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, 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

Dian-Yong Chen

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

Lepton number violation decay $ \omega \to \pi^+ \pi^+ e^-e^- +c.c. $ is searched for via $ J/\psi \to \omega\eta $ using a data sample of $ (1.0087 \pm 0.0044) \times 10^{10} $ $ J/\psi $ events collected via the BESIII detector at the BEPCII collider. No significant signal is observed, and the upper limit on the branching fraction of $ \omega \to \pi^+ \pi^+ e^-e^- +c.c. $ at the 90% confidence level is determined for the first time to be $ 2.8 \times 10^{-6} $ .

Z.H. Duan

Search for the lepton number violation decay $\textit{ω}$→$\textit{π}$ $^{+}$ $\textit{π}$ $^{+}$ $\textit{e}$ $^{−}$ $\textit{e}$ $^{−}$+$\textit{c}$.$\textit{c}$. * Supported in part by National Key R&D Program of China (2023YFA1606000, 2023YFA1606704); National Natural Science Foundation of China (NSFC) (12035009, 11875170, 11635010, 11935015, 11935016, 11935018, 12025502, 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); ERC (758462); 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; Polish National Science Centre (2024/53/B/ST2/00975); STFC (United Kingdom); Swedish Research Council (2019.04595); U. S. Department of Energy (DE-FG02-05ER41374)

While charged lepton-flavor-violating tau decays to strange mesons provide powerful probes of the underlying <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi><mo stretchy="false">→</mo><mo>ℓ</mo><mi>d</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math> transition, the corresponding decay modes involving hyperons are kinematically forbidden. To address this gap, we propose the quasielastic scattering processes <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>−</mo></msup><mi>N</mi><mo stretchy="false">→</mo><msup><mi>τ</mi><mo>−</mo></msup><mi>Y</mi></math>. Within a general low-energy effective Lagrangian, we perform a comprehensive analysis of the final-state polarizations of both the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi></math> lepton and the hyperon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi></math>, systematically addressing the theoretical uncertainty driven by the model dependence of form factors. Our analysis demonstrates that while this uncertainty leads to large variations in predicted rates, the polarization observables can potentially distinguish between the form factor models, and help to determine the chiral nature of the vectorial new physics interaction. Finally, we forecast the event rates for future facilities, revealing a strong dependence on the form factor models, with predicted yields ranging from potentially observable levels to rates far below current detection thresholds.

Xin-Shuai Yan

Zhen-Qing Hu

Qin Chang

Ya-Dong Yang

Polarization probes of new physics in lepton-flavor-violating hyperon production from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>−</mo></msup><mi>N</mi><mo stretchy="false">→</mo><msup><mi>τ</mi><mo>−</mo></msup><mi>Y</mi></math> scattering

Starting from a theory on $\textit{S}$ × $\textit{S}$ and dimensionally reducing, we compute the full partition function, including flux and instanton contributions, for an $$ \mathcal{N} $$ = 1 theory of vector multiplets and hypermultiplets on five-dimensional toric Sasakian manifolds $\textit{Y}$ . Dimensionally reducing, we obtain the partition function for Pestun-like theories on a class of manifolds whose topology is $\textit{S}$ × $\textit{S}$ . Generalizing the procedure starting from branched covers of $\textit{S}$ × $\textit{S}$ , we reduce to a theory on $\textit{Y}$ with codimension two twist defects. Exploiting a proposed equivalence with partition functions on spaces with orbifold singularities, our results provide the partition function of an $$ \mathcal{N} $$ = 2 theory on the product of two spindles.

Lorenzo Ruggeri

Exact results for SYM on $\textit{Y}$

In this study, we investigate the production of doubly charmed baryons from anti-bottom charmed mesons. Using the effective Lagrangian approach, we discuss triangle diagrams at the hadronic level to access the branching ratios of $\overline{B}_c\to {\cal{B}}_{ccq}+{\cal{B}}_{\bar c\bar q\bar q}$ . Apparently, the specific process $\overline {B}_c \to \Xi_{cc}^{+} \, \overline {\Xi}_{\bar c}^{'0}$ occupies the largest possibility on the order of $9.1\times 10^{-5}$ . In addition, although the production of undiscovered $\Omega_{cc}^+$ is Cabibbo suppressed in $\overline B_c\to \Omega_{cc}^+ \, \overline {\Xi}_{\bar c}^0$ , its branching ratio can still reach a level of $10^{-7}$ . These results are expected to provide valuable support for future experiments.

Ye Xing

Ji Xu

Searching for doubly charmed baryons from ${ \overline{\boldsymbol B}_{\boldsymbol c}}$ meson decays * Y. X. support by National Natural Science Foundation of China (12005294), and the Fundamental Funds for Key disciplines in Physics (2022WLXK05). J. X. supported by National Natural Science Foundation of China (12105247)

We continue the study of 2D gravity—“matrix model” duality on the example of a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mi>p</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></math> minimal string. We propose a reformulation of the duality, related to a more conventional one by “<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>x</mi><mtext>−</mtext><mi>y</mi></mrow></math> swap” in the language of topological recursion. This formulation elucidates some conceptual and technical difficulties in the dictionary of the duality and relation to other examples. In particular, it allows to circumvent the necessity to use “resonance transformations,” which were previously introduced to match the world sheet and “matrix model” correlators, and the expressions for minimal string amplitudes in this approach are reminiscent of the ones obtained recently for “complex Liouville string” theory. Using this new approach, we also formulate a conjecture on how one can compute amplitudes with operators other than tachyons in the dual theory.

Aleksandr Artemev

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>x</mi><mtext>−</mtext><mi>y</mi></mrow></math> swap for a (2, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mi>p</mi><mo>+</mo><mn>1</mn></mrow></math>) minimal string

We investigate the properties of the radially excited charged pion, with a specific focus on its electromagnetic form factor (EFF) and its box contribution to the hadronic light-by-light (HLbL) component of the muon's anomalous magnetic moment, $ a_{\mu} $ . Utilizing a coupled non-perturbative framework combining Schwinger-Dyson and Bethe-Salpeter equations, we first compute the mass and weak decay constant of the pion's first radial excitation. Initial results are provided for the Rainbow-Ladder (RL) approximation, followed by an extended beyond RL (BRL) analysis that incorporates meson cloud effects. Building on our previous work, this analysis demonstrates that an accurate description of the first radial excitation can be achieved without the need for a reparametrization of the interaction kernels. Having demonstrated the effectiveness of the truncation scheme, we proceed to calculate the corresponding EFF, from which we derive the contribution of the pion's first radial excitation to the HLbL component of the muon's anomalous magnetic moment, producing $ a_{\mu}^{\pi_1-\text{box}}(\text{RL}) = -(2.03 \pm 0.12) \times 10 ^{-13} $ , $ a_{\mu}^{\pi_1-\text{box}}(\text{BRL}) = $ $ -(2.02 \pm 0.10) \times 10 ^{-13} $ . Our computation also sets the groundwork for calculating related pole contributions of excited pseudoscalar mesons to $ a_{\mu} $ .

Mexico

Angel S. Miramontes

K. Raya

A. Bashir

P. Roig

G. Paredes-Torres

Radially excited pion: electromagnetic form factor and the box contribution to the muon's $\textit{g}$-2 * A. S. Miramontes acknowledges $\textit{Consejo Nacional de Ciencia, Humanidades y Tecnología}$ (CONAHCyT), Mexico, for the financial support received through the program '$\textit{Postdoctorados Nacionales por México}$', additionally, has been partially funded by the 'PROMETEO' programme of the 'Generalitat Valenciana' grant CIPROM/2022/66, and by the Spanish 'Agencia Estatal de Investigación', MCIN/AEI/10.13039/501100011033, through the grants PID2020-113334GB-I00 and PID2023-151418NB-I00. A. Bashir thanks $\textit{Coordinación de la Investigación Científica}$ of the $\textit{Universidad Michoacana de San Nicolás de Hidalgo}$ Grant No. 4.10., CONAHCyT grant CBF2023-2024-3544 and $\textit{Ayudas Beatriz Galindo}$, Spain. P. Roig acknowledges Conahcyt (México) funding through project CBF2023-2024-3226 as well as Spanish support during his sabbatical year through projects MCIN/AEI/10.13039/501100011033, grant PID2020-114473GB-I00, and Generalitat Valenciana grant PROMETEO/2021/071. G. Paredes-Torres acknowledges CONAHCyT, Mexico, for the financial support provided to him through the program '$\textit{Beca de Posgrado en México}$'. The work of A. Bashir and K. Raya is supported by Spanish Ministry of Science and Innovation (MICINN grant no. PID2022-140440NB-C22) and Junta de Andalucía (grant P18-FR-5057)

Using 20.3 fb$^{–1}$ of $e^+e^-$ annihilation data collected at a center-of-mass energy of 3.773 GeV with the BESIII detector, we report on an improved search for the radiative leptonic decay $D^+\to\gamma e^+\nu_e$ . An upper limit on its partial branching fraction for photon energies $E_\gamma \gt 10 $ MeV was determined to be $1.2\times10^{-5}$ at a 90% confidence level; this excludes most current theoretical predictions. A sophisticated deep learning approach, which includes thorough validation and is based on the Transformer architecture, was implemented to efficiently distinguish the signal from massive backgrounds.

G. Chelkov

C. Chen

Y.T. Feng

M. Fritsch

C.D. Fu

Search for radiative leptonic decay $\textit{D}$ $^{+}$→$\textit{γe}$ $^{+}$ ν$_{e}$ using deep learning * This work is supported in part by National Key R&D Program of China (2020YFA0406400, 2023YFA1606000, 2020YFA0406300); National Natural Science Foundation of China (NSFC) (11635010, 11735014, 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; the CAS Center for Excellence in Particle Physics (CCEPP); Joint Large-Scale Scientific Facility Funds of the NSFC and CAS (U1832207); CAS (YSBR-101); 100 Talents Program of CAS; CAS Project for Young Scientists in Basic Research (YSBR-117); 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 (2019/35/O/ST2/02907); Swedish Research Council (2019.04595); The Swedish Foundation for International Cooperation in Research and Higher Education (CH2018-7756); U. S. Department of Energy (DE-FG02-05ER41374)