An $\textit{SU}$(3) flavor projection operator technique is implemented to construct the baryon-meson scattering amplitude within the framework of the $1/N_c$ expansion of quantum chromodynamics (QCD), where $N_c$ represents the number of color charges. The operator technique is implemented to evaluate not only the lowest-order scattering amplitude but also effects from the first-order perturbative $\textit{SU}$(3) flavor symmetry breaking and strong isospin breaking. The most general expression is obtained by explicitly accounting for the effects of the decuplet-octet baryon mass difference. At order ${\cal{O}}(1/N_c^2)$ , a large number of unknown operator coefficients appear, and therefore, there is little additional predictive power unless leading and subleading terms are retained. Although the resultant expression is sufficiently general that it can be applied to any incoming and outgoing baryons and pseudo scalar mesons, provided that the Gell-Mann--Nishijima scheme is respected, results for $N\pi\to N\pi$ scattering processes are explicitly considered.

Víctor Miguel Banda Guzmán

Rubén Flores-Mendieta

Johann Hernández

Use of $\textit{SU}$(3) flavor projection operators to construct baryon-meson scattering amplitudes in the 1/ N$_{c}$ expansion * The authors are grateful to Consejo Nacional de Humanidades, Ciencias y Tecnologías (Mexico) for support through the $\textit{Ciencia de Frontera}$ project CF-2023-I-162

We investigate the soft behavior of the tree-level Rutherford scattering processes mediated via $\textit{t}$-channel one-graviton exchange. We consider two types of Rutherford scattering processes: a low-energy massless structureless projectile (up to spin-1) hits a static massive composite particle carrying various spins (up to spin-2), and slowly moving light projectile hits a heavy static composite target. The unpolarized cross sections in the first type exhibit universal forms at the first two orders in $ 1/M $ expansion, yet differ at the next-to-next-to-leading order, though some terms at this order still remain universal or depend on the target spin in a definite manner. The unpolarized cross sections in the second type are universal at the lowest order in projectile velocity expansion and through all orders in $ 1/M $ , independent on the spins of both projectile and target. The universality partially breaks down at relative order- $ v^2/M^2 $ , albeit some terms at this order still depend on the target spin in a specific manner.

China

Yu Jia

Jichen Pan

United States

Jia-Yue Zhang

Soft pattern of gravitational Rutherford scattering from heavy target mass expansion * This work is supported in part by the National Natural Science Foundation of China (11925506, 12475090). J.-Y. Z. is supported in part by the US Department of Energy (DE-AC05-06OR23177), under which Jefferson Science Associates, LLC operates Jefferson Lab.

Electroweak (EW) amplitudes in the gauge-Goldstone five-component formalism have a distinctive property: gauge symmetry is imprinted in the amplitudes, manifested as the massive Ward identity (MWI) $ k^M{\cal{M}}_M=0 $ . In this study, we used the HELAS package to numerically study gauge symmetry in EW amplitudes. First, we directly tested gauge symmetry by examining the MWI of amplitudes. Second, we modified the couplings within a vertex and among vertices to check if and how the MWI changes. Third, we tested gauge symmetry by considering the couplings modified by operators from the standard model effective field theory (SMEFT). Similar to the standard model, there are relations between different couplings that are protected by gauge symmetry. We observed that, if we modify the couplings to deviate from the relations, the MWI is violated. In contrast, the MWI is restored when the relations between couplings reduce to those in the SMEFT.

Wang-Fa Li

Junmou Chen

Qian-Jiu Wang

Zhao-Huan Yu

Numerical study on the gauge symmetry of electroweak amplitudes * Junmou Chen is supported by National Natural Science Foundation of China (12205118), Wang-Fa Li, Qian-Jiu Wang, and Zhao-Huan Yu are supported by the Guangzhou Science and Technology Planning Project (2024A04J4026)

Quantum teleportation, a protocol that has received extensive and intensive attention in quantum information processing, allows a quantum state to be transferred from one particle to another. In this study, we analytically investigate fidelity ( <italic>F</italic>), logarithmic negativity (LN), local quantum uncertainty (LQU) and local quantum Fisher information (LQFI) as a discord-like measure of quantum correlations in <math altimg='si1.svg'><mrow><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>&#8722;</mo></msup><mo>&#8594;</mo><mtext>Y</mtext><mover accent='true'><mtext>Y</mtext><mo>&#175;</mo></mover></mrow></math> processes at BESIII through noisy channels, using experimental feasible parameters, where Y and <math altimg='si3.svg'><mover accent='true'><mtext>Y</mtext><mo>&#175;</mo></mover></math> refer to the spin-1/2 hyperon and its antihyperon, respectively. We discuss the dependence of LN, LQU and LQFI on the scattering angle <italic>&#952;</italic> for different hyperon-antihyperon pairs ( <math altimg='si6.svg'><mrow><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle><mover accent='true'><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle><mo>&#175;</mo></mover></mrow></math>, <math altimg='si38.svg'><mrow><msup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mn>0</mn></msup><mover accent='true'><msup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mn>0</mn></msup><mo>&#175;</mo></mover></mrow></math>, <math altimg='si17.svg'><mrow><msup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mo>&#8722;</mo></msup><mover accent='true'><msup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mo>+</mo></msup><mo>&#175;</mo></mover></mrow></math>, <math altimg='si39.svg'><mrow><msup><mstyle mathvariant='normal'><mi>&#931;</mi></mstyle><mo>+</mo></msup><mover accent='true'><msup><mstyle mathvariant='normal'><mi>&#931;</mi></mstyle><mo>&#8722;</mo></msup><mo>&#175;</mo></mover></mrow></math>), produced by electron-positron annihilation via charmonium decay. Without a dephasing effect, we show that, LN, LQU, and LQFI vanish at <math altimg='si40.svg'><mrow><mi>&#966;</mi><mo linebreak='goodbreak'>=</mo><mo>&#177;</mo><mi>&#960;</mi></mrow></math> and are symmetric around <math altimg='si14.svg'><mrow><mi>&#966;</mi><mo linebreak='goodbreak'>=</mo><mi>&#960;</mi><mo linebreak='goodbreak'>/</mo><mn>2</mn></mrow></math>. Furthermore, LN reaches its maximum when the scattering angle equals <math altimg='si14.svg'><mrow><mi>&#966;</mi><mo linebreak='goodbreak'>=</mo><mi>&#960;</mi><mo linebreak='goodbreak'>/</mo><mn>2</mn></mrow></math>, while LQU and LQFI reach their maxima at different angles. We also explore the LN, LQU, and LQFI for different <math altimg='si32.svg'><mrow><mtext>Y</mtext><mover accent='true'><mtext>Y</mtext><mo>&#175;</mo></mover></mrow></math> pairs subjected to three distinct types of decoherence channels. Specifically, we show that amplitude damping (AD) and phase damping (PD) lead to a decrease in LN, LQU, and LQFI with an increasing decoherence parameter <italic>s</italic>. In contrast, the phase flip (PF) channel exhibits symmetric behavior around <math altimg='si41.svg'><mrow><mi>s</mi><mo linebreak='goodbreak'>=</mo><mn>1</mn><mo linebreak='goodbreak'>/</mo><mn>2</mn></mrow></math>. Besides, we realize for teleportation, optimal fidelity for different hyperon-antihyperon pairs ( <math altimg='si6.svg'><mrow><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle><mover accent='true'><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle><mo>&#175;</mo></mover></mrow></math>, <math altimg='si38.svg'><mrow><msup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mn>0</mn></msup><mover accent='true'><msup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mn>0</mn></msup><mo>&#175;</mo></mover></mrow></math>, <math altimg='si17.svg'><mrow><msup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mo>&#8722;</mo></msup><mover accent='true'><msup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mo>+</mo></msup><mo>&#175;</mo></mover></mrow></math>, <math altimg='si39.svg'><mrow><msup><mstyle mathvariant='normal'><mi>&#931;</mi></mstyle><mo>+</mo></msup><mover accent='true'><msup><mstyle mathvariant='normal'><mi>&#931;</mi></mstyle><mo>&#8722;</mo></msup><mo>&#175;</mo></mover></mrow></math>). We discuss the influence of noisy channels, specifically (AD, PF and PD), on the fidelity of quantum teleportation and on quantum correlations that can exist even beyond entanglement. Furthermore, the results show that the fidelity remains above the classical limit of 2/3 in all three channels, even as the noise increases. This is a significant finding because it shows that not all quantum noise is detrimental. These results can have promising applications in quantum information and particle physics.

Morocco

Elhabib Jaloum

Mohamed Amazioug

Quantum teleportation, entanglement, LQU and LQFI in <math altimg='si1.svg'><mrow><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>&#8722;</mo></msup><mo>&#8594;</mo><mtext>Y</mtext><mover accent='true'><mtext>Y</mtext><mo>&#175;</mo></mover></mrow></math> processes at BESIII through noisy channels

To resolve ambiguities from multiple solutions in experimental measurements, we construct a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>χ</mi><mn>2</mn></msup></math> function incorporating constraints such as isospin conservation and amplitude relations. By minimizing the global <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>χ</mi><mn>2</mn></msup></math>, we identify physical solutions for seven hidden-charm decay channels of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4230</mn><mo stretchy="false">)</mo></math>. Crucially, the physical solution for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4230</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mi>J</mi><mo>/</mo><mi>ψ</mi></math> corresponds to the largest among four experimental solutions, potentially modifying inputs for theoretical calculations. Additionally, we predict <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Γ</mi><mrow><mi>e</mi><mi>e</mi></mrow></msub><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><mi>Y</mi><mo stretchy="false">(</mo><mn>4230</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>ψ</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math> based on our results, acknowledging substantial uncertainties in current measurements.

Jie Yuan

Yadi Wang

Kai Zhu

Pinpointing physical solutions in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4230</mn><mo stretchy="false">)</mo></math> decays

In the present work, we perform a combined analysis of the cross sections for $$e^+ e^- \rightarrow K^+ K^-$$ and $$e^+ e^- \rightarrow K_S^0 K_L^0$$ by including the interference between direct coupling process and resonance intermediate process. When setting the isospin factor as a free parameter, we can well reproduce the structures in the cross sections for $$e^+ e^- \rightarrow K^+ K^-$$ and $$e^+ e^- \rightarrow K_S^0 K_L^0,$$ however, the isospin factor deviates with the isospin symmetry conservation predicted value of one. By fixing the isospin factor to be one, we find the cross sections for $$e^+ e^-\rightarrow K^+ K^-$$ can be accurately fitted, while the same model parameters fail to adequately reproduce the observed cross section for the process $$e^+ e^- \rightarrow K_S^0 K_L^0,$$ which indicate that there should be contributions from other vector meson states, such as $$\rho (2150)$$ and $$\omega (2220).$$ The combined analysis with $$\phi (2170),$$ $$\omega (2220)$$ and $$\rho (2150)$$ indicate that the inclusion of $$\rho (2150)$$ can improve the descriptions of the cross sections for $$e^+ e^-\rightarrow K^+ K^-$$ and $$e^+ e^- \rightarrow K_S^0 K_L^0.$$

Dian-Yong Chen

Jing Liu

Yu Bai

Chun-Hua Liu

Wen-Biao Yan

Zhao-Xia Meng

A combined analysis of $\textit{Y}$(2240) in the $$e^+ e^- \rightarrow K^+ K^-$$ and $$e^+ e^- \rightarrow K_S^0 K_L^0$$ processes

Based on a sample of $2.7\times10^{9}$ $\psi(3686)$ events collected by the BESIII detector operating at the BEPCII collider, the decay $\psi(3686)\to\gamma\chi_{cJ}, \chi_{cJ}\to\eta\eta\eta^{\prime}$ is analyzed. The decay modes $\chi_{c1}$ and $\chi_{c2}\to\eta\eta\eta^{\prime}$ are observed for the first time, and their corresponding branching fractions are determined to be ${\cal{B}}(\chi_{c1}\to\eta\eta\eta^{\prime}) = $ $ (1.40\, \pm 0.13\, (\text{stat.}) \pm 0.09\, (\text{sys.})) \times 10^{-4}$ and ${\cal{B}}(\chi_{c2}\to\eta\eta\eta^{\prime}) = (4.18\, \pm 0.84\, (\text{stat.}) \pm 0.48\, (\text{sys.})) \times 10^{-5}$ . An upper limit on the branching fraction of $\chi_{c0}\to\eta\eta\eta^{\prime}$ is set as $2.59 \times 10^{-5}$ at a 90% confidence level (CL). A partial wave analysis (PWA) of the decay $\chi_{c1}\to\eta\eta\eta^{\prime}$ is performed to search for the $1^{-+}$ exotic state $\eta_1(1855)$ . The PWA result indicates that the structure in the $\eta\eta^{\prime}$ mass spectrum is attributed to $f_0(1500)$ , while in the $\eta\eta$ mass spectrum, it is attributed to the $0^{++}$ phase space. The upper limit of ${\cal{B}}(\chi_{c1}\to\eta_{1}(1855)\eta) \cdot {\cal{B}}(\eta_{1}(1855)\to\eta\eta^{\prime}) \lt $ $ 9.79 \times 10^{-5}$ is set based on the PWA at 90% CL.

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

Germany

R. Aliberti

Italy

A. Amoroso

Q. An

Y. Bai

O. Bakina

Y. Ban

H.R. Bao

Poland

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

R.A. Briere

A. Brueggemann

H. Cai

M.H. Cai

X. Cai

A. Calcaterra

G.F. Cao

N. Cao

Türkiye

S.A. Cetin

X.Y. Chai

J.F. Chang

G.R. Che

Y.Z. Che

C.H. Chen

Chao Chen

G. Chen

H.S. Chen

H.Y. Chen

M.L. Chen

S.J. Chen

S.L. Chen

S.M. Chen

T. Chen

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z. Chen

Z.J. Chen

Z.K. Chen

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

United Kingdom

J. Cottee-Meldrum

J.J. Cui

H.L. Dai

J.P. Dai

A. Dbeyssi

R.E. de Boer

D. Dedovich

C.Q. Deng

Z.Y. Deng

A. Denig

I. Denysenko

M. Destefanis

F. De Mori

B. Ding

X.X. Ding

Y. Ding

Y.X. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. Dong

M.C. Du

S.X. Du

Y.Y. Duan

P. Egorov

G.F. Fan

J.J. Fan

Y.H. Fan

J. Fang

S.S. Fang

W.X. Fang

Y.Q. Fang

R. Farinelli

L. Fava

F. Feldbauer

G. Felici

C.Q. Feng

J.H. Feng

L. Feng

Q.X. Feng

Search for $\textit{η}$ $_{1}$(1855) in $\textit{χ}$ $\textit{cJ}$ → $\textit{ηηη}$′ decays * Supported in part by National Key R&D Program of China (2023YFA1606000, 2023YFA1606704); National Natural Science Foundation of China (NSFC) (11635010, 11935015, 11935016, 11935018, 12025502, 12035009, 12035013, 12061131003, 12192260, 12192261, 12192262, 12192263, 12192264, 12192265, 12221005, 12225509, 12235017, 12361141819); the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; CAS (YSBR-101); 100 Talents Program of CAS; The Institute of Nuclear and Particle Physics (INPAC) and Shanghai Key Laboratory for Particle Physics and Cosmology; Agencia Nacional de Investigación y Desarrollo de Chile (ANID), Chile (ANID PIA/APOYO AFB230003); German Research Foundation DFG (FOR5327); Istituto Nazionale di Fisica Nucleare, Italy; Knut and Alice Wallenberg Foundation (2021.0174, 2021.0299); Ministry of Development of Turkey (DPT2006K-120470); National Research Foundation of Korea ( NRF-2022R1A2C1092335); National Science and Technology fund of Mongolia; National Science Research and Innovation Fund (NSRF) via the Program Management Unit for Human Resources Institutional Development, Research and Innovation of Thailand ( B50G670107); Polish National Science Centre (2024/53/B/ST2/00975); Swedish Research Council (2019.04595); U. S. Department of Energy (DE-FG02-05ER41374)

The isomeric yield ratio (IYR) of fission products is an observable that carries relevant information about the fragments emerging from the scission of a fissioning nucleus. We report on IYR of 96,98,100Y and 100,102Nb, together with the previously reported values for 97Y and 99Nb, produced in the 28 MeV <italic>&#945;</italic>-induced fission of 232Th at the Ion Guide Isotope Separation On-Line (IGISOL) facility of the University of Jyv&#228;skyl&#228;. We measured the IYR using two different techniques, the phase-imaging ion-cyclotron-resonance (PI-ICR) and the multiple-reflection time-of-flight mass spectrometry (MR-TOF-MS) methods. Moreover, we measured the masses of the long-lived states in 98,100Y and 100,102Nb populated via in-trap <italic>&#946;</italic>-decay of their precursors. Since the <italic>&#946;</italic>-decay selectively populates states with a favourable spin-parity, we could identify the measured state and show that the ground state is the low-spin state in the cases of 98Y and 100Nb, while it is the high-spin state in the cases of 100Y and 102Nb. This measurement confirms the spin-parity assignments of all the nuclei as they are reported in the NUBASE2020 evaluations, disagreeing with the assignment for 100Y reported in the ENSDF evaluation.

Simone Cannarozzo

Stephan Pomp

Finland

Anu Kankainen

Iain Moore

Marek Stryjczyk

Ali Al-Adili

Andreas Solders

Ville Virtanen

Tommi Eronen

Zhihao Gao

Zhuang Ge

Arthur Jaries

Mattias Lantz

Maxime Mougeot

Heikki Penttilä

Andrea Raggio

Jouni Ruotsalainen

Isomeric yield ratios and mass spectrometry of Y and Nb isotopes in the neutron-rich N=60 region: The unusual case of 98Y

We, using an effective Lagrangian approach, investigated the dipionic transition of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4500</mn><mo stretchy="false">)</mo></math> newly well established in the process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><mi>J</mi><mo>/</mo><mi>ψ</mi></math>. In this study, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4500</mn><mo stretchy="false">)</mo></math> was considered as a mixture of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>5</mn><mi>S</mi><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>ψ</mi><mo stretchy="false">(</mo><mn>4</mn><msub><mrow><mmultiscripts><mrow><mi>D</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">)</mo></mrow></math>, and its dipionic decay to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> was assumed to occur via charmed meson loops including box and two kinds of triangle loops. The calculated invariant mass spectra due to the different loop mechanisms exhibit distinct differences. These spectrum patterns are found to be nearly independent of the cutoff parameter, especially for the box and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">R</mi></math> loops. By means of comparing our calculated results with the future experimental measurements of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>±</mo></msup><mi>J</mi><mo>/</mo><mi>ψ</mi></math> invariant mass distributions, we could judge which loop mechanism is of more importance in this dipionic transition. The interference among the different kinds of loops is also exhibited. Despite the unknown phase angles between different kinds of loop diagrams, the partial decay width for the process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4500</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mi>J</mi><mo>/</mo><mi>ψ</mi></math> is estimated to be 250–700 keV, aligning with the estimation obtained by combining BESIII Collaboration measurements and theoretical predictions for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4500</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><mi>J</mi><mo>/</mo><mi>ψ</mi></math>. We hope that the present calculations would be tested by the future BESIII or Belle II experiments.

Shi-Dong Liu

Qi Wu

Gang Li

Dipionic transitions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4500</mn><mo stretchy="false">)</mo></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math>

Motivated by the recent LHCb Collaboration analysis, we have investigated the process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>−</mo></msup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>η</mi><mo>′</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> by considering the contributions from the resonances <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4710</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>1430</mn><mo stretchy="false">)</mo></math>. Our results are in good agreement with the measured invariant mass distributions and the Dalitz plot of LHCb, which supports the existence of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>1430</mn><mo stretchy="false">)</mo></math> and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4710</mn><mo stretchy="false">)</mo></math> in the process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>−</mo></msup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>η</mi><mo>′</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math>. Since the decay mode of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4710</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>η</mi><mo>′</mo></msup></math> is Okubo-Zweig-Iizuka suppressed for the charmonium state, the measurements of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><mi>Y</mi><mo stretchy="false">(</mo><mn>4710</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mrow><mi>η</mi></mrow><mrow><mo>′</mo></mrow></msup><mo stretchy="false">)</mo></mrow></math> through the process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>−</mo></msup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>η</mi><mo>′</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> or other processes is helpful to understanding the nature of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4710</mn><mo stretchy="false">)</mo></math>. Thus, we advocate that Belle II and LHCb Collaborations could perform the more precise analysis to confirm the evidence of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4710</mn><mo stretchy="false">)</mo></math> state, which could be helpful to reduce the experimental uncertainties of its mass and width and to explore its nature.

Wen-Tao Lyu

Spain

Man-Yu Duan

De-Min Li

Bing Wang

En Wang

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>−</mo></msup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>η</mi><mo>′</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> reaction and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4710</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>1430</mn><mo stretchy="false">)</mo></math> contributions