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.

China

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

United States

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)

We study the pole trajectory of the recently established subthreshold negative-parity nucleon pole, namely the $N^*(920)$ , with varying pion masses in the scheme of linear $\textit{σ}$ model with nucleons, using the $N/D$ unitarization method. We find that, as the pion mass increases, the pole moves toward the real axis. For larger pion masses, at tree level, the pole falls to a specific point on $\textit{u}$-channel cut and crosses to the adjacent Riemann sheet defined by the logarithmic $\textit{u-}$channel cut. At the one-loop level, the pole does not meet the $\textit{u}$-cut up to $m_\pi=0.36$ GeV. We also re-examined the $\textit{σ}$ pole trajectory and found it to be in good agreement with the Roy equation analysis result.

Qu-Zhi Li

Zhiguang Xiao

Han-Qing Zheng

On the pole trajectory of the subthreshold negative parity nucleon with varying pion masses * Supported by China National Natural Science Foundation (12335002, 12375078). This work is also supported by “the Fundamental Research Funds for the Central Universities”

By capturing the characteristics of the Bethe-Salpeter amplitude for the pion excitation state, we construct an algebraic model to provide the overall features of the pion’s first excitation state parton distribution amplitude and distribution function. We find that, at the hadronic scale, the distribution amplitude of the excited state exhibits nodes, while the distribution function is unimodal, with a peak at $x=1/2 $ and distinct concave and convex fluctuations in the valence region. These findings provide new insights into the partonic structure of excited mesons and contribute significantly to our understanding of hadronic excitations.

Xiaobin Wang

Lei Chang

Unveiling the inner structure of the Pion’s first excited state * This work is financially supported by the National Natural Science Foundation of China (12135007)

The study of extra charged gauge bosons beyond the Standard Model has always been of great interest. Future muon colliders will have a significant advantage in discovering exotic particles. In this paper, by studying the $ \mu^+ \mu^- \to W^{\prime +} W^{\prime -} \to e^+ e^- n_e \bar{n}_e $ process, we explore the properties of $ W^\prime $ in the alternative left-right model. The cross section and angular distribution of the final electron are investigated in a scenario of different $ W^\prime $ masses and right-handed coupling constants. The forward-backward asymmetry is also an important observable to reflect the properties of $ W^\prime $ . We provide a method to effectively suppress the background processes by imposing constraints on the transverse momentum $ P_T $ and azimuthal angle of the final-state electrons $\textit{α}$. With cuts of $ 600 \lt P_T \lt 3500 $ GeV and $ 0.5 \lt \alpha \lt 3 $ , the significance exceeds 5$\textit{σ}$ for 4.8 TeV $ W^\prime $ at a collision energy of 10 TeV.

Liuxin Zhao

Honglei Li

Zhi-Long Han

Fei Huang

Xinyi Yan

Extra charged gauge boson $\textit{W}$′ in Alternative Left-Right Model at future muon collider * This work is supported by the Natural Science Foundation of Shandong Province (ZR2022MA065, ZR2024QA138), and University of Jinan Disciplinary Cross-Convergence Construction Project 2024 (XKJC-202404)

We perform the first computation of phase-transition parameters to cubic order in $ \lambda\sim m^2/T^2 $ , where $\textit{m}$ is the scalar mass and $\textit{T}$ is the temperature, in a simple model resembling the Higgs sector of the SMEFT. We use dimensional reduction, including 1-loop matching corrections for terms of dimension 6 (in 4-dimensional units), 2-loop contributions for dimension-4 ones and 3-loops for the squared mass. We precisely quantify the size of the different corrections, including renormalization-group running as well as quantum effects from light fields in the effective theory provided by the Coleman-Weinberg potential, and discuss briefly the implications for gravitational waves. Our results suggest that, for strong phase transitions, 1-loop corrections from dimension-6 operators can compete with 2-loop ones from quartic couplings and largely surpass those from 3-loop thermal masses.

Spain

Mikael Chala

Luis Gil

Zhe Ren

Phase transitions in dimensional reduction up to three loops * Supported by MCIN/AEI (10.13039/501100011033) and ERDF (grants PID2021-128396NB-I00 and PID2022-139466NB-C22), from the Junta de Andalucía grants FQM 101 and P21-00199 and from Consejería de Universidad, Investigación e Innovación, Gobierno de España and Unión Europea – NextGenerationEU under grants AST22 6.5 and CNS2022-136024. MC and LG are further supported by the RyC and FPU programs under contract numbers RYC2019-027155-I and FPU23/02026, respectively.

This paper presents a systematic study of hyperon non-leptonic two-body decays induced by light quark transitions, particularly the $ s \rightarrow u\bar{u}d $ process, within the framework of $\textit{SU}$(3) flavor symmetry. The effective weak Hamiltonian is decomposed into irreducible $\textit{SU}$(3) representations, including the 27-plet and octet components, and applied to analyze decays of octet and decuplet baryons and charmed baryons. Both the irreducible representation amplitude (IRA) approach and the topological diagrammatic analysis (TDA) are employed to construct decay amplitudes and constrain the parameter space. $\textit{SU}$(3) symmetry-breaking effects arising from the strange quark mass are incorporated systematically. A global fit to current experimental data allows us to extract form factors and predict branching ratios and asymmetry parameters for several decay channels. Our results demonstrate the predictive power of $\textit{SU}$(3) flavor symmetry while highlighting significant symmetry-breaking effects, especially in amplitudes related to the 27-plet. Notably, the $ \Sigma^+ \rightarrow p\pi^0 $ decay channel exhibits a deviation exceeding $ 1\sigma $ from experimental measurements, suggesting the possible presence of new decay mechanisms or contributions beyond the Standard Model. Besides, we also evaluate the size of symmetry breaking. However, the large uncertainty of the experimental data makes it difficult to precisely determine the value of symmetry breaking. We strongly recommend that future experimental efforts aim to reduce the measurement uncertainties, especially for the processes $ \Lambda^0\to p\pi^- $ and $ \Lambda^0\to n\pi^0 $ , which have larger experimental errors compared to other data and play an important role in determining the symmetry breaking parameter. This study provides a systematic framework for future tests of the Standard Model and the search for new physics in hyperon decays.

Xin Wu

Qi Chen

Ye Xing

Zhi-Peng Xing

Ruilin Zhu

$\textit{SU}$(3) flavor symmetry analysis of hyperon non-leptonic two body decays * Ruilin Zhu is supported by NSFC (12322503, 12075124) and the Natural Science Foundation of Jiangsu (BK20211267). Zhi-Peng Xing is supported by NSFC (12375088, 12335003, 12405113). Ye Xing is supported by NSFC (12005294)

Leptoquark models are prime candidates for new physics (NP) explanations of the longstanding anomalies in semileptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> decays; <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mo stretchy="false">→</mo><mi>c</mi><mi>τ</mi><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover></math> [encoded in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo stretchy="false">(</mo><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo></math>] and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mo stretchy="false">→</mo><mi>s</mi><mo>ℓ</mo><mover accent="true"><mo>ℓ</mo><mo stretchy="true">¯</mo></mover><mo stretchy="false">(</mo><mo>ℓ</mo><mo>=</mo><mi>e</mi><mo>,</mo><mi>μ</mi><mo stretchy="false">)</mo></math> transitions. Furthermore, Belle II and NA62 reported weaker-than-expected limits on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><mi>ν</mi><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><mi>ν</mi><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover></math>, respectively. While the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo stretchy="false">(</mo><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mo stretchy="false">→</mo><mi>s</mi><mo>ℓ</mo><mover accent="true"><mo>ℓ</mo><mo stretchy="true">¯</mo></mover></math> measurements can be explained with NP contributions at the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mn>10</mn><mo>%</mo><mo stretchy="false">)</mo></math> level, the neutrino channels suggest that the NP effect could be comparable in size to the Standard Model one. In this context, we consider the two types of leptoquark models with minimal sets of the couplings that can best describe the semileptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> anomalies and lead at the same time to effects in the neutrino modes, the singlet-triplet scalar leptoquark model (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>S</mi><mn>1</mn></msub><mo>+</mo><msub><mi>S</mi><mn>3</mn></msub></math>) and the singlet vector leptoquark model (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>U</mi><mn>1</mn></msub></math>). More specifically, the neutrino channels pose nontrivial constraints on the parameter space, and we find that large effects (i.e., accounting for the current central value) in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msup><mi>K</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><mi>ν</mi><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover></math> are only possible in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>S</mi><mn>1</mn></msub><mo>+</mo><msub><mi>S</mi><mn>3</mn></msub></math> setup, while both models can account for the central value of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><mi>ν</mi><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover></math>.

Switzerland

Andreas Crivellin

Japan

Syuhei Iguro

Teppei Kitahara

Discriminating tauphilic leptoquark explanations of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> anomalies via <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mo stretchy="false">→</mo><mi>π</mi><mi>ν</mi><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>K</mi><mi>ν</mi><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover></math>

We discuss the appearance of superconducting strings in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>E</mi><mn>6</mn></msub></math> grand unification, keeping track of the magnetic monopole flux that precedes the formation of the string flux tube. This flux matching ensures compatibility with the quantum tunneling of a monopole-antimonopole pair on a metastable string. We identify two realistic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>E</mi><mn>6</mn></msub></math> models with superconducting (metastable) strings that also carry zero modes of the right-handed Majorana neutrinos and dark matter particles. Depending on the symmetry breaking scale associated with the strings, the latter could be a source of observable gravitational waves, intermediate scale dark matter, and the observed baryon asymmetry via leptogenesis. Topologically stable superconducting strings also appear if the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>E</mi><mn>6</mn></msub></math> symmetry breaking leaves unbroken the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>2</mn></msub></math> subgroup of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>4</mn></msub></math>, the center of SO(10). The zero modes of the Standard Model fermions are the charge carriers in this case. Finally, the flux matching condition ensures that the Aharonov-Bohm phase change in going around the metastable strings is an integer multiple of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>π</mi></math> for all fields. The fields in the spinorial representation of SO(10) acquire a phase change of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>exp</mi><mo stretchy="false">(</mo><mo>±</mo><mi>i</mi><mi>π</mi><mo stretchy="false">)</mo></math> if taken around the topologically stable <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>2</mn></msub></math> string.

South Korea

Rinku Maji

Qaisar Shafi

Superconducting strings in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>E</mi><mn>6</mn></msub></math>

The infinite series of 4D <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>2</mn></math> superconformal field theories with central charge relation <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mrow><mn>4</mn><mi mathvariant="normal">D</mi></mrow></msub><mo>=</mo><msub><mi>c</mi><mrow><mn>4</mn><mi mathvariant="normal">D</mi></mrow></msub></math> are closely related to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></math> super Yang-Mills theory. In this paper, we study the modular properties of their associated vertex operator algebras <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="double-struck">V</mi><mo stretchy="false">[</mo><msub><mi mathvariant="script">T</mi><mrow><mi>p</mi><mo>,</mo><mi>N</mi></mrow></msub><mo stretchy="false">]</mo></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">T</mi><mrow><mi>p</mi><mo>,</mo><mi>N</mi></mrow></msub></math> are those <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mo>=</mo><mi>c</mi></math> theories with an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></math> gauge group. We exploit the closed-form formula for the Schur index of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></math> theories <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">T</mi><mrow><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></mrow></msub></math> to derive the space of characters of the vertex operator algebra <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="double-struck">V</mi><mo stretchy="false">[</mo><msub><mi mathvariant="script">T</mi><mrow><mi>p</mi><mo>,</mo><mi>N</mi></mrow></msub><mo stretchy="false">]</mo></math> and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>S</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>T</mi></mrow></math> matrices, and find the (nonmonic) modular linear differential equations that constrain the module characters when possible. We investigate the geometric interpretation of some of these modular data from the viewpoint of 4D mirror symmetry. Using insights from the flavored modular differential equation and defect index, we investigate a map between module characters of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="double-struck">V</mi><mo stretchy="false">[</mo><msub><mi mathvariant="script">T</mi><mrow><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></mrow></msub><mo stretchy="false">]</mo></math> and those of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="double-struck">V</mi><mo stretchy="false">[</mo><msub><mi mathvariant="script">T</mi><mrow><mi>p</mi><mo>,</mo><mi>N</mi></mrow></msub><mo stretchy="false">]</mo></math>.

Yiwen Pan

Peihe Yang

Modularity, 4d mirror symmetry, and vertex operator algebra modules of 4D <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>2</mn></mrow></math> SCFTs with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mo>=</mo><mi>c</mi></math>

In our previous work [<a href="http://dx.doi.org/10.1103/PhysRevC.101.014003">Phys. Rev. C 101, 014003 (2020)</a>], we analyzed all available data on differential cross sections and spin density matrix elements for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>γ</mi><mi>p</mi><mo>→</mo><msup><mi>K</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><mi mathvariant="normal">Λ</mi></mrow></math> reaction using an effective Lagrangian approach. There, the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>-channel <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi><mo>,</mo><mo> </mo><msup><mi>K</mi><mo>*</mo></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>κ</mi></math> exchanges, the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math>-channel <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Λ</mi><mo>,</mo><mo> </mo><mi mathvariant="normal">Σ</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="normal">Σ</mi><mo>*</mo></msup></math> exchanges, the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math>-channel <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>,</mo><mo> </mo><mrow><mi>N</mi><mrow><mo>(</mo><mn>2060</mn><mo>)</mo></mrow><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>N</mi><mrow><mo>(</mo><mn>2000</mn><mo>)</mo></mrow><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></mrow></math> exchanges, and the interaction current were taken into account in constructing the reaction amplitudes. It was found that, overall, the agreement of the theoretical results with the corresponding data is fairly good. However, noticeable discrepancies between the model results and the data on spin density matrix elements <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>ρ</mi><mn>00</mn></msub></math> are still observed in the center-of-mass energy region around <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>W</mi><mo>≈</mo><mn>2.08</mn></mrow></math> GeV, indicating the need for additional reaction mechanisms. On the other hand, the hidden-strange pentaquark-like state <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>N</mi><mrow><mo>(</mo><mn>2080</mn><mo>)</mo></mrow><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow></math>, which is proposed to be a <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>K</mi><mo>*</mo></msup><mi mathvariant="normal">Σ</mi></mrow></math> molecular state as the strange partner of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>P</mi><mi>c</mi></msub><mrow><mo>(</mo><mn>4457</mn><mo>)</mo></mrow></mrow></math> hadronic molecule, has been found to play quite active roles in reproducing the data for <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>K</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><msup><mi mathvariant="normal">Σ</mi><mn>0</mn></msup></mrow><mo>,</mo><mo> </mo><mrow><msup><mi>K</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup><msup><mi mathvariant="normal">Σ</mi><mo>+</mo></msup></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ϕ</mi><mi>p</mi></mrow></math> photoproduction reactions. Based on these observations, in the present work, we reanalyze the data for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>γ</mi><mi>p</mi><mo>→</mo><msup><mi>K</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><mi mathvariant="normal">Λ</mi></mrow></math> reaction by incorporating the pentaquark-like state <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>N</mi><mrow><mo>(</mo><mn>2080</mn><mo>)</mo></mrow><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow></math> in our previously proposed model. The results show that, with the inclusion of the contributions of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>N</mi><mrow><mo>(</mo><mn>2080</mn><mo>)</mo></mrow><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow></math>, the quality of the theoretical description of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>γ</mi><mi>p</mi><mo>→</mo><msup><mi>K</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><mi mathvariant="normal">Λ</mi></mrow></math> data can be considerably improved. In particular, the data on spin density matrix elements <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>ρ</mi><mn>00</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Re</mi><mspace width="0.16em"></mspace><msub><mi>ρ</mi><mn>10</mn></msub></mrow></math> in the near-threshold energy region are significantly better reproduced. This achievement indicates that the hypothesis of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>N</mi><mrow><mo>(</mo><mn>2080</mn><mo>)</mo></mrow><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow></math> molecular state is compatible with the available data for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>γ</mi><mi>p</mi><mo>→</mo><msup><mi>K</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><mi mathvariant="normal">Λ</mi></mrow></math> reaction. The reaction mechanism of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>γ</mi><mi>p</mi><mo>→</mo><msup><mi>K</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><mi mathvariant="normal">Λ</mi></mrow></math> is analyzed and the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>N</mi><mrow><mo>(</mo><mn>2080</mn><mo>)</mo></mrow><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow><mo>,</mo><mo> </mo><mrow><mi>N</mi><mrow><mo>(</mo><mn>2060</mn><mo>)</mo></mrow><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow><mo>,</mo><mo> </mo><mrow><mi>N</mi><mrow><mo>(</mo><mn>2000</mn><mo>)</mo></mrow><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi></math> exchanges are found to provide dominant contributions.

Wen-Ya Tian

Neng-Chang Wei

Yu-Fei Wang

Bing-Song Zou

Effects of the hadronic molecule <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>N</mi><mrow><mo>(</mo><mn>2080</mn><mo>)</mo></mrow><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow></math> on <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>K</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><mi mathvariant="normal">Λ</mi></mrow></math> photoproduction