The analysis of the latest most accurate experimental data on neutron decay for the possibility of the existence of the right vector boson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mi>W</mi><mi>R</mi></msub></mrow></math> is carried out. As a result of the analysis within the framework of the left-right symmetric model, it was found that there is an indication of the existence of the right vector boson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mi>W</mi><mi>R</mi></msub></mrow></math> with a mass of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mi>M</mi><mrow><msub><mi>W</mi><mi>R</mi></msub></mrow></msub><mo>=</mo><msubsup><mn>304</mn><mrow><mo>−</mo><mn>20</mn></mrow><mrow><mo>+</mo><mn>24</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>, and a mixing angle with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mi>W</mi><mi>L</mi></msub></mrow></math>: <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>ζ</mi><mo>=</mo><mo>−</mo><mn>0.039</mn><mo>±</mo><mn>0.0</mn><mn>1</mn><mn>4</mn></mrow></math>. It is shown that this result does not contradict the experiments at colliders to search for a hypothetical vector boson. In addition, it is shown that it is possible to describe the effects of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> violation in decays of neutral <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math>-mesons and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>-mesons using the parameters of the extended left-right symmetric model obtained from neutron decay, i.e., squared masses of the left and right bosons ratio and the mixing angle. The formation of baryon-lepton asymmetry of the Universe is considered within the framework of the left-right model of weak interaction with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> violation.

Russia

A.P. Serebrov

O.M. Zherebtsov

A.K. Fomin

R.M. Samoilov

N.S. Budanov

Analysis of experimental data on neutron decay for the possibility of the existence of the right vector boson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>W</mi><mi>R</mi></msub></math>

The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>R</mi><mn>2</mn></msup></math>-Higgs inflation is one of the simplest yet best-fit models consistent with Planck data. The higher spectral index <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi>s</mi></msub></math> recently reported by the combined cosmic microwave background (CMB) data from the Atacama Cosmology Telescope (ACT), South Pole Telescope (SPT), and Planck, along with baryonic acoustic oscillation data from the Dark Energy Spectroscopic Instrument (DESI), disfavors the single-field-like regime of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>R</mi><mn>2</mn></msup></math>-Higgs inflation at approximately <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>σ</mi></math>. Following a doubly covariant formalism, we show that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>R</mi><mn>2</mn></msup></math>-Higgs inflation, when modified by a dimension-six <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>R</mi><mn>3</mn></msup></math> term, can account for the high <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi>s</mi></msub></math> reported by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>CMB</mi><mo>+</mo><mi>BAO</mi></mrow></math>. In this regard, we find that preheating may play a pivotal role. We also show that if the nonminimal coupling between the Ricci scalar <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math> and the Higgs field is <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></math>, then preheating via the production of Higgs quanta may help explain the reported observations.

India

Tanmoy Modak

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>R</mi><mn>2</mn></msup></math>-Higgs inflation: <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>R</mi><mn>3</mn></msup></math> contribution and preheating after ACT and SPT data

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

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)

The anisotropic distribution of ultra high energy cosmic rays (UHECRs) remains a compelling and deeply informative observable in astro-particle physics, illuminating their enigmatic origins, extreme acceleration processes, and trajectories shaped by the cosmic large-scale structure. Among the hierarchy of anisotropy modes, the dipole stands out as a particularly sensitive tracer reflecting both the spatial configuration of sources and the foundational cosmological model. In this work, we conduct a rigorous comparative analysis of dipolar anisotropy within the diffusive propagation regime, evaluating its evolution across three gravitational framework: the standard ΛCDM model, a power-law extension of <italic>f</italic>( <italic>R</italic>) modified gravity, and the Starobinsky inflationary scenario. Our objective is to disentangle the gravitational signatures embedded in UHECR anisotropy, with particular emphasis on deviations arising from extended theories of gravity within the <italic>f</italic>( <italic>R</italic>) formalism. The results reveal a striking dependence on the underlying gravitational paradigm: the power-law model predicts significantly enhanced anisotropies, &#923;CDM consistently produces the most suppressed amplitudes, and the Starobinsky model exhibits an intermediate profile with partial convergence toward &#923;CDM. These findings reinforce the notion that UHECR anisotropy is not merely a reflection of astrophysical processes, but also a subtle messenger of the fundamental gravitational laws governing the universe offering a novel and promising avenue for testing physics beyond the standard cosmological framework.

Pakistan

Iftikhar Ahmad

Muhammad Mahtisham

Azerbaijan

Adnan Malik

Saudi Arabia

Fatemah Mofarreh

Model-dependent predictions for UHECR dipolar anisotropies in a <italic>f</italic>( <italic>R</italic>) modified gravity

We investigate the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mo>=</mo><mn>2</mn></math> SYK model with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math>-para-particles (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mtext>−</mtext><msub><mrow><mi>PSYK</mi></mrow><mn>2</mn></msub></math>), analyzing its thermodynamics and spectral form factor (SFF) using random matrix theory. The Hamiltonian is quadratic, with coupling coefficients randomly drawn from the Gaussian unitary ensemble. The model displays self-averaging behavior and exhibits an exponential ramp in its SFF dynamics: <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">K</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>∼</mo><msup><mi>e</mi><mrow><msub><mi>C</mi><mn>0</mn></msub><mi>t</mi></mrow></msup></math>. The growth rate <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>C</mi><mn>0</mn></msub></math> tends toward either a constant or infinity in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">→</mo><mi>∞</mi></math> limit, depending on specific statistics of the model. These results provide novel perspectives on quantum systems with unconventional statistics.

Tingfei Li

Note on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mo>=</mo><mn>2</mn></math> R-para-fermionic SYK model

In this work, we explore the viability of minimal Higgs inflation with $$(R^2)$$ term in Palatini gravity within the framework of the swampland program. Our analysis focuses on three central conjectures: the Further Refined de Sitter Swampland Conjecture (FRDSSC), the Scalar Weak Gravity Conjecture (SWGC), and the Strong Scalar Weak Gravity Conjecture (SSWGC). By examining theoretical predictions alongside observational constraints, we investigate how the free parameters of the model influence its consistency with these conjectures. The results demonstrate that the model remains compatible with the FRDSSC across a broad parameter space and aligns well with recent data from the Atacama Cosmology Telescope (ACT), reinforcing its standing as a promising inflationary scenario. A detailed study of the SWGC and SSWGC further reveals that the model’s compatibility is highly sensitive to variations in the scalar coupling parameter. A threshold behavior is identified, above which the parameter space supporting consistency expands significantly. Moreover, the SSWGC exhibits a wider region of validity compared to the SWGC, highlighting the stronger conjecture’s broader applicability. Taken together, these findings confirm that minimal Higgs inflation with $$(R^2)$$ term in Palatini gravity is consistent with multiple swampland criteria and possesses robustness under parameter variations.

Iran

Saeed Gashti

Mohammad Afshar

Mohammad Alipour

Behnam Pourhassan

Jafar Sadeghi

From minimal Higgs inflation with $$(R^2)$$ term in palatini gravity to Swampland conjectures under ACT constraints

We discuss the conversion mechanism from scalar field to gravitational waves in magnetic background in <italic>f</italic>( <italic>R</italic>) gravity minimal coupled to the Maxwell electrodynamics. Applying the conversion in early universe with primordial magnetic field and the neutron star with strong magnetosphere, the generated gravitational waves, converted from the scalar field, exhibit distinct power spectra which can be potentially probed by future experiments such as DECIGO, BBO, CE and ET.

Salvatore Capozziello

Qingyu Gan

Gravitational waves in minimal Maxwell <italic>f</italic>( <italic>R</italic>) gravity

In this work, we explore the existence of wormhole geometries within the framework of <italic>f</italic>( <italic>R, T</italic>) gravity by employing a novel functional form based on the Capozziello-De Laurentis model, given by <math altimg='si18.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mi>&#945;</mi><msup><mi>R</mi><mi>n</mi></msup><mo linebreak='goodbreak'>&#8722;</mo><mi>&#946;</mi><msup><mi>R</mi><mrow><mo>&#8722;</mo><mi>q</mi></mrow></msup><mo linebreak='goodbreak'>+</mo><mi>R</mi><mo linebreak='goodbreak'>+</mo><mi>&#955;</mi><mi>T</mi></mrow></math>. We assume a static, spherically symmetric spacetime and analyze the viability of wormhole solutions by imposing appropriate constraints on the shape function. Our investigation reveals specific parameter regions where traversable wormhole configurations can be realized without the necessity of exotic matter. Furthermore, we extend our analysis to perfect fluid models and two different equation-of-state (EoS) scenarios: <math altimg='si19.svg'><mrow><msub><mi>P</mi><mi>r</mi></msub><mo linebreak='goodbreak'>=</mo><mi>k</mi><mi>&#961;</mi></mrow></math> and <math altimg='si20.svg'><mrow><msub><mi>P</mi><mi>t</mi></msub><mo linebreak='goodbreak'>=</mo><mi>k</mi><mi>&#961;</mi></mrow></math>. For each case, we confirm that the obtained shape functions satisfy the required conditions for wormhole existence. Additionally, we examine the energy conditions and find that they remain valid, reinforcing the physical plausibility of the constructed wormhole solutions. Our results demonstrate that viable wormhole geometries can emerge in <italic>f</italic>( <italic>R, T</italic>) gravity under suitable parameter choices, providing further insights into the role of modified gravity in astrophysical structures.

M. Ilyas

Khalid Masood

South Korea

Nehad Ali Shah

Fawad Khan

Traversable wormhole solutions through Capozziello-De Laurentis model in <italic>f</italic>( <italic>R, T</italic>) gravity

We study the symmetries and conserved quantities in $$f(R)$$ gravity for the static, spherically symmetric Reissner–Nordström spacetime using two complementary frameworks: Noether symmetries and Mei symmetries. Starting from a canonical Lagrangian for radial metric functions and the curvature scalar $$R$$ , we derive the associated Hamiltonian and show that the Legendre map is regular whenever both the first derivative of $\textit{f}$($\textit{R}$) with respect to $\textit{R}$ and the second derivative with respect to $\textit{R}$ is non-zero. Within Noether’s approach (variational and Lie-derivative forms), we obtain general, canonical, and internal symmetry classes and identify explicit generators; for the quadratic model $$f(R)=R^{2}$$ these include radial translations and scaling symmetries. We then formulate Mei symmetry conditions as invariance of the Euler–Lagrange equations under the first prolongation, which yields an overdetermined partial differential equation (PDE) system for the generator components. Solving this system for $$f(R)=R^{2}$$ , we find eight independent Mei generators and construct the corresponding conserved currents, some with no direct Noether analogue. The analysis demonstrates that Mei symmetries extend the standard Noether framework for higher-order Lagrangians and provide additional conserved quantities relevant to black-hole dynamics in modified gravity. We conclude with a comparison of the two symmetry schemes and outline applications to broader $$f(R)$$ models and to rotating spacetimes.

Egypt

Tahia Dabash

Moataz Emam

Lukas Schöppner

Symmetry and conserved quantities in $$ f(R) $$ -gravity: Mei vs. Noether approaches

The recent observation of multiple near-threshold structures in <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></math> annihilation—including <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3770</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo stretchy="false">(</mo><mn>3760</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo stretchy="false">(</mo><mn>3780</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo stretchy="false">(</mo><mn>3810</mn><mo stretchy="false">)</mo></math>—reveals limitations in existing models of charmonium and exotic hadrons. In this paper, we propose a unified coupled-channel description that simultaneously incorporates all five near-threshold structures using parameters constrained by hadron spectroscopy. Our model accurately reproduces the line shapes in both <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> and nonopen-charm hadron (nOCH) channels, resolves the asymmetric profile of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3770</mn><mo stretchy="false">)</mo></math>, and produces the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math> bump. We identify the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo stretchy="false">(</mo><mn>3780</mn><mo stretchy="false">)</mo></math> as the dominant manifestation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3770</mn><mo stretchy="false">)</mo></math>, attribute <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo stretchy="false">(</mo><mn>3760</mn><mo stretchy="false">)</mo></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">→</mo><mtext>nOCH</mtext></math> rescattering and suggest that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo stretchy="false">(</mo><mn>3810</mn><mo stretchy="false">)</mo></math> arises from coupling between the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo></math> state and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mi>c</mi></msub><mi>π</mi><mi>π</mi></math> channel. The significant non-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> decay of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3770</mn><mo stretchy="false">)</mo></math> is explained by its near-threshold position. This analysis provides a coherent, unquenched framework centered on a charmonium <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo></math> core for near-threshold phenomena and offers a predictive approach extendable to bottomonium systems and future data from Belle II.

Ri-Qing Qian

Xiang Liu

Unified coupled-channel description for the five near-threshold structures <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>ψ</mi><mo stretchy="false">(</mo><mn>3770</mn><mo stretchy="false">)</mo></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo stretchy="false">(</mo><mn>3760</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo stretchy="false">(</mo><mn>3780</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo stretchy="false">(</mo><mn>3810</mn><mo stretchy="false">)</mo></math> from <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></math> annihilation