arXiv subjects

Zi-Yang Lin

Publications and source records attributed to Zi-Yang Lin.

15 recordsLinked to original sources

arXiv2026

Decoding $Z_c(4430)$ and $Z_c(4200)$: The role of $P$-wave charmed mesons

In this work, we perform a systematic investigation of the hidden-charm tetraquark states with $I^G(J^{PC})=1^+(1^{+-})$ within the hadronic molecular picture, placing particular emphasis on systems composed of an $S$-wave $(D, D^*)$ meson and a $P$-wave $(D_0^*(2300), D_1(2430), D_1(2420), D_2^*(2460))$ meson. Adopting the One-Boson Exchange potential, we solve the Schr\"odinger equation in momentum space via the Complex Scaling Method. A crucial feature of our approach is the rigorous treatment of the unstable nature of the $P$-wave constituents by incorporating three-body decay effects arising from self-energy corrections and the static limit approximation. Our results demonstrate that these three-body dynamics play a crucial role in determining the pole positions, specifically in reproducing the large decay widths observed experimentally. We identify several broad resonances in the $D^*\bar{D}_1(2420)$ and $D^*\bar{D}_2^*(2460)$ systems as candidates for the $Z_c(4430)$, while the significantly broader resonances in the $D\bar{D}_0^*(2300)$ and $D\bar{D}_1(2430)$ sectors are suggested as candidates for the $Z_c(4200)$. Focusing on the $D^*\bar{D}_2^*(2460)$ assignment as a specific case study, we further analyze the line shape of the $Z_c(4430)$ candidate using a Flatt\'e-like parametrization with energy-dependent self-energy terms, providing predictions for its open-charm decay modes to guide future experimental searches.

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arXiv2025

Emergence of the exotic bottomoniumlike state $Y(10650)$ and support from Belle and Belle II data

Near-threshold exotic hadrons are usually associated with $S$-wave hadron-hadron dynamics, while higher partial waves are expected to be strongly suppressed by the centrifugal barrier. We show that this expectation can be overturned in the bottomonium sector. In a coupled-channel meson exchange framework combined with the complex scaling method, we find a $J^{PC}=1^{--}$ pole, denoted as $Y(10650)$, generated dominantly by the $P$-wave $B^*\bar B^*$ interaction and located close to the $B^*\bar B^*$ threshold. This pole naturally accounts for the anomalous enhancement observed just above the opening of the $B^*\bar B^*$ threshold in $e^+e^-\to B^*\bar B^*$. Once its production strength is fixed by this threshold enhancement, the corresponding cross sections of $\sigma[e^+e^-\to Y(10650)\to B\bar B^*]$ are predicted by the pole residues and phase-space factors, giving a characteristic dip-or-peak structure consistent with the available Belle (II) data. We further study the hidden-bottom transition $Y(10650)\to \Upsilon(2S)\eta$ through a near-threshold $B^*\bar B^*$ loop mechanism. The resulting $\mathcal{O}(10\sim100~\mathrm{keV})$ width for $Y(10650)\to \Upsilon(2S)\eta$ is sufficient to account for the corresponding cross sections measured by Belle II. The simultaneous appearance of this state in open- and hidden-bottom channels provides a direct experimental path to test a $P$-wave near-threshold mechanism and makes $Y(10650)$ a strong candidate for the first neutral isoscalar exotic bottomoniumlike state in the spectral gap between $\Upsilon(4S)$ and $\Upsilon(5S)$.

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arXiv2024

Double pole structures of $X_1(2900)$ as the $P$-wave $\bar{D}^K^$ resonances

We reveal the double pole structures of the manifestly exotic tetraquark state $X_1(2900)$ in the scenario of $P$-wave $\bar{D}^*K^*$ dimeson resonance. We find that the observed enhancement signal associated with $X_1(2900)$ in $B^+ \to D^+D^-K^+$ by LHCb contains two $P$-wave poles denoted as $T_{cs1-}(2900)$ and $T^{\prime}_{cs1-}(2900)$, respectively. After considering the channel couplings among the $\bar{D}K$, $\bar{D}^*K$, $\bar{D}K^*$ and $\bar{D}^*K^*$ and the width of the $K^*$ meson, the masses and widths of the $S$-wave pole $T_{cs0+}(2900)$ and two $P$-wave poles $T_{cs1-}(2900)$ and $T^{\prime}_{cs1-}(2900)$ coincide with those of the $X_0(2900)$ and $X_1(2900)$ remarkably, which provides strong support for identifying $X_0(2900)$ and $X_1(2900)$ as $\bar{D}^{(*)}K^{(*)}$ dimeson states. Furthermore, we extensively calculate all $S$-wave and $P$-wave $\bar{D}^{(*)}K^{(*)}$ systems up to $J=3$ and predict four new isoscalar charmed-strange dimeson-type tetraquark states: an $S$-wave state $T_{cs1+}(2900)$ with quantum number $J^P=1^+$, three $P$-wave states $T_{cs1-}(2760)$ with $J^P=1^-$, $T_{cs0-}(2760)$ with $J^P=0^-$ and $T_{cs2-}(2900)$ with $J^P=2^-$. These near-threshold poles can be searched for at LHCb, Belle II and BESIII.

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arXiv2024

Uncovering the mystery of $X(3872)$ with the coupled-channel dynamics

The $X(3872)$, as the first and the most crucial member in the exotic charmoniumlike $XYZ$ family, has been studied for a long time. However, its dynamical origin, whether stemming from a $D\bar{D}^*$ hadronic molecule or the first excited $P$-wave charmonium $\chi_{c1}(2P)$, remains controversial. In this Letter, we demonstrate that the $X(3872)$ definitely does not result from the mass shift of the higher bare $\chi_{c1}(2P)$ resonance pole in the coupled-channel dynamics involving a short-distance $c\bar{c}$ core and the long-distance $D\bar{D}^*$ channels. Instead, it originates from either the $D\bar{D}^*$ molecular pole or the shadow pole associated with the anti-resonance of the $P$-wave charmonium, depending on the weak or strong coupling mode, respectively. To differentiate these origins and fully exploit the nature of $X(3872)$, we conduct a comprehensive analysis in a couple-channel dynamics framework, including the isospin violation, the three-body $D\bar{D}\pi$ effect, the dynamical width of $D^*$, and non-open-charm decays of the bare $\chi_{c1}(2P)$. Our findings highlight the pivotal role of the coupled-channel dynamics in explaining the disparity between the pole widths of $X(3872)$ and $T_{cc}^+$, while also predicting a new resonance with $J^{PC}=1^{++}$ around 4.0 GeV. By matching the newly observed $\chi_{c1}(4010)$ by the LHCb Collaboration to our predicted resonance, we conclude that the $X(3872)$ most likely originates from the $D\bar{D}^*$ pole with a confidence level exceeding $99.7\%$.

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arXiv2024

Identification of the $G(3900)$ as the P-wave $D\bar{D}^/\bar{D}D^$ resonance

The BESIII Collaboration recently performed a precise measurement of the $e^+e^-\rightarrow D\bar{D}$ Born cross sections, and confirmed the $G(3900)$ structure reported by BaBar and Belle with high significance. We identify the $G(3900)$ as the first P-wave $\DDbar$ molecular resonance. The experimental and theoretical identification of the P-wave dimeson state holds paramount importance in enhancing our comprehension of the non-perturbative QCD and few-body physics. Its existence is firmly established in a unified meson-exchange model which simultaneously depicts the features of the $\chi_{c1}(3872)$, $Z_c(3900)$ and $T_{cc}(3875)$. This scenario can be directly examined in the $e^+e^-\rightarrow D\bar{D}^*/\bar{D}D^*$ cross section by seeing whether a resonance exists at the threshold. The credibility of the investigations is also ensured by the fact that the P-wave interaction dominantly arises from the well-known long-range pion exchange. Additionally, thanks to the centrifugal barrier, it is easier to form resonances in P-wave than in S-wave. We extensively calculate all systems up to P-wave with various quantum numbers and predict a dense population of the $\DDbar$ and $\DD$ states, where the S-wave $\DDbar$ state with $I^G (J^{PC})=0^- (1^{+-})$, P-wave $\DDbar$ state with $I^G(J^{PC})=0^+(0^{-+})$, and P-wave $\DD$ state with $I(J^P)=0(0^-)$ are more likely to be observed in experiments.

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arXiv2023

Cut structures and an observable singularity in the three-body threshold dynamics: the $T_{cc}^+$ case

The three-body threshold effect, the distinctive and intriguing non-perturbative dynamics in the low-energy hadron-hadron scattering, has acquired compelling significance in the wake of the recent observation of the double-charm tetraquark $T_{cc}^+$. This dynamics is characterized by the emergence of singular points and branch cuts within the interaction potential, occurring when the on-shell condition of the mediated particle is satisfied. The presence of these potential singularities indicates that the system is no longer Hermitian and also poses intractable challenges in obtaining exact solutions for dynamical scattering amplitudes. In this work, we develop a complex scaled Lippmann-Schwinger equation as an operation of analytical continuation of the $T$ matrix to resolve this problem. Through a practical application to the $DD^* \to DD^*$ process, we reveal complicated cut structures of the three-body threshold dynamics in the complex plane, primarily stemming from the one-pion exchange. Notably, our methodology succeeds in reproducing the $T_{cc}^+$ structure, in alignment with the quasi-bound pole derived from the complex scaling method within the Schr\"odinger equation framework. More remarkably, after solving the on-shell $T$ matrix on the positive real axis of momentum plane, we find an extra new structure in the $DD^*$ mass spectrum, which arises from a right-hand cut at a physical pion mass and should be observable in Lattice QCD simulations and future high-energy experiments.

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arXiv2023

Virtual states in the coupled-channel problems with an improved complex scaling method

We improve the complex scaling method (CSM) to obtain virtual states, which were previously challenging in the conventional CSM. Our approach solves the Schr\"odinger equation in the momentum space as an eigenvalue problem by choosing the flexible contours. It proves to be highly effective in identifying the poles across the different Riemann sheets in the multichannel scatterings. It is more straightforward and efficient than searching for the zeros of the Fredholm determinant of the Lippmann-Schwinger equation using the root-finding algorithms. This advancement significantly extends the capabilities of the CSM in accurately characterizing the resonances and virtual states in quantum systems.

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arXiv2023

$P_c$ states and their open-charm decays with the complex scaling method

A partial width formula is proposed using the analytical extension of the wave function in momentum space. The distinction of the Riemann sheets is explained from the perspective of the Schrodinger equation. The analytical form in coordinate space and the partial width are derived subsequently. Then a coupled-channel analysis is performed to investigate the open-charm branching ratios of the $P_c$ states, involving the contact interactions and one-pion-exchange potential with the three-body effects. The low energy constants are fitted using the experimental masses and widths as input. The $P_c(4312)$ is found to decay mainly to $\Lambda_c\bar{D}^*$, while the branching ratios of the $P_c(4440)$ and $P_c(4457)$ in different channels are comparable. Under the reasonable assumption that the off-diagonal contact interactions are small, the $J^P$ quantum numbers of the $P_c(4440)$ and the $P_c(4457)$ prefer $\frac{1}{2}^-$ and $\frac{3}{2}^-$ respectively. Three additional $P_c$ states at 4380 MeV, 4504 MeV and 4516 MeV, together with their branching ratios, are predicted. A deduction of the revised one-pion-exchange potential involving the on-shell three-body intermediate states is performed.

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arXiv2023

$Z_{cs}$, $Z_c$ and $Z_b$ states under the complex scaling method

We investigate the $Z_b$, $Z_c$ and $Z_{cs}$ states within the chiral effective field theory framework and the $S$-wave single channel molecule picture. With the complex scaling method, we accurately solve the Schr\"odinger equation in momentum space. Our analysis reveals that the $Z_b(10610)$, $Z_b(10650)$, $Z_c(3900)$ and $Z_c(4020)$ states are the resonances composed of the $S-$wave $(B\bar{B}^{*}+B^{*}\bar{B})/\sqrt{2}$, $B^{*}\bar{B}^*$, $(D\bar{D}^{*}+D^{*}\bar{D})/\sqrt{2}$ and $D^{*}\bar{D}^*$, respectively. Furthermore, although the $Z_{cs}(3985)$ and $Z_{cs}(4000)$ states exhibit a significant difference in width, these two resonances may originate from the same channel, the $S-$wave $(D_{s}\bar{D}^{*}+D_{s}^{*}\bar{D})/\sqrt{2}$. Additionally, we find two resonances in the $S-$wave $D_s^*\bar{D}^*$ channel, corresponding to the $Z_{cs}(4123)$ and $Z_{cs}(4220)$ states that await experimental confirmation.

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arXiv2022

A comparison between the $P_c$ and $P_{cs}$ systems

We construct the effective potentials of the $P_c$ and $P_{cs}$ states based on the SU(3)$_{\text{f}}$ symmetry and heavy quark symmetry. Then we perform the coupled-channel analysis of the lowest isospin $P_c$ and $P_{cs}$ systems. The coupled-channel effects play different roles in the $P_c$ and $P_{cs}$ systems. In the $P_c$ systems, this effect gives minor corrections to the masses of the $P_c$ states. In the $P_{cs}$ system, the $\Lambda_c\bar{D}_s-\Xi_c\bar{D}$ coupling will shift the mass of the $P_{cs}(4338)$ close to the $\Xi_c\bar{D}$ threshold. The $\Lambda_c\bar{D}^{(*)}_s-\Xi_c\bar{D}^{(*)}$ coupling will also produce extra $P_{cs}$ states. We discuss the correspondence between the $P_c$ and $P_{cs}$ states. Our results prefer that the SU(3) partners of the observed $P_{c}(4312)$, $P_{c}(4440)$, and $P_{c}(4457)$ in the $P_{cs}$ system have not been found yet.

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arXiv2022

Double-charm and hidden-charm hexaquark states under the complex scaling method

We investigate the double-charm and hidden-charm hexaquarks as molecules in the framework of the one-boson-exchange potential model. The multichannel coupling and $S-D$ wave mixing are taken into account carefully. We adopt the complex scaling method to investigate the possible quasibound states, whose widths are from the three-body decay channel $\Lambda_c\Lambda_c\pi$ or $\Lambda_c\bar{\Lambda}_c\pi$. For the double-charm system of $I(J^P)=1(1^+)$, we obtain a quasibound state, whose width is 0.50 MeV if the binding energy is -14.27 MeV. And the $S$-wave $\Lambda_c\Sigma_c$ and $\Lambda_c\Sigma_c^*$ components give the dominant contributions. For the $1(0^+)$ double-charm hexaquark system, we do not find any pole. We find more poles in the hidden-charm hexaquark system. We obtain one pole as a quasibound state in the $I^G(J^{PC})=1^+(0^{--})$ system, which only has one channel $(\Lambda_c\bar{\Sigma}_c+\Sigma_c\bar{\Lambda}_c)/\sqrt{2}$. Its width is 1.72 MeV with a binding energy of -5.37 MeV. But, we do not find any pole for the scalar $1^-(0^{-+})$ system. For the vector $1^-(1^{-+})$ system, we find a quasibound state. Its energies, widths and constituents are very similar to those of the $1(1^+)$ double-charm case. In the vector $1^+(1^{--})$ system, we get two poles -- a quasibound state and a resonance. The quasibound state has a width of 0.6 MeV with a binding energy of -15.37 MeV. For the resonance, its width is 2.72 MeV with an energy of 63.55 MeV relative to the $\Lambda_c\bar{\Sigma}_c$ threshold. And its partial width from the two-body decay channel $(\Lambda_c\bar{\Sigma}_c-\Sigma_c\bar{\Lambda}_c)/\sqrt{2}$ is apparently larger than the partial width from the three-body decay channel $\Lambda_c\bar{\Lambda}_c\pi$.

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arXiv2022

$T_{cc}^+$ and $X(3872)$ with the complex scaling method and $DD(\bar{D})\pi$ three-body effect

We use the leading order (LO) contact interactions and OPE potentials to investigate the newly observed double-charm state $T_{cc}^+$. The $DD\pi$ three-body effect is important in this system since the intermediate states can go on shell. We keep the dependence of the pion propagators on the center-of-mass energy, which results in a unitary cut of the OPE potential at the $DD\pi$ three-body threshold. By solving the complex scaled Schr\"odinger equation, we find a pole corresponding to the $T_{cc}^+$ on the physical Riemann sheet. Its width is around 80 keV and nearly independent of the choice of the cutoff. Assuming the $D\bar{D}\pi$ and $D\bar{D}^*$ channels as the main decay channels, we apply the similar calculations to the $X(3872)$, and find its width is even smaller. Besides, the isospin breaking effect is significant for the $X(3872)$ while its impact on the $T_{cc}^+$ is relatively small.

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arXiv2022

Double-charm tetraquark under the complex scaling method

The LHCb Collaboration discovered a double-charm tetraquark $T_{cc}^{+}$ with a very small width. We investigate the $T_{cc}^{+}$ as a $DD^{*}$ molecule with $J^{P}=1^{+}$ in the framework of the one-boson-exchange potential model. The isospin breaking effect and $S-D$ wave coupling are taken into account carefully. We adopt the complex scaling method (CSM) to study the $DD^{*}$ system and obtain a quasibound state corresponding to the $T_{cc}^{+}$. Its binding energy relative to the $D^{0}D^{*+}$ and width are $-354$ keV and $61$ keV respectively. The isospin breaking effect is found to be enormous, and the $S-$wave $D^{0}D^{*+}$ and $D^{+}D^{*0}$ components give dominant contributions with the probabilities of $72.1\%$ and $27.1\%$ respectively. In addition, we do not find any resonances in the $DD^{*}$ system. As a by-product, we study the $X(3872)$ as a $(D\bar{D}^*-D^*\bar{D})/\sqrt{2}$ molecule with $J^{PC}=1^{++}$. We also find a quasibound state corresponding to the $X(3872)$. Its binding energy relative to the $D^{0}\bar{D}^{*0}$ threshold and width are $-111$ keV and $26$ keV respectively. The $S-$wave $(D^{0}\bar{D}^{*0}-D^{*0}\bar{D}^{0})/\sqrt{2}$ component dominates this state with the probability of $92.7\%$.

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arXiv2022

Phase shifts of the light pseudoscalar meson and heavy meson scattering in heavy meson chiral perturbation theory

We calculate the complete $T$ matrices of the elastic light pseudoscalar meson and heavy meson scattering to the third order in heavy meson chiral perturbation theory. We determine the low-energy constants by fitting the phase shifts and scattering lengths from lattice QCD simulations simultaneously and predict the phase shifts at the physical meson masses. The phase shifts in the $D\pi(I=1/2)$, $DK(I=0)$, $D\bar{K}(I=0)$, $D_s\bar{K}$, $D\eta$ and $D_s\eta$ $S$ waves are so strong that bound states or resonances may be generated dynamically in all these channels. The $DK(I=0)$ channel corresponds to the well-known exotic state $D_{s0}^{*}(2317)$. The $DK(I=0)$ channel corresponds to the well-known exotic state $D_{s0}^{*}(2317)$. The coupled-channel $D\pi$, $D\eta$ and $D_s\bar{K}$ scattering corresponds to $D_{0}^{*}(2400)$. The coupled-channel $D\pi$, $D\eta$ and $D_s\bar{K}$ scattering corresponds to $D_{0}^{*}(2400)$. We also predict the scattering lengths and scattering volumes and observe good convergence in the scattering volumes. Our calculations provide a possibility to accurately investigate the exotic state in the light pseudoscalar meson and heavy meson interactions.

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arXiv2021

Light pseudoscalar meson and heavy meson scattering lengths to $\mathcal{O}(p^4)$ in heavy meson chiral perturbation theory

We calculate the threshold $T$ matrices of the light pseudoscalar meson and heavy meson scattering to fourth order in heavy meson chiral perturbation theory. We determine the low-energy constants by fitting to the lattice QCD data points through both the perturbative and iterated methods and obtain the physical scattering lengths in both formalisms. The values of the scattering lengths tend to be convergent at fourth order for most of the channels in the perturbative method. The value of the scattering length for the channel $DK (I=0)$, which involves the bound state $D_{s0}^{*}(2317)$, is obtained correctly in the iterated method. Based on the heavy diquark-antiquark symmetry, we also estimate the meson and doubly charmed (bottom) baryon scattering lengths, and find that the bound states can be generated with high probability in the channels $\bar{K}\Xi_{cc}(I=0)$ and $\bar{K}\Xi_{bb}(I=0)$. We strongly urge the LHCb Collaboration to look for the very narrow $\bar{K}\Xi_{cc}$ state with $IJ^P=0{1\over 2}^-$ through either the electromagnetic decay or the iso-spin violating strong decay $\Omega_{cc} \pi$.

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