We perform a theoretical study of the decay process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mo>−</mo></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> in search of the doubly heavy tetraquark states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> with quark content <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>d</mi><mo stretchy="false">¯</mo></mover></math>. These <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> states are assumed to be dynamically generated molecular states from the S-wave interactions between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mi>s</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mn>0</mn></mrow></msubsup><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mn>0</mn></mrow></msup><msubsup><mi>D</mi><mi>s</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msubsup></math> meson pairs. Based on the total angular momentum and the type of the constituent mesons (pseudoscalars <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math> or vectors <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi></math>), they are labeled as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>P</mi><mi>P</mi></mrow></msubsup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>2</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math>, respectively. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> invariant mass distribution for this decay is calculated using current algebra, incorporating contributions from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> states arising from final-state interactions. Our results reveal a clear peak structure in the 7415–7425 MeV region, which is attributed to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>2</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math> state. Additionally, a distinct dip structure appears near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mrow><mo>*</mo><mn>0</mn></mrow></msup><msubsup><mi>D</mi><mi>s</mi><mrow><mo>*</mo><mo>+</mo></mrow></msubsup></math> threshold, characteristic of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>2</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math> as a hadronic molecular state. A near-threshold enhancement associated with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>P</mi><mi>P</mi></mrow></msubsup></math> state and a dip arising from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math> state are also identified, though the manifestation of these features depends sensitively on model parameter fine-tuning. Therefore, with increased experimental statistics, the decay channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mo>−</mo></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> offers a promising avenue for discovering and characterizing the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> states.

China

Wen-Ying Liu

Hua-Xing Chen

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> states in the process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mo>−</mo></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math>

We investigate the electromagnetic properties of the axial-vector molecular states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><mi>K</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>K</mi><mo>*</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>*</mo></msup><mi>K</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><msup><mi>K</mi><mo>*</mo></msup></math>, which are used to model the charmed states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow><mo>+</mo></msubsup><mo stretchy="false">(</mo><mn>2460</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow><mo>+</mo></msubsup><mo stretchy="false">(</mo><mn>2536</mn><mo stretchy="false">)</mo></math>, and their bottom partners with quantum numbers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>1</mn><mo>+</mo></msup></math>. To our knowledge, this presents the first comprehensive calculation of the magnetic and quadrupole moments for these specific molecular configurations. Employing the QCD light-cone sum rule method with molecular-type interpolating currents, we compute these moments and perform a detailed flavor decomposition to reveal the internal distribution of the electromagnetic charge and spin. Our results demonstrate that the light up and down quarks dominate the electromagnetic response, with negligible contributions from the heavy quarks. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><mi>K</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>*</mo></msup><mi>K</mi></math> states exhibit negative quadrupole moments and slightly oblate charge distributions, whereas the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>K</mi><mo>*</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><msup><mi>K</mi><mo>*</mo></msup></math> states possess positive quadrupole moments and prolate distributions, with significant contributions from the strange quark. The predicted moments provide benchmarks for lattice QCD calculations and are testable through their influence on radiative transitions and photo- and electroproduction observables at high-luminosity facilities, offering crucial insights into the internal structure and nature of these axial-vector states.

Türkiye

Ulaş Özdem

Electromagnetic properties of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow><mo>+</mo></msubsup><mo stretchy="false">(</mo><mn>2460</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow><mo>+</mo></msubsup><mo stretchy="false">(</mo><mn>2536</mn><mo stretchy="false">)</mo></math>, and their bottom partners in a molecular configuration

The particle origin of dark matter (DM) remains elusive despite decades of direct, indirect, and collider searches. Several groups have reported a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math>-ray excess toward the Galactic Center commonly referred to as the Galactic Center excess (GCE). Its spectrum is consistent with annihilation of weakly interacting massive particles (WIMPs) of mass <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mn>10</mn><mo>−</mo><mn>100</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math> and a thermal-relic cross section. Although many concrete WIMP models reproduce the GCE spectrum, most are now excluded by direct detection experiments that are approaching the neutrino floor. We investigate a class of anomaly-free extensions of the Standard Model featuring gauged differences of lepton number, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><msub><mi>L</mi><mi>i</mi></msub><mo>−</mo><msub><mi>L</mi><mi>j</mi></msub></mrow></msub></math>, and gauged baryon minus lepton number, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></math>. We show that these models can reproduce the GCE while remaining compatible with the observed relic abundance. We then impose collider and direct detection constraints, accounting for both tree-level and loop-induced kinetic mixing. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>e</mi></msub></math> model gives the best fit to the GCE: a DM mass of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>χ</mi></mrow></msub><mo>∼</mo><mn>40</mn><mo>−</mo><mn>50</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math> remains consistent with the muon and electron magnetic moment anomalies, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mi>g</mi><mo>−</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mrow><mi>μ</mi><mo>,</mo><mi>e</mi></mrow></msub></math>, as well as current collider and direct detection limits, for mediator masses in the range <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>m</mi></mrow><mrow><msup><mrow><mi>A</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub><mo>∼</mo><mn>70</mn><mo>−</mo><mn>86</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math> and a DM mediator coupling of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mn>5</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow></math>. By contrast, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>L</mi><mi>e</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></math> models yield poorer fits; satisfying both the relic density and experimental bounds forces the DM mass to lie very close to resonance (i.e. approximately half the mediator mass). Finally, while the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo>−</mo><mi>L</mi></math> model also matches the GCE well, its parameter space is almost entirely ruled out by strong direct detection limits, except for the narrow resonance region where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>χ</mi></msub></math> should be equal to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><msup><mi>A</mi><mo>′</mo></msup></msub><mo>/</mo><mn>2</mn></math> requiring a fine-tuning at the few-percent level.

Italy

Jordan Koechler

Mattia Di Mauro

Leptophilic dark matter in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><msub><mi>L</mi><mi>i</mi></msub><mo>−</mo><msub><mi>L</mi><mi>j</mi></msub></mrow></msub></math> models: A solution to the Fermi-LAT Galactic Center excess consistent with cosmological and laboratory observations

The first measurement at midrapidity (|$\textit{y}$|$\textit{ <}$ 0$\textit{.}$5) of the production yield of the strange-charm baryons $${\Xi }_{\text{c}}^{+}$$ and $${\Xi }_{\text{c}}^{0}$$ as a function of transverse momentum ($\textit{p}$ ) in different charged-particle multiplicity classes in proton-proton collisions at $$\sqrt{s}=13$$ TeV with the ALICE experiment at the LHC is reported. The $${\Xi }_{\text{c}}^{+}$$ baryon is reconstructed via the $${\Xi }_{\text{c}}^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}$$ decay channel in the range 4 $\textit{< p}$ $\textit{<}$ 12 GeV$\textit{/c}$, while the $${\Xi }_{\text{c}}^{0}$$ baryon is reconstructed via both the $${\Xi}_{\text{c}}^{0}\to {\Xi}^{-}{\pi }^{+}$$ and $${\Xi}_{\text{c}}^{0}\to {\Xi}^{-}{\text{e}}^{+}{\nu }_{\text{e}}$$ decay channels in the range 2 $\textit{< p}$ $\textit{<}$ 12 GeV$\textit{/c}$. The baryon-to-meson $$\left({\Xi}_{\text{c}}^{0,+}/{\text{D}}^{0}\right)$$ and the baryon-to-baryon $$\left({\Xi}_{\text{c}}^{0,+}/{\Lambda}_{\text{c}}^{+}\right)$$ production yield ratios show no significant dependence on multiplicity. In addition, the observed yield ratios are not described by theoretical predictions that model charm-quark fragmentation based on measurements at e e and e p colliders, indicating differences in the charm-baryon production mechanism in pp collisions. A comparison with different event generators and tunings, including different modelling of the hadronisation process, is also discussed. Moreover, the branching-fraction ratio of $${\text{BR}}\left({\Xi}_{\text{c}}^{0}\to {\Xi }^{-}{\text{e}}^{+}{\nu }_{\text{e}}\right)/{\text{BR}}\left({\Xi}_{\text{c}}^{0}\to {\Xi }^{-}{\pi }^{+}\right)$$ is measured as 0.825 ± 0.094 (stat.) ± 0.081 (syst.). This value supersedes the previous ALICE measurement, improving the statistical precision by a factor of 1.6.

United States

I. Abualrob

S. Acharya

Switzerland

G. Aglieri Rinella

L. Aglietta

M. Agnello

N. Agrawal

India

Z. Ahammed

S. Ahmad

Slovakia

I. Ahuja

Indonesia

ZUL. Akbar

A. Akindinov

Germany

V. Akishina

M. Al-Turany

D. Aleksandrov

B. Alessandro

H. Alfanda

Mexico

R. Alfaro Molina

B. Ali

A. Alici

South Korea

A. Alkin

Norway

J. Alme

G. Alocco

T. Alt

A. Altamura

I. Altsybeev

Romania

C. Andrei

United Kingdom

N. Andreou

A. Andronic

E. Andronov

V. Anguelov

F. Antinori

P. Antonioli

N. Apadula

H. Appelshäuser

S. Arcelli

R. Arnaldi

Brazil

J. Arneiro

I. Arsene

M. Arslandok

A. Augustinus

R. Averbeck

M. Azmi

Japan

H. Baba

A. Babu

A. Badalà

J. Bae

Y. Bae

Y. Baek

X. Bai

R. Bailhache

Y. Bailung

R. Bala

France

A. Baldisseri

Poland

B. Balis

S. Bangalia

Z. Banoo

V. Barbasova

F. Barile

L. Barioglio

Greece

M. Barlou

B. Barman

Hungary

G. Barnaföldi

L. Barnby

E. Barreau

V. Barret

L. Barreto

K. Barth

E. Bartsch

N. Bastid

G. Batigne

D. Battistini

B. Batyunya

D. Bauri

Peru

J. Bazo Alba

Denmark

I. Bearden

P. Becht

D. Behera

S. Behera

I. Belikov

V. Bella

F. Bellini

R. Bellwied

L. Beltran

Y. Beltran

G. Bencedi

A. Bensaoula

S. Beole

Y. Berdnikov

A. Berdnikova

L. Bergmann

L. Bernardinis

L. Betev

P. Bhaduri

T. Bhalla

A. Bhasin

B. Bhattacharjee

S. Bhattarai

L. Bianchi

Czechia

J. Bielčík

J. Bielčíková

Multiplicity dependence of $${\Xi }_{\text{c}}^{+}$$ and $${\Xi }_{\text{c}}^{0}$$ production in pp collisions at $$\sqrt{s}=13$$ TeV

We revisit the calculation of exclusive <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> production in electron-proton scattering within the QCD dipole model, employing a refined description of the proton in terms of gluonic hot spots in the dilute regime. In contrast to earlier studies, we incorporate key missing elements; the event-by-event fluctuations in both the number of hot spots and their local saturation scales, as well as the first relativistic corrections to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> wave function. We perform a Bayesian analysis to constrain the model parameters using HERA data. These enhancements significantly improve the agreement with HERA data. Saturation scale fluctuations are found to be more important than fluctuations in the number of hot spots. Including the first relativistic correction is found to be important, especially in order to describe the observed power-law behavior in the incoherent cross section at large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi></math>.

Finland

Anh Dung Le

Heikki Mäntysaari

Exclusive <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> production off a dilute proton within a refined hotspot description

Based on available experimental results on $ \chi _{cJ}(J=0,1,2) $ decays, we investigated the $ \chi_{cJ}\to PP $ , $ VV $ , $ PV $ , and $ PT $ decays using the $\textit{SU}$(3) flavor symmetry/breaking approach, where $\textit{P}$, $\textit{V}$, and $\textit{T}$ denote light pseudoscalar, vector, and tensor mesons, respectively. With the decay amplitude relations determined by $\textit{SU}$(3) flavor symmetry/breaking, we present the branching ratios for all $ \chi_{cJ}\to PP $ and $ \chi_{cJ}\to VV $ modes, including those without experimental data. While theoretical considerations strongly suppress or even forbid most $ \chi_{cJ}\to PV $ and $ PT $ decays, we also provide quantitative predictions constrained by existing experimental data. Our results are expected to be accessible in future experiments at BESIII and the planned Super Tau-Charm Facility.

Bo Lan

Qin-Ze Song

Jin-Huan Sheng

Yi Qiao

Ru-Min Wang

Study of χ$_{cJ}$ ($\textit{J}$ = 0,1,2) decays to light meson pairs based on $\textit{SU}$(3) flavor symmetry/breaking analysis * Supported by the National Natural Science Foundation of China (12175088, 12305100, 12365014) and Graduate Innovation Fund Project of Jiangxi Provincial Department of Education (YJS2024091)

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

R. Aliberti

A. Amoroso

Q. An

Y. Bai

O. Bakina

Y. Ban

H.R. Bao

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

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

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)