The production of heavy-quark (HQ) jets is a new area that addresses the mass effect of jet quenching in heavy-ion physics. This paper presents a theoretical study of HQ jet yield suppression in Pb+Pb collisions at the Large Hadron Collider (LHC) and focuses on the energy loss of HQ jets produced by different mechanisms. The $\textit{p+p}$ baseline is provided by the generator simulation of high-energy reactions of particles (SHERPA), and the jet-medium interactions are described by the SHELL transport model, which considers the elastic and inelastic partonic energy loss in the quark-gluon plasma (QGP). In $\textit{p+p}$ collisions, our numerical results indicate that the HQ jets from gluon splitting ( $ g \rightarrow Q $ -jet) are the dominant contribution at high $ p_T $ , displaying more dispersive structures than the HQ-initiated ( $ Q \rightarrow Q $ -jet). In nucleus-nucleus collisions, our calculations were consistent with the inclusive and b-jet $ R_{AA} $ recently measured by the ATLAS collaboration, revealing a remarkable manifestation of the mass effect of jet energy loss. As a result of the dispersive substructure, the $ g \rightarrow Q $ -jet loses more energy than the $ Q \rightarrow Q $ -jet in the QGP. Due to the significant contribution of $ g \rightarrow c $ -jet, the $ R_{AA} $ of $\textit{c}$-jet is comparable or even smaller than that of inclusive jet. To experimentally distinguish the $ g \rightarrow Q $ -jet and $ Q \rightarrow Q $ -jet, we propose event selection strategies based on their topological features and test their performances. By isolating the $ c \rightarrow c $ -jet, $ b \rightarrow b $ -jet, and the jets initiated by heavy quarks, we predicted that the order of their $ R_{AA} $ are in line with the mass hierarchy of energy loss. Future measurements on the $ R_{AA} $ of $ Q \rightarrow Q $ -jet and $ g \rightarrow Q $ -jet will provide a unique opportunity for testing the flavor/mass dependence of energy loss at the jet level.

China

Sa Wang

Shuang Li

Yao Li

Ben-Wei Zhang

Enke Wang

Probing the mass effect of heavy quark jets in high-energy nuclear collisions * Supported by the MajorProject of Basic and Applied Basic Research of Guangdong Province, China (2020B0301030008, 2023A1515011460), and the National Natural Science Foundation of China (11935007, 12035007, 12247127, 12375137). Sa Wang is supported by the Open Foundation of Key Laboratory of Quark and Lepton Physics (MOE) (QLPL2023P01) and the Talent Scientific Star-up Foundation of the China Three Gorges University, China (CTGU) (2024RCKJ013)

<p>Since searches for the low-lying excited baryons <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">(</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Σ</mi><mo stretchy="false">(</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math> are crucial to deepening our understanding of the light baryon spectrum, we have investigated the Cabibbo-favored process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msup><mi>π</mi><mo>+</mo></msup></math> by taking into account the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave pseudoscalar meson-octet baryon interactions within the chiral unitary approach, which could dynamically generate the resonances <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">(</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Σ</mi><mo stretchy="false">(</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math>. The contributions from the excited kaons are double Cabibbo suppressed, and the contribution from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Σ</mi><mo stretchy="false">(</mo><mn>1385</mn><mo stretchy="false">)</mo></math> is also suppressed due to Korner-Pati-Woo theory; thus, those states are expected to play negligible contributions in this process. We have predicted the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><mi mathvariant="normal">Λ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><mi mathvariant="normal">Λ</mi></math> invariant mass distributions, which have the clear signals of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">(</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Σ</mi><mo stretchy="false">(</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math>. Thus, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msup><mi>π</mi><mo>+</mo></msup></math> is an ideal process to search for the low-lying baryons <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">(</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Σ</mi><mo stretchy="false">(</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math>, and we make a call for a precise measurements of this process in experiments, such as Belle II, LHCb, and the proposed Super Tau-Charm Facility.</p>

Ying Li

Wen-Tao Lyu

Guan-Ying Wang

Longke Li

Wen-Cheng Yan

En Wang

Study of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi mathvariant="normal">Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><msup><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> and search for the low-lying baryons <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">(</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Σ</mi><mo stretchy="false">(</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math>

Recently, the LHCb Collaboration has measured the processes $$B^+\rightarrow D^-D_s^+\pi ^+$$ and $$B^+\rightarrow \bar{D}^0D_s^+\pi ^+$$ , where the $$D_s^+\pi ^-$$ and $$D_s^+\pi ^+$$ invariant mass distributions show the significant signals of two new open-flavored tetraquark states $$T_{c\bar{s}}(2900)^0$$ and $$T_{c\bar{s}}(2900)^{++}$$ , as the two of the isospin triplet. In this work, we have investigated the process $$\Lambda _b\rightarrow K^0D^0\Lambda $$ by taking into account the tetraquark state $$T_{c\bar{s}}(2900)^0$$ and the intermediate nucleon resonance $$N^*(1535)$$ , which could be dynamically generated by the interactions of the $$D^*K^*/D^*_s\rho $$ and the pseudoscalar meson-octet baryon, respectively. Our results show that a clear peak of the open-flavored tetraquark $$T_{c\bar{s}}(2900)$$ may appear in the $$K^0D^0$$ invariant mass distribution of the process $$\Lambda _b\rightarrow K^0D^0\Lambda $$ , which could be tested by future experiments.

Yun-He Lyu

Man-Yu Duan

Dian-Yong Chen

Theoretical study of the open-flavored tetraquark $$T_{c\bar{s}}(2900)$$ in the process $$\Lambda _b\rightarrow K^0D^0\Lambda $$

Inspired by the newly observed <math><mi>X</mi><mo>(</mo><mn>2085</mn><mo>)</mo></math> by the BESIII Collaboration, we study the strong decay behaviors of excited axial-vector strange mesons within the quark pair creation model. Our results indicate that the <math><msub><mi>K</mi><mn>1</mn></msub><mo>(</mo><mn>1793</mn><mo>)</mo><mo>/</mo><msub><mi>K</mi><mn>1</mn></msub><mo>(</mo><mn>1861</mn><mo>)</mo></math> can be regarded as the same <math><msub><mi>K</mi><mn>1</mn></msub><mo>(</mo><mn>2</mn><mi>P</mi><mo>)</mo></math> state, and the <math><msub><mi>K</mi><mn>1</mn></msub><mo>(</mo><mn>1911</mn><mo>)</mo></math> is assigned as the <math><msub><mi>K</mi><mn>1</mn></msub><mo>(</mo><mn>2</mn><msup><mi>P</mi><mo>′</mo></msup><mo>)</mo></math> state. Considering the mass, spin-parity, and decay behaviors, we interpret the newly observed <math><mi>X</mi><mo>(</mo><mn>2085</mn><mo>)</mo></math> as the radially excited <math><msub><mi>K</mi><mn>1</mn></msub><mo>(</mo><mn>3</mn><mi>P</mi><mo>)</mo></math> state, which mainly decays into the <math><msup><mi>K</mi><mo>*</mo></msup><mo>(</mo><mn>1410</mn><mo>)</mo><mi>π</mi></math>, <math><mi>ρ</mi><msup><mi>K</mi><mo>*</mo></msup></math>, <math><mi>ω</mi><mo>(</mo><mn>1420</mn><mo>)</mo><mi>K</mi></math>, <math><mi>ρ</mi><mo>(</mo><mn>1450</mn><mo>)</mo><mi>K</mi></math>, and <math><mi>ρ</mi><mi>K</mi></math> final states. Also, the width of the <math><msub><mi>K</mi><mn>1</mn></msub><mo>(</mo><mn>3</mn><msup><mi>P</mi><mo>′</mo></msup><mo>)</mo></math> state is predicted to be about 300 MeV, which can be searched for by future experiments. We expect that present calculations can help us to better understand the nature of the <math><mi>X</mi><mo>(</mo><mn>2085</mn><mo>)</mo></math> structure and near-threshold enhancements in the baryon-antibaryon invariant mass distributions.

Tian-Ge Li

Sheng-Chao Zhang

Qi-Fang Lü

Canonical interpretation of the newly observed <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>1</mn><mo>+</mo></msup></math> structure <math><mi>X</mi><mo>(</mo><mn>2085</mn><mo>)</mo></math>

Recently, the Belle and LHCb Collaborations have measured the $$\Lambda ^+_c \rightarrow p K^- \pi ^+$$ decay and reported the $$K^- p$$ invariant mass distribution, which shows a clear cusp structure around the $$\eta \Lambda $$ threshold. In this work, we have analyzed this process by considering the triangle mechanism and the -wave pseudoscalar meson-octet baryon interactions within the chiral unitary approach, which dynamically generates the $$\Lambda (1670)$$ . Our results are in good agreement with the Belle measurements, which implies that the cusp structure around $$\eta \Lambda $$ threshold could be associated with the $$\Lambda (1670)$$ with the molecular nature.

Spain

Jing-Yu Zhu

Explore the properties of $$\Lambda (1670)$$ in the Cabibbo-favored process $$\Lambda ^+_c \rightarrow p K^- \pi ^+$$

Motivated by the Belle measurements of the process <math><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo>→</mo><mi>η</mi><msup><mi>π</mi><mo>+</mo></msup><mi>Λ</mi></math>, we investigate this process by considering the contributions from the <math><mi>Λ</mi><mo>(</mo><mn>1670</mn><mo>)</mo></math>, <math><msub><mi>a</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo></math>, and <math><mi>Σ</mi><mo>(</mo><mn>1385</mn><mo>)</mo></math>. In addition, we also consider the predicted low-lying baryon <math><msup><mi>Σ</mi><mo>*</mo></msup><mo>(</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>)</mo></math>. Our results involving the <math><msup><mi>Σ</mi><mo>*</mo></msup><mo>(</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>)</mo></math> are favored by fitting to the Belle data of the <math><mi>η</mi><mi>Λ</mi></math> and <math><msup><mi>π</mi><mo>+</mo></msup><mi>Λ</mi></math> invariant mass distributions. Furthermore, we predict the <math><mi>η</mi><msup><mi>π</mi><mo>+</mo></msup></math> invariant mass distribution and the angular distribution <math><mi>d</mi><mi>Γ</mi><mo>/</mo><mi>d</mi><mi>cos</mi><mi>θ</mi></math>, which are significantly different depending on whether or not the contribution from the <math><msup><mi>Σ</mi><mo>*</mo></msup><mo>(</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>)</mo></math> is considered. Finally, we show that, with the contribution from the <math><msup><mi>Σ</mi><mo>*</mo></msup><mo>(</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>)</mo></math>, the calculated Dalitz plot agrees with the Belle measurements. Future precise measurements of the process <math><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo>→</mo><mi>η</mi><msup><mi>π</mi><mo>+</mo></msup><mi>Λ</mi></math> could shed further light on the existence of the low-lying <math><msup><mi>Σ</mi><mo>*</mo></msup><mo>(</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>)</mo></math>.

Jia-Jun Wu

Li-Sheng Geng

Ju-Jun Xie

Evidence of the low-lying baryon <math><mrow><msup><mrow><mi>Σ</mi></mrow><mrow><mo>*</mo></mrow></msup><mo>(</mo><mn>1</mn><mo>/</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo></mrow></math> in the process <math><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo>→</mo><mi>η</mi><msup><mi>π</mi><mo>+</mo></msup><mi>Λ</mi></math>

Recently, the Belle Collaboration has measured the <math><mrow><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>→</mo><mi>η</mi><mi>Λ</mi><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> decay and reported the <math><mi>η</mi><mi>Λ</mi></math> and <math><mrow><mi>Λ</mi><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> invariant mass distributions, which show the clear signals of the resonances <math><mrow><mi>Λ</mi><mo>(</mo><mn>1670</mn><mo>)</mo></mrow></math> and <math><mrow><mi>Σ</mi><mo>(</mo><mn>1385</mn><mo>)</mo></mrow></math>, respectively. Based on our previous works [Eur. Phys. J. C 76, 496 (2016) and Phys. Rev. D 95, 074024 (2017)], we reanalyze this process by considering the <math><mi>S</mi></math>-wave <math><mi>η</mi><mi>Λ</mi></math> and <math><mi>η</mi><msup><mi>π</mi><mo>+</mo></msup></math> final state interactions within the chiral unitary approach, which dynamically generate the <math><mrow><mi>Λ</mi><mo>(</mo><mn>1670</mn><mo>)</mo></mrow></math> and <math><msub><mi>a</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo></math>, respectively. Our results are in agreement with the Belle measurements of the <math><mi>η</mi><mi>Λ</mi></math> and <math><msup><mi>π</mi><mo>+</mo></msup><mi>Λ</mi></math> invariant mass distributions. In addition, the <math><msup><mi>π</mi><mo>+</mo></msup><mi>η</mi></math> invariant mass distribution is also calculated and a cusp structure of <math><msub><mi>a</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo></math> is clearly shown around the <math><mi>K</mi><mover><mi>K</mi><mo>¯</mo></mover></math> mass threshold.

Neng-Chang Wei

Hui-Min Yang

Roles of <math><mrow><msub><mrow><mi>a</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>980</mn><mo>)</mo></mrow></math>, <math><mrow><mi>Λ</mi><mo>(</mo><mn>1670</mn><mo>)</mo></mrow></math>, and <math><mrow><mi>Σ</mi><mo>(</mo><mn>1385</mn><mo>)</mo></mrow></math> in the <math><mrow><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>→</mo><mi>η</mi><mi>Λ</mi><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> decay

We have evaluated the strong decays of the <math><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo>(</mo><mn>1950</mn><mo>)</mo></math> and <math><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo>(</mo><mn>2130</mn><mo>)</mo></math> within the <math><mrow><mmultiscripts><mrow><msub><mrow><mi>P</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow></math> model by employing the meson wave functions from the relativized quark model. By comparing with the experimental measurements, the <math><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo>(</mo><mn>2130</mn><mo>)</mo></math> could be assigned as <math><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo>(</mo><msup><mn>3</mn><mn>3</mn></msup><msub><mi>P</mi><mn>0</mn></msub><mo>)</mo></math>, while the <math><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo>(</mo><mn>1950</mn><mo>)</mo></math> is difficult to be explained as the <math><mi>q</mi><mover><mi>q</mi><mo>¯</mo></mover></math> meson. We also predict that the <math><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo>(</mo><msup><mn>2</mn><mn>3</mn></msup><msub><mi>P</mi><mn>0</mn></msub><mo>)</mo></math> state has a mass of about 1811 MeV and a width of about 656 MeV, while the <math><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo>(</mo><msup><mn>4</mn><mn>3</mn></msup><msub><mi>P</mi><mn>0</mn></msub><mo>)</mo></math> state has a mass of about 2404 MeV and a width of about 180 MeV.

Zhuo Gao

De-Min Li

Jingya Zhu

Possible assignments of the scalar <math><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo>(</mo><mn>1950</mn><mo>)</mo></math> and <math><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo>(</mo><mn>2130</mn><mo>)</mo></math> within the <math><mrow><mmultiscripts><mrow><msub><mrow><mi>P</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow></math> model

The <math><msub><mi>D</mi><mrow><mi>s</mi><mn>0</mn></mrow></msub><mo>(</mo><mn>2590</mn><msup><mo>)</mo><mo>+</mo></msup></math> resonance observed by LHCb Collaboration is a strong candidate of the <math><msub><mi>D</mi><mi>s</mi></msub><mo>(</mo><msup><mn>2</mn><mn>1</mn></msup><msub><mi>S</mi><mn>0</mn></msub><mo>)</mo></math> state according to its spin parity and strong decay mode. However, the measured mass seems relatively lower than the previous theoretical predictions, which interests the coupled channel interpretations in the literature. In this work, we adopt an alternate approach, taking into account the screening effects in the potential model, to describe the <math><msub><mi>D</mi><mrow><mi>s</mi><mn>0</mn></mrow></msub><mo>(</mo><mn>2590</mn><msup><mo>)</mo><mo>+</mo></msup></math> resonance. The mass spectrum and strong decays of the excited charmed-strange mesons are investigated within the modified relativized quark model and <math><mrow><mmultiscripts><mrow><msub><mrow><mi>P</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow></math> model. The calculated mass and width of the <math><msub><mi>D</mi><mrow><mi>s</mi><mn>0</mn></mrow></msub><mo>(</mo><mn>2590</mn><msup><mo>)</mo><mo>+</mo></msup></math> are consistent with the experimental observations, which indicate that it can be reasonably interpreted as the <math><msub><mi>D</mi><mi>s</mi></msub><mo>(</mo><msup><mn>2</mn><mn>1</mn></msup><msub><mi>S</mi><mn>0</mn></msub><mo>)</mo></math> state.

Gao-Feng Zhao

Canonical interpretation of the <math><msub><mi>D</mi><mrow><mi>s</mi><mn>0</mn></mrow></msub><mo>(</mo><mn>2590</mn><msup><mo>)</mo><mo>+</mo></msup></math> resonance

Within the framework of the local hidden gauge formalism, we have reanalyzed the hidden-charm vector-vector meson <math><msup><mi>D</mi><mo>*</mo></msup><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math>, <math><msup><mi>K</mi><mo>*</mo></msup><msup><mover><mi>K</mi><mo>¯</mo></mover><mo>*</mo></msup></math>, and <math><mi>ρ</mi><mi>ρ</mi></math> interactions with the quantum numbers <math><mi>I</mi><mo>(</mo><msup><mi>J</mi><mi>P</mi></msup><mo>)</mo><mo>=</mo><mn>1</mn><mo>(</mo><msup><mn>1</mn><mo>+</mo></msup><mo>)</mo></math>. The estimation indicates that <math><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> system could form a bound state around 4010 MeV. By comparing our theoretical estimation with the BESIII measurements of the <math><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>→</mo><mo>(</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>*</mo></mrow></msup><msup><mrow><mo>)</mo></mrow><mrow><mo>±</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>∓</mo></mrow></msup></mrow></math> and <math><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>→</mo><mo>(</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>*</mo></mrow></msup><msup><mrow><mo>)</mo></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> reactions at <math><mrow><msqrt><mrow><mi>s</mi></mrow></msqrt><mo>=</mo><mn>4.26</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>, we find that the enhancement structure of the <math><msub><mi>Z</mi><mi>c</mi></msub><mo>(</mo><mn>4025</mn><mo>)</mo></math> in the <math><msup><mi>D</mi><mo>*</mo></msup><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math> invariant mass distribution observed by BESIII could be interpreted by a shallow <math><msup><mi>D</mi><mo>*</mo></msup><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math> bound state.

Revisiting the <math><msub><mi>Z</mi><mi>c</mi></msub><mo>(</mo><mn>4025</mn><mo>)</mo></math> structure observed by BESIII in <math><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>→</mo><mo>(</mo><mrow><mi>D</mi><msup><mrow><mtext> </mtext></mrow><mrow><mo>*</mo></mrow></msup><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><msup><mrow><mtext> </mtext></mrow><mrow><mo>*</mo></mrow></msup><msup><mrow><mo>)</mo></mrow><mrow><mo>±</mo><mo>,</mo><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>∓</mo><mo>,</mo><mn>0</mn></mrow></msup></mrow></math> at <math><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>4.26</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>