Conformal field theory (CFT) can be placed on disparate space-time manifolds to facilitate investigations of their properties. For (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional [<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mi mathvariant="normal">D</mi></mrow></math>] theories, one useful choice is the real projective space <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mi mathvariant="double-struck">RP</mi><mn>3</mn></msup></mrow></math> obtained by identifying antipodal points on the boundary sphere of a three-dimensional ball. One-point functions of scalar primary fields on this manifold generally do not vanish and encode the so-called crosscap coefficients. These coefficients also manifest on the sphere as the overlaps between certain crosscap states and CFT primary states. Taking the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mi mathvariant="normal">D</mi></mrow></math> Ising CFT as a concrete example, we demonstrate that crosscap coefficients can be extracted from microscopic models. We construct crosscap states in both lattice models defined on polyhedrons and continuum models in Landau levels, where the degrees of freedom at antipodal points are entangled in Bell-type states. By computing their overlaps with the eigenstates of many-body Hamiltonians, we obtain results consistent with those from conformal bootstrap. Importantly, our approach directly reveals the absolute values of crosscap overlaps, whereas bootstrap calculations typically yield only their ratios. Furthermore, we investigate the finite-size scaling of these overlaps and their evolution under perturbations away from criticality.

China

Jia-Ming Dong

Germany

Yueshui Zhang

Kai-Wen Huang

Hong-Hao Tu

Ying-Hai Wu

Numerical extraction of crosscap coefficients in microscopic models for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mi mathvariant="normal">D</mi></mrow></math> conformal field theory

The study of a wide peaking structure in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mi>γ</mi></math> mass spectrum is reported using a data sample of proton-proton collisions collected by the LHCb detector at center-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>9</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. The observed structure is consistent with the lowest excited <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup></math> states and exhibits a statistical significance exceeding 7 standard deviations relative to the background-only hypothesis. A two-peak model serves as an effective description of the data, with various theory-constrained models further explored to provide physical interpretation. Based on the predictions for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mi>P</mi><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math> spectrum, the relative production cross section of the overall <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mi>P</mi><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math> states with respect to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup></math> ground state with the transverse momentum <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>p</mi><mi mathvariant="normal">T</mi></msub></math> and rapidity <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>y</mi></math> of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup></math> mesons in the regions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>p</mi><mi mathvariant="normal">T</mi></msub><mo>&lt;</mo><mn>20</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>/</mo><mi>c</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2.0</mn><mo>&lt;</mo><mi>y</mi><mo>&lt;</mo><mn>4.5</mn></math> at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> is measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0.20</mn><mo>±</mo><mn>0.03</mn><mo>±</mo><mn>0.02</mn><mo>±</mo><mn>0.03</mn></math>, where the uncertainty terms represent statistical, systematic, and uncertainties related to the choice of theoretical models, respectively. The results provide a test of theoretical models and deepen our understanding of quantum chromodynamics.

Netherlands

R. Aaij

United Kingdom

A.S.W. Abdelmotteleb

Switzerland

C. Abellan Beteta

F. Abudinén

T. Ackernley

United States

A.A. Adefisoye

Spain

B. Adeva

M. Adinolfi

P. Adlarson

France

C. Agapopoulou

C.A. Aidala

Z. Ajaltouni

S. Akar

K. Akiba

Italy

P. Albicocco

J. Albrecht

CERN

F. Alessio

Z. Aliouche

P. Alvarez Cartelle

R. Amalric

Brazil

S. Amato

J.L. Amey

Y. Amhis

L. An

L. Anderlini

M. Andersson

P. Andreola

M. Andreotti

S. Andres Estrada

A. Anelli

D. Ao

F. Archilli

Z Areg

M. Argenton

Costa Rica

S. Arguedas Cuendis

A. Artamonov

M. Artuso

E. Aslanides

R. Ataíde Da Silva

M. Atzeni

B. Audurier

J.A. Authier

D. Bacher

I. Bachiller Perea

S. Bachmann

M. Bachmayer

J.J. Back

P. Baladron Rodriguez

V. Balagura

A. Balboni

W. Baldini

L. Balzani

H. Bao

J. Baptista de Souza Leite

C. Barbero Pretel

M. Barbetti

I.R. Barbosa

R.J. Barlow

M. Barnyakov

S. Barsuk

W. Barter

J. Bartz

Poland

S. Bashir

B. Batsukh

P.B. Battista

A. Bay

A. Beck

M. Becker

F. Bedeschi

I.B. Bediaga

N.A. Behling

S. Belin

K. Belous

I. Belov

I. Belyaev

G. Benane

G. Bencivenni

E. Ben-Haim

A. Berezhnoy

R. Bernet

S. Bernet Andres

A. Bertolin

C. Betancourt

F. Betti

J. Bex

Ia. Bezshyiko

O. Bezshyyko

J. Bhom

M.S. Bieker

N.V. Biesuz

P. Billoir

A. Biolchini

M. Birch

F.C.R. Bishop

A. Bitadze

A. Bizzeti

T. Blake

F. Blanc

J.E. Blank

S. Blusk

Study of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub><mo stretchy="false">(</mo><mn>1</mn><mi>P</mi><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> states in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mi>γ</mi></math> mass spectrum

We present a systematic study of baryonic flux tubes in SU(3) Yang-Mills theory in (2+1) dimensions. A recent next-to-leading-order derivation within the Effective String Theory framework has, for the first time, made explicit the corrections proportional to the mass of the baryon junction $\textit{M}$, up to order 1/$\textit{R}$ (where $\textit{R}$ is the length of the confining strings), opening the possibility of its non-perturbative determination. One of the main goals of this paper is, through high precision simulations of the three-point Polyakov loop correlator, to measure for the first time the baryon junction mass. By isolating the predicted 1/$\textit{R}$ term in the open string channel, we obtain the value $$M/\sqrt{\sigma }=0.1355\left(36\right)$$ , similar to the phenomenological value which is used to describe hadrons, although our computation was done in (2 + 1) dimensions. In addition, studying the high temperature behavior of the baryon, we present a new test of the Svetitsky-Yaffe conjecture for the SU(3) theory in three dimensions. Focusing on the high temperature regime, just below the deconfinement transition, we compare our lattice results for Polyakov loop correlators with the quantitative predictions obtained by applying conformal perturbation theory to the three-state Potts model in two dimensions and find excellent agreement.

Michele Caselle

Nicodemo Magnoli

Dario Panfalone

Lorenzo Verzichelli

The mass of the baryon junction: a lattice computation in 2 + 1 dimensions

In 1914, Ramanujan unveiled 17 extraordinary infinite series for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><mi>π</mi></math>. In this Letter, we uncover their physics origin by relating them to 2D logarithmic conformal field theories (LCFTs), which emerge in diverse settings such as the fractional quantum Hall effect, percolation, polymers, and even holography. Through this LCFT connection, we reinterpret such infinite series in terms of fundamental CFT data-the operator spectrum and OPE coefficients. This perspective leads to novel physics-inspired approximations for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><mi>π</mi></math>. Drawing lessons from Ramanujan’s formulas, we construct a new family of bases for expanding LCFT correlators that converge far more rapidly than the standard conformal block decomposition. This is achieved using recently developed stringy/parametric crossing-symmetric dispersion relations. Remarkably, when working with these new expansions, the action of a certain differential operator (which arises naturally from the Ramanujan connection) dramatically enhances convergence, with the entire contribution collapsing to that of the logarithmic identity operator. This striking simplification hints at a universal property of LCFTs. Finally, we discuss a new holographic interpretation of this unexpected mathematics-physics connection.

India

Faizan Bhat

Canada

Aninda Sinha

Ramanujan’s <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mo>/</mo><mi>π</mi></mrow></math> Series and Conformal Field Theories

We propose an explanation for the recently reported ultrahigh-energy neutrino signal at KM3NeT, which shows no clear association with known astrophysical sources. While decaying dark matter in the Galactic Center is a natural candidate, the observed arrival direction strongly suggests an extragalactic origin. We introduce a multicomponent dark matter scenario in which the components are part of a supermultiplet, with supersymmetry ensuring a nearly degenerate mass spectrum among the fields with different spins. In this setup, a cosmologically long-lived fermionic state decays into a slightly lighter bosonic dark matter state, producing a boosted neutrino spectrum with energy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>E</mi><mi>ν</mi></msub><mo>∼</mo><mn>100</mn><mtext> </mtext><mtext> </mtext><mi>PeV</mi></math>, determined by the mass difference. The heavy-to-light decay occurs at a cosmological redshift of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>z</mi><mo>∼</mo><mrow><mi mathvariant="normal">a</mi><mtext> </mtext><mi>few</mi></mrow></math> or higher, leading to an isotropic directional distribution of the signal.

South Korea

Yongsoo Jho

Seong Chan Park

Chang Sub Shin

Superheavy supersymmetric dark matter as the origin of the KM3NeT ultrahigh energy signal

NuMI Off-axis <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ν</mi><mi>e</mi></msub></math> Appearance (NOvA) experiment is an ongoing long-baseline neutrino oscillation experiment. The primary channels of interest are the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ν</mi><mi>e</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mi>e</mi></msub></math> appearance, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ν</mi><mi>μ</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mi>μ</mi></msub></math> disappearance channels analyzed in the energy window <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>&lt;</mo><msub><mi>E</mi><mi>ν</mi></msub><mo>&lt;</mo><mn>4</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. However, NOvA far detector sees nontrivial high-energy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ν</mi><mi>e</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mi>e</mi></msub></math> events in the energy range <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>4</mn><mo>&lt;</mo><msub><mi>E</mi><mi>ν</mi></msub><mo>&lt;</mo><mn>20</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. These high-energy events provide us with an opportunity to investigate the subleading new physics scenarios. In this context, we study the sensitivity of the NOvA experiment to constrain the nonstandard interaction (NSI) parameters and environmental decoherence parameters. We observe that by including high energy events (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>signal</mi><mo>+</mo><mtext>background</mtext></mrow></math>) the degeneracy around <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ε</mi><mrow><mi>e</mi><mi>τ</mi></mrow></msub><mo>∼</mo><mn>1.6</mn></math> can be removed throughout the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>δ</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>δ</mi><mrow><mi>e</mi><mi>τ</mi></mrow></msub></math> range. Further, we examine the role of signal versus beam background events in removing this degeneracy. In addition, we constrain the decoherence parameter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Γ</mi></math> considering events from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mo>&lt;</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>ν</mi></mrow></msub><mo>&lt;</mo><mn>20</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>. Later, assuming the presence of decoherence in nature we obtain the allowed regions in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>θ</mi><mn>23</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>δ</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub></math> plane.

Chinmay Bera

K.N. Deepthi

Probing new physics scenarios using high energy events at the NOvA far detector

The standard model of the universe, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi><mi>CDM</mi></math>, is based on the Friedmann-Lemaître-Robertson-Walker metric with a flat three-dimensional coordinate space and the Friedmann equations Navas et al. [<a href="http://dx.doi.org/10.1103/PhysRevD.110.030001">Phys. Rev. D 110, 030001 (2024)</a>.]. The cosmological constant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math> provides the cancellation of the matter field contributions in the flat (Minkowski) space, as was proposed long ago in 1967 by Zeldovich for the first time to our knowledge Zeldovich [JETP Lett. 6, 316 (1967)]; see also Krasinski and Zeldovich [<a href="http://dx.doi.org/10.1070/PU1968v011n03ABEH003927">Sov. Phys. Usp. 11, 381 (1968)</a>]. The dynamical dark energy appears on the surface of the vacuum energy of matter fields at the flat (Minkowski) space. Within the Standard Model, the gluon Yang-Mills (YM) fields are playing a specific role since the properties of their vacuum, where there is the presence of the gluon condensate, provide the nonperturbative vacuum energy. It is natural to apply the successful instanton liquid model of the QCD vacuum and its lowest excitations. Our aim is to calculate the contribution of gluon YM fields to the dark energy density. We find that the universe metric is generating the QCD vacuum excitation, which gives the contribution to the dark energy density. But this one may hardly play a central role in the dynamics of the universe, since its timescale is too small. We also find the equation-of-state parameters <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>w</mi><mn>0</mn></msub><mo>=</mo><mo>−</mo><mn>1</mn><mo>,</mo><msub><mi>w</mi><mi>a</mi></msub><mo>=</mo><mn>0</mn></math> in accordance with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi><mi>CDM</mi></math>, while the newest data, analyzed at Shajib and Frieman [<a href="http://dx.doi.org/10.1103/kjpb-r698">Phys. Rev. D 112, 063508 (2025)</a>.], give them at least in the range <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>0.91</mn><mo>&lt;</mo><msub><mi>w</mi><mn>0</mn></msub><mo>&lt;</mo><mo>−</mo><mn>0.73</mn><mo>,</mo><mspace linebreak="goodbreak"></mspace><mo>−</mo><mn>1.05</mn><mo>&lt;</mo><msub><mi>w</mi><mi>a</mi></msub><mo>&lt;</mo><mo>−</mo><mn>0.65</mn></math>. They are requesting a contribution from an ultralight scalar such as an axion, or from YM field topological configurations with the nontrivial holonomy due to the deviation from a pure de Sitter state Van Waerbeke and Zhitnitsky [DESI results and dark energy from QCD topological sectors, <a href="http://arXiv.org/abs/2506.14182">arXiv:2506.14182</a>.].

Uzbekistan

M.M. Musakhanov

Dark energy and QCD instanton vacuum in a Friedmann-Lemaître-Robertson-Walker universe

Models with classically degenerate vacua often support quasiclassical configurations of nontrivial topology. In (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>0</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional quantum mechanics with a double-well potential, for example, instantons induce mixing between the two perturbative ground states in the purely bosonic case, while in the supersymmetric version, the tunneling amplitude is suppressed. In this work, we investigate (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional models featuring classically Bogomol’nyi-Prasad-Sommerfield saturated kinks with degenerate masses and identical topology. Recent studies suggest that such kinks may undergo mixing mediated by scalar-field instantons. We analyze this phenomenon in a supersymmetric framework and demonstrate that, whereas mixing indeed occurs in the bosonic theory, the presence of fermionic zero modes in the supersymmetric case leads to the vanishing of the transition amplitude. To illustrate these results, we examine two examples featuring Wess-Zumino models with two and four supercharges. The latter example is motivated by the Affleck-Dine-Seiberg superpotential. We also present a number of developments of instanton calculus in the case of instantons in kink backgrounds.

Evgenii Ievlev

Mikhail Shifman

Degenerate kinks and kink-instantons in two-dimensional scalar field models with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><mi mathvariant="script">N</mi></mrow><mo>=</mo><mn>1</mn></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>2</mn></mrow></math> supersymmetry

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

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

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

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)