentaquark molecules by reproducing the masses and widths of $P_ψ^{N}(4312)$, $P_ψ^{N}(4440)$, and $P_ψ^{N}(4457)$. Assuming that the pentaquark molecules are produced in the $Λ_b$ decay via the triangle diagrams, where $Λ_{b}$ firstly decays into $D_{s}^{(\ast)}Λ_{c}$, then $D_{s}^{(\ast)}$ scatters into $\bar{D}^{(\ast)}K$, and finally the molecules are dynamically generated by the $\bar{D}^{(\ast)}Λ_{c}$ interactions, we calculate the branching fractions of the decays $Λ_b \to {P_ψ^{N}}K$ using the effective Lagrangian approach. With the partial decay widths of these pentaquark molecules, we further estimate the branching fraction of the decays $ Λ_b \to ( P_ψ^{N} \to J/ψp )K $ and $ Λ_b \to ( P_ψ^{N}\to \bar{D}^* Λ_c )K $. Our results show that the pentaquark states $P_ψ^{N}(4312)$, $P_ψ^{N}(4440)$, and $P_ψ^{N}(4457)$ as hadronic molecules can be produced in the $Λ_b$ decay, and on the other hand their heavy quark spin symmetry partners are invisible in the $J/ψp$ invariant mass distribution because of the small production rates. Our studies show that is possible to observe some of the pentaquark states in the $Λ_b\to \bar{D}^*Λ_c K$ decays.

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arXiv2023

Long-range $S$-wave $DD^*$ interaction in covariant chiral effective field theory

Motivated by the recent lattice QCD study of the $DD^*$ interaction at unphysical quark masses, we perform a theoretical study of the $DD^*$ interaction in covariant chiral effective field theory (ChEFT). In particular, we calculate the relevant leading-order two-pion exchange contributions. The results compare favorably with the lattice QCD results, supporting the conclusion that the intermediate-range $DD^*$ interaction is dominated by two-pion exchanges and the one-pion exchange contribution is absent. At a quantitative level, the covariant ChPT results agree better with the lattice QCD results than their non-relativistic counterparts, showing the relevance of relativistic corrections in the charm sector.

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arXiv2023

Distinguishing the spins of $P_c(4440)$ and $P_c(4457)$ with femtoscopic correlation functions

The spins of the pentaquark states $P_c(4440)$ and $P_c(4457)$ play a decisive role in unraveling their nature, but remain undetermined experimentally. Assuming that they are $Σ_c\bar{D}^{*}$ bound states, we demonstrate how one can determine their spins by measuring the $Σ_c^+\bar{D}^{(*)0}$ correlation functions. We show that one can use the $Σ_c^+\bar{D}^0$ correlation function to fix the size of the Gaussian source and then determine the strength of the $Σ_c^+\bar{D}^{*0}$ interaction of spin $1/2$ and $3/2$ and therefore the spins of the $P_c(4440)$ and $P_c(4457)$ states. The method proposed can be applied to decipher the nature of other hadronic molecules and thus deepen our understanding of the nonperturbative strong interaction.

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arXiv2022

Production rates of $D_{s}^{+}D_{s}^{-}$ and $D\bar{D}$ molecules in $B$ decays

Motivated by the recent discovery of a charmonium $X(3960)$ in $B$ decays by the LHCb Collaboration, the likely existence of two bound/virtual states (denoted by $ X_{s\bar{s}}$ and $ X_{q\bar{q}}$) below the $D_{s}^{+}D_{s}^{-}$ and $\bar{D}D$ mass thresholds has been re-examined recently. In this work, we employ the effective Lagrangian approach to calculate their production rates in $B$ decays utilizing triangle diagrams. Our results show that the production yields of $B^{+}\to X_{s\bar{s}} K^{+}$ and $B^{+}\to X_{q\bar{q}} K^{+}$ are of the order of $10^{-4}$, in agreement with the relevant experimental data, which indicates that, if the $D_{s}^{+}D_{s}^{-}$ and $\bar{D}D$ bound states indeed exist, they can be detected in $B$ decays. Moreover, we calculate the production rate of $B^{+}\to X(3960) K^{+}$ assuming that $X(3960)$ is a resonant state of $D_{s}^{+}D_{s}^{-}$ and find that it is also of the order of $10^{-4}$ but a bit smaller than that as a $D_s^+D_s^-$ bound state.

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arXiv2022

Production of $D^_{s0}(2317)$ and $D_{s1}(2460)$ in $B$ decays as $D^{()}K$ and $D^{(*)}_sη$ molecules

The molecular nature of $D_{s0}^{\ast}(2317)$ and $D_{s1}(2460)$ have been extensively studied from the perspective of their masses, decay properties, and production rates. In this work, we study the weak decays of $B \to \bar{D}^{(\ast)}D_{s0}^{*}(2317)$ and $B \to \bar{D}^{(\ast)}D_{s1}(2460)$ by invoking triangle diagrams where the $B$ meson first decays weakly into $\bar{D}^{(\ast)}D_{s}^{(\ast)}$ and $J/ψK$($η_{c}K$), and then the $D_{s0}^{\ast}(2317)$ and $D_{s1}(2460)$ are dynamically generated by the final-state interactions of $D_{s}^{(\ast)}η$ and $D^{(\ast)}K$ via exchanges of $η$ and $D^{(\ast)}$ mesons. The obtained absolute branching fractions of Br$[B \to \bar{D}^{(\ast)}D_{s0}^{*}(2317)]$ are in reasonable agreement with the experimental data, while the branching fractions of Br$[B \to \bar{D}^{(\ast)}D_{s1}(2460)]$ are smaller than the experimental central values by almost a factor of two to three. We tentatively attribute such a discrepancy to either reaction mechanisms missing in the present work or the likely existence of a relatively larger $c\bar{s}$ component in the $D_{s1}(2460)$ wave function.

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arXiv2022

Search for hidden-charm pentaquark states in three-body final states

The three pentaquark states, $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$, discovered by the LHCb Collaboration in 2019, are widely recognized as $\bar{D}^{(\ast)}Σ_{c}$ hadronic molecules. Together with their four $\bar{D}^{(*)}Σ_{c}^{\ast}$ partners dictated by heavy quark spin symmetry they present a complete multiplet of hadronic molecules of $\bar{D}^{(\ast)}Σ_{c}^{(\ast)}$. It is widely recognized that to understand their nature, other discovery channels play an important role. In this work, we investigate two three-body decay modes of the $\bar{D}^{(\ast)}Σ_{c}^{(\ast)}$ molecules. The tree-level modes proceed via off-shell $Σ_{c}^{(\ast)}$ baryons, $\bar{D}^{(\ast)}Σ_{c}^{(\ast)} \to \bar{D}^{(\ast)}\left(Σ_{c}^{(\ast)}\to Λ_{c}π\right)\to\bar{D}^{(\ast)}Λ_{c}π$, while the triangle-loop modes proceed through $\bar{D}^{\ast}Σ_{c}^{(\ast)}\to J/ψNπ$, $η_{c}Nπ$ via $\bar{D}Σ_{c}^{(\ast)}$ rescattering to $J/ψN$ and $η_{c}N$. Our results indicate that the decay widths of the $P_{c}(4457)$ and $\bar{D}^{(\ast)}Σ_{c}^{\ast}$ states into $\bar{D}^{(\ast)}Λ_{c}π$ are several MeV, as a result can be observed in the upcoming Run 3 and Run 4 of LHC. The partial decay widths into $\bar{D}^{(\ast)}Λ_{c}π$ of the $P_{c}(4312)$ and $P_{c}(4440)$ states range from tens to hundreds of keV. In addition, the partial decay widths of $\bar{D}^{\ast}Σ_{c}$ molecules into $J/ψN π$ and $η_c N π$ are several keV and tens of keV, respectively, and the partial decay widths of $\bar{D}^{\ast}Σ_{c}^{\ast}$ molecules into $J/ψN π$ vary from several keV to tens of keV. These three-body decay modes of the pentaquark states are of great value to further observations of the pentaquark states and to a better understanding of their nature.

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arXiv2022

Five-flavor pentaquarks and other light- and heavy-flavor symmetry partners of the LHCb hidden-charm pentaquark

The discovery of three pentaquark peaks -- the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ -- by the LHCb collaboration has a series of interesting consequences for hadron spectroscopy. If these hidden-charm objects are indeed hadronic molecules, as suspected, they will be constrained by heavy-flavor and SU(3)-flavor symmetries. The combination of these two symmetries will imply the existence of a series of five-flavor pentaquarks with quark content $\bar{b} c s d u$ and $b \bar{c} s d u$, that is, pentaquarks that contain each of the five quark flavors that hadronize. In addition, from SU(3)-flavor symmetry alone we expect the existence of light-flavor partners of the three $P_c$ pentaquarks with strangeness $S=-1$ and $S=-2$. The resulting structure for the molecular pentaquarks is analogous to the light-baryon octet -- we can label the pentaquarks as $P_{Q' \bar{Q}}^N$, $P_{Q' \bar{Q}}^Λ$, $P_{Q' \bar{Q}}^Σ$, $P_{Q' \bar{Q}}^Ξ$ depending on their heavy- and light-quark content (with $N$, $Λ$, $Σ$, $Ξ$ the member of the light-baryon octet to which the light-quark structure resembles and $Q'$, $\bar Q$ the heavy quark-antiquark pair). In total we predict $45$ new pentaquarks from heavy- and light-flavor symmetries alone, which extend up to $109$ undiscovered states if we also consider heavy-quark spin symmetry. If an isoquartet ($I={3/2}$) hidden-charm pentaquark is ever observed, this will in turn imply a second multiplet structure resembling the light-baryon decuplet: $P_{Q' \bar{Q}}^Δ$, $P_{Q' \bar{Q}}^{Σ^*}$, $P_{Q' \bar{Q}}^{Ξ^*}$, $P_{Q' \bar{Q}}^Ω$.

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arXiv2022

Hadronic molecules composed of a doubly charmed tetraquark state and a charmed meson

The three pentaquark states, $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$, discovered by the LHCb Collaboration in 2019, can be arranged into a complete heavy quark spin symmetry multiplet of hadronic molecules of $\bar{D}^{(\ast)}Σ_{c}^{(\ast)}$. In the heavy quark mass limit, the $Σ_{c}^{(\ast)}$ baryons can be related to the doubly charmed tetraquark states of isospin 1, i.e., $T_{\bar{c}\bar{c}}^{(\ast)}$( $T_{\bar{c}\bar{c}}^{0}$, $T_{\bar{c}\bar{c}}^{1}$, $T_{\bar{c}\bar{c}}^{2}$), via heavy antiquark diquark symmetry, which dictates that the $\bar{D}^{(\ast)}Σ_{c}^{(\ast)}$ interactions are the same as the $\bar{D}^{(\ast)}T_{\bar{c}\bar{c}}^{(\ast)}$ interactions up to { heavy antiquark diquark symmetry} breakings. In this work, we employ the contact-range effective field theory to systematically study the $\bar{D}^{(\ast)}T_{\bar{c}\bar{c}}^{(\ast)}$ systems, and we show the existence of a complete heavy quark spin symmetry multiplet of hadronic molecules composed of a doubly charmed tetraquark state and a charmed meson. These are a new kind of hadronic molecules and, if discovered, can lead to a better understanding of the many exotic hadrons discovered so far. In addition, we summarise the triply charmed hexaquark states formed by different combinations of hadrons. In particular, we show that $\barΩ_{ccc}{p}$ system can bind by the Coulomb force, which is analogous to a hydrogenlike atom.

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arXiv2022

$Z_{cs}(3985)$ in next-to-leading-order chiral effective field theory -- the first truncation uncertainty analysis

We revisit the $D_s^-D^{*0}$/$D_s^{*-}D^0$ interaction and the $Z_{cs}(3985)$ state in chiral effective field theory(EFT) up to the next-to-leading order. We examine the relative importance of the leading-order contact, one-eta exchange, next-to-leading-order contact, and two-kaon-exchange contributions. We show that the leading-order and next-to-leading-order contact contributions play the most important role such that the $Z_{cs}(3985)$ state qualifies as a $D_s^-D^{*0}$/$D_s^{*-}D^0$ resonance. On the other hand, the weak one-eta-exchange and weakly energy-dependent two-kaon-exchange contributions are less important in dynamically generating the $Z_{cs}(3985)$ state, indicating that chiral EFT is less predictive in the present situation. Furthermore, we apply the Bayesian method to estimate chiral truncation uncertainties and find that they are of similar magnitude as their statistical counterparts. Our study shows that if $Z_c(3900)$ exists, then SU(3)-flavor symmetry also predicts $Z_{cs}(3985)$ with a certain robustness, i.e., both can be accommodated in the chiral EFT with dominant contact contributions.

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arXiv2022

Multi-hadron molecules: status and prospect

Starting from 2003, the discovery of a large amount of the so-called exotic hadronic states, i.e., the $XYZ$ states, the pentaquark states as well as the tetraquark states, have not only revived studies of hadron spectroscopy, but also hinted at the existence of new multi-hadron states made of hadrons other than nucleons and hyperons. We briefly comment on some of the latest studies on multi-hadron molecules in the light and heavy flavor sectors and highlight what should be done in the future.

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arXiv2022

Triple-charm molecular states composed of $D^D^D$ and $D^D^D^*$

Inspired by the newly observed $T_{cc}^+$ state, we systematically investigate the $S$-wave triple-charm molecular states composed of $D^*D^*D$ and $D^*D^*D^*$. We employ the one-boson-exchange model to derive the interactions between $D(D^*)$ and $D^*$ and solve the three-body Schrödinger equations with the Gaussian expansion method. The $S$-$D$ mixing and coupled channel effects are carefully assessed in our study. Our results show that the $I(J^P)=\frac{1}{2}(0^-,1^-,2^-)$ $D^*D^*D$ and $I(J^P)=\frac{1}{2}(0^-,1^-,2^-,3^-)$ $D^*D^*D^*$ systems could form bound states, which can be viewed as three-body hadronic molecules. We present not only the binding energies of the three-body bound states, but also the root-mean-square radii of $D $-$D^*$ and $D^*$-$D^*$, which further corroborate the molecular nature of these states. These predictions could be tested in the future at LHC or HL-LHC.

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arXiv2022

Three-body molecules $\bar{D}\bar{D}^{\ast}Σ_{c}$- understanding the nature of $T_{cc}$, $P_{c}(4312)$, $P_{c}(4440)$ and $P_{c}(4457)$

The nature of the three pentaquark states, $P_{c}(4312)$, $P_{c}(4440)$ and $P_{c}(4457)$, discovered by the LHCb Collaboration in 2019, is still under debate, although the $\bar{D}^{(\ast)}Σ_{c}$ molecular interpretation seems to be the most popular. In this work, by adding a $\bar{D}$ meson into the $\bar{D}^{\ast}Σ_{c}$ pair, we investigate the mass and decay width of the three-body molecules $\bar{D}\bar{D}^{\ast}Σ_{c}$ and explore the correlation between the existence of the $\bar{D}\bar{D}^{\ast}Σ_{c}$ molecules with the existence of $\bar{D}^{(\ast)}Σ_{c}$ and $\bar{D}^{\ast}\bar{D}$ two-body molecules. The latter can be identified with the doubly charmed tetraquark state $T_{cc}$ recently discovered by the LHCb Collaboration. Based on the molecular nature of $P_{c}(4312)$, $P_{c}(4440)$, $P_{c}(4457)$, and $T_{cc}$, our results indicate that there exist two three-body bound states of $\bar{D}\bar{D}^{\ast}Σ_{c}$ with $I(J^{P})=1(1/2^{+})$ and $I(J^{P})=1(3/2^{+})$, and binding energies $37.24$ MeV and $29.63$ MeV below the $\bar{D}\bar{D}^{\ast}Σ_{c}$ mass threshold. In addition, we find that the mass splitting of these two three-body molecules are correlated to the mass splitting of $P_{c}(4440)$ and $P_{c}(4457)$, which offers a non-trivial way to reveal the molecular nature of these states. The partial widths of two $\bar{D}\bar{D}^{\ast}Σ_{c}$ molecules decaying into $J/ψp \bar{D}$ and $J/ψp \bar{D}^{\ast}$ are found to be several MeV. We recommend the experimental searches for the $\bar{D}\bar{D}^{\ast}Σ_{c}$ molecules in the $J/ψp \bar{D}$ and $J/ψp \bar{D}^{\ast}$ invariant mass distributions.

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arXiv2022

Can we understand the decay width of the $T_{cc}^+$ state?

Inspired by the recent discovery of a doubly charmed tetraquark state $T_{cc}^+$ by the LHCb Collaboration, we employ the effective Lagrangian approach to investigate the decay width of $T_{cc}^{+}\to D^{+} D^{0}π^{0}/D^{0} D^{0}π^{+}$ and $T_{cc}^{+}\to D^{0}D^{+}γ$ with the assumption that $T_{cc}^{+}$ is an isoscalar $DD^{\ast}$ molecule. We show that both the $T_{cc}\to D Dπ$ and $T_{cc}\to DDγ$ modes contribute to the decay width of $T_{cc}$, with the former being dominant. The resulting total decay width of about $Γ=63$ keV is smaller than the experimental decay width obtained from the Breit-Wigner fit of the LHCb data, $Γ=410\pm 165\pm 43^{+18}_{-38}$ keV, while close to the number obtained from the alternative unitary analysis, $Γ=48\pm 2^{+0}_{-14}$ keV, which supports the molecular nature of $T_{cc}$.

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arXiv2021

Masses and strong decays of open charm hexaquark states $Σ_{c}^{(\ast)}Σ_{c}^{(\ast)}$

Inspired by the recent discovery of the doubly charmed tetraquark state $T_{cc}^{+}$ by the LHCb Collaboration, we perform a systematic study of masses and strong decays of open charm hexaquark states $Σ_{c}^{(\ast)}Σ_{c}^{(\ast)}$. Taking into account heavy quark spin symmetry breaking, we predict several bound states of isospin $I=0$, $I=1$, and $I=2$ in the one boson exchange model. Moreover, we adopt the effective Lagrangian approach to estimate the decay widths of $Σ_{c}^{(\ast)}Σ_{c}^{(\ast)} \to Λ_{c}Λ_{c}$ and their relevant ratios via the triangle diagram mechanism, which range from a few MeV to a few tens of MeV. We strongly recommend future experimental searches for the $Σ_{c}^{(\ast)}Σ_{c}^{(\ast)}$ hexaquark states in the $Λ_cΛ_c$ invariant mass distributions.

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