Inspired by the observation of the ${\eta}_{t}$ meson at the LHC and the promising prospect of the ${\eta}_{t}$ meson available at the approaching HL-LHC, branching ratios for the ${\eta}_{t}$ ${\to}$ $f\bar{f}$ , $gg$ , ${\gamma}{\gamma}$ , $W^{+}W^{-}$ , $Z^{0}Z^{0}$ , $Z^{0}{\gamma}$ , and $Z^{0}H$ decays are roughly estimated. It is found that tens of opposite-charge dilepton events from the ${\eta}_{t}$ ${\to}$ $W^{+}W^{-}$ decay and hundreds of events from the ${\eta}_{t}$ ${\to}$ $Z^{0}H$ ${\to}$ ${\ell}^{+}{\ell}^{-}H$ decay using the single $Z^{0}$ boson tagging method are expected to be accessible. This estimation provides a reference for future experimental study on the ${\eta}_{t}$ meson.

China

Yueling Yang

Bingbing Yang

Jiazhi Li

Zhaojie Lü

Junfeng Sun

Searching for the toponium ${{\boldsymbol\eta}_{\boldsymbol t}}$ with the ${{\boldsymbol\eta}_{\boldsymbol t}}$ ${\boldsymbol\to}$ ${{\boldsymbol W}^{\bf +}{\boldsymbol W}^{\bf -}}$ decay * Supported by the National Natural Science Foundation of China (12275068, 12275067), the National Key R&D Program of China (2023YFA1606000), the Natural Science Foundation of Henan Province (252300421491, 242300420250), and the Science and Technology R&D Program Joint Fund Project of Henan Province (225200810030), as well as the Science and Technology Innovation Leading Talent Support Program of Henan Province (254200510039)

Neutrino oscillation experiments have confirmed that neutrinos are massive particles and that lepton flavors are mixed. To explain the observed lepton mass spectra and flavor mixing patterns, flavor symmetry plays a crucial and unique role. In this paper, we propose a useful symmetry-breaking scheme by applying $S_{3L} \times S_{3R} \rightarrow $ $ S_{2L} \times S_{2R} \rightarrow \emptyset$ within both charged-lepton and neutrino sectors at the mass-matrix level. For the three distinct residual subgroups $S_{2L}^{(23)} \times S_{2R}^{(23)}$ , $S_{2L}^{(13)} \times S_{2R}^{(13)}$ , and $S_{2L}^{(12)} \times S_{2R}^{(12)}$ that are under consideration, we systematically analyze the various parameterizations of the lepton mass matrices. It is shown that all three scenarios are in good agreement with current neutrino oscillation data. Notably, within the latest best-fit values of neutrino oscillation parameters, the predicted values of the Dirac CP-violating phase $\textit{δ}$ are $294.6^\circ$ , $302.3^\circ$ , and $287.0^\circ$ , respectively. To further assess the viability of the model, a comprehensive numerical analysis is performed by utilizing neutrino oscillation parameters at the $3\sigma$ level. It is found that the allowed ranges of $\textit{δ}$ are $281.2^\circ \rightarrow 338.7^\circ$ , $287.0^\circ \rightarrow 342.2^\circ$ , and $282.7^\circ \rightarrow 297.0^\circ$ , which all fall within its $3\sigma$ range. These results indicate that the proposed symmetry-breaking scheme $S_{3L} \times S_{3R} \rightarrow S_{2L} \times S_{2R} \rightarrow \emptyset$ can naturally explain the realistic lepton mass hierarchy and mixing pattern, thereby providing valuable theoretical perspectives for future research.

Chang-Qi Hu

Chun-Yuan Li

Xiao Liang

Xing-Hua Yang

Dai-Xing Zhang

Further study on lepton mass spectra and flavor mixing with $\textit{S}$ 3$\textit{L}$ × $\textit{S}$ 3$\textit{R}$ flavor symmetry * Supported in part by the National Natural Science Foundation of China (12105162, 12305106), the Natural Science Foundation of Shandong Province (ZR2021QA058, ZR2021QA040) and the Youth Innovation Technology Project of Higher School in Shandong Province (2023KJ146)

Utilizing data samples of electron-positron collisions recorded with the BESIII detector at the center of mass energy of 3.773 GeV, corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>20.28</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math>, we report the first search for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> forbidden 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><mi>ψ</mi><mo stretchy="false">(</mo><mn>3773</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mi>D</mi><mn>0</mn></msup><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><mo stretchy="false">→</mo><mo stretchy="false">(</mo><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msup><mi>π</mi><mn>0</mn></msup><mo stretchy="false">)</mo><mo stretchy="false">(</mo><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msup><mi>π</mi><mn>0</mn></msup><mo stretchy="false">)</mo></math>. No significant signal is observed. We set the upper limit on the observed cross section to be 7.37 fb, and the upper limit on the joint branching fraction of the C-odd correlated neutral <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math> pair <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><mo stretchy="false">(</mo><msup><mrow><mi>D</mi></mrow><mn>0</mn></msup><msup><mrow><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mn>0</mn></msup><msub><mrow><mo stretchy="false">)</mo></mrow><mrow><mi mathvariant="normal">C</mi><mtext>−</mtext><mtext>odd</mtext></mrow></msub><mo stretchy="false">→</mo><mo stretchy="false">(</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi></mrow><mn>0</mn></msubsup><msup><mrow><mi>π</mi></mrow><mn>0</mn></msup><mo stretchy="false">)</mo><mo stretchy="false">(</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi></mrow><mn>0</mn></msubsup><msup><mrow><mi>π</mi></mrow><mn>0</mn></msup><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo>&lt;</mo><mn>2.04</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow></math> at the 90% confidence level.

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

Germany

R. Aliberti

Italy

A. Amoroso

Q. An

Y. Bai

JINR

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

South Korea

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

Y.T. Feng

Search for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation 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><mo stretchy="false">→</mo><mi>ψ</mi><mo stretchy="false">(</mo><mn>3770</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mi>D</mi><mn>0</mn></msup><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup></math> via <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mo stretchy="false">→</mo><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msup><mi>π</mi><mn>0</mn></msup></math>

The Galactic Center excess (GCE) of GeV <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math> rays may hint at dark matter (DM), yet its origin remains debated. Motivated by this, we survey weakly interacting massive particle (WIMP) models that can fit the GCE while satisfying relic-density, direct-detection (DD), and indirect-detection (ID) bounds. We group candidates into hadronic (Higgs portals; simplified scalar/vector mediators), leptonic [<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 mixed [<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>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math>-portal] classes. Across all cases, present DD and dwarf-spheroidal <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math>-ray limits exclude wide regions, leaving mainly narrow resonant funnels with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mrow><mi>DM</mi></mrow></msub><mo>≃</mo><msub><mi>m</mi><mrow><mi>med</mi></mrow></msub><mo>/</mo><mn>2</mn></math> and portal couplings <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>≪</mo><mn>1</mn></math>. In hadronic setups, scalar and vector Higgs portals survive only in a thin strip near <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>h</mi></msub><mo>/</mo><mn>2</mn><mo>≃</mo><mn>62.5</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> with portal couplings <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, while the Dirac Higgs and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> portals are essentially excluded. The UV-complete vector Higgs portal retains resonant bands whose viable portal strength depends on the mixing angle. Simplified scalars allow small windows for complex-scalar or vector DM; Dirac DM is strongly disfavored, whereas a pseudoscalar with Dirac DM remains viable over a broader parameter range. For a simplified <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> mediator, a pure vector coupling leaves only a marginal region, while pure axial is excluded by DD/ID bounds. In leptonic scenarios, inverse-Compton emission is essential: <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> (and, to a lesser extent, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo>−</mo><mi>L</mi></math>) fits the GCE with near-thermal cross sections, while <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> is disfavored. Overall, viable WIMP explanations are constrained to the finely tuned resonant regime, with leptophilic vectors and pseudoscalar portals emerging as the most robust options.

Chuiyang Kong

Mattia Di Mauro

Comprehensive study of WIMP models explaining the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>F</mi><mi>e</mi><mi>r</mi><mi>m</mi><mi>i</mi></math>-LAT Galactic Center excess

We consider properties of non-linear theories of a chiral 4-form gauge field $\textit{A}$ in ten space-time dimensions with an emphasis on a subclass of these theories which are invariant under the $\textit{D}$ = 10 conformal symmetry. We show that general results regarding a peculiar structure of duality-invariant abelian gauge theories in four and six space-time dimensions do not extend to non-linear chiral 4-form theories in ten dimensions. This discrepancy arises primarily from the large number 81 of independent invariants constructible from the self-dual part of the five-form field strength $\textit{F}$ = $\textit{dA}$ in $\textit{D}$ = 10, in stark contrast to the single independent (fourth-order) invariants which are building blocks of the actions in the lower dimensional cases. In particular, unlike the $\textit{D}$ = 4 and $\textit{D}$ = 6 cases, where non-linear duality-invariant theories can be viewed as stress-tensor ( $$ T\overline{T} $$ -like) deformations of seed theories, the flow equations in $\textit{D}$ = 10 generally involve both stress-tensor invariants and additional higher-order structures constructed from $\textit{F}$ . In passing, we prove the equivalence of three Lagrangian formulations of non-linear duality-invariant $\textit{p}$-form theories: the PST, the Ivanov-Nurmagambetov-Zupnik and the “clone” one.

Jessica Hutomo

Kurt Lechner

Dmitri Sorokin

On non-linear chiral 4-form theories in $\textit{D}$ = 10

We present a novel robust framework for systematically constructing $\textit{D}$-dimensional four-point higher-derivative contact amplitudes. Our modular block (“LEGO”-like) approach builds amplitudes directly from manifestly gauge-invariant kinematic blocks, color-weight factors, and scalar Mandelstam polynomials. Symmetries (Bose/Fermi) are imposed algebraically, acting as filters on combinations of compatible pieces. This framework operates entirely in $\textit{D}$ dimensions, naturally incorporating evanescent operators crucial for loop-level consistency. Scaling to arbitrary mass dimension is achieved in a highly controlled manner using permutation-invariant scalar polynomials, avoiding combinatorial explosion. A key feature is its manifest compatibility with the double-copy program, allowing the systematic generation of operator towers not only for gauge theories but also for gravity and other theories within the double-copy web.

John Carrasco

Sai Chava

Alex Edison

Aslan Seifi

$\textit{D}$-dimensional modular assembly of higher-derivative four-point contact amplitudes involving fermions

In this paper, we investigate the traversable wormhole solutions in the presence of charge within the framework of <italic>f</italic>( <italic>R, &#981;</italic>) gravity, where <italic>R</italic> represents the Ricci scalar and <italic>&#981;</italic> denotes the scalar potential, respectively. We also consider the Karmarkar condition for the discussion of wormhole geometry. The obtained shape function satisfies all necessary Morris-Thorne criteria for traversability. We derive and graphically examine the physical characteristics, including energy density and pressure components, for a specific linear charge distribution. Our analysis confirms the violation of the null energy condition in the radial direction. The violation of these energy conditions indicates the presence of exotic matter, which is the main candidate for the existence of a wormhole. Under some sensible conditions, the analysis may give an assurance of the existence of wormhole geometries in the <italic>f</italic>( <italic>R, &#981;</italic>) theory of gravity. Furthermore, we investigate the stability of the wormhole through the Tolman-Oppenheimer-Volkov equation, namely the equilibrium condition. By comparing four distinct <italic>f</italic>( <italic>R, &#981;</italic>) models, we demonstrate the robustness of traversable wormhole solutions in this modified gravity setting and identify parameter ranges that minimize energy condition violations. The results affirm that <italic>f</italic>( <italic>R, &#981;</italic>) gravity, augmented by an electromagnetic field, can support stable, traversable wormhole geometries.

Azerbaijan

Pakistan

Adnan Malik

M. Waqas Aslam

Wenbin Lin

Muhammad Kashif Shafiq

Saudi Arabia

Fatemah Mofarreh

Ramy M. Hafez

Impact of charge on traversable wormhole solutions and modified <italic>f</italic>( <italic>R, &#981;</italic>) gravity

By using the integrable lattice model proposed by Maulik and Okounkov, we derive the (higher) Hamiltonians of the (generalized) trigonometric Calogero-Sutherland models. Then in terms of these (higher) Hamiltonians, we further construct certain nested structures and derive the commutative operators which coincide with the (higher) Hamiltonians of the (generalized) rational Calogero-Sutherland models.

Yue Li

Fan Liu

Rui Wang

Jie Yang

The (higher) Hamiltonians of (generalized) trigonometric and rational Calogero-Sutherland models by MO <italic>R</italic>-matrix

We investigate the gravitational baryogenesis scenario within the context of $\textit{F}$($\textit{R}$) gravity’s rainbow which incorporates both modified gravity and energy-dependent spacetime. This study explores a mechanism for generating baryon asymmetry based on the interaction between the derivative of the Ricci scalar $\textit{R}$ and the baryon current within the framework of $\textit{F}$($\textit{R}$) gravity’s rainbow. The rainbow functions, arising from quantum gravity effects, modify the gravitational interaction and the Friedmann equations, leading to a distinct evolution of the baryon asymmetry compared to standard $\textit{F}$($\textit{R}$) gravity. We analyze the conditions under which a viable baryon asymmetry can be produced, taking into account the constraints from cosmological observations and the specific form of the $\textit{F}$($\textit{R}$) function. By examining the cosmological equations in the context of $\textit{F}$($\textit{R}$) gravity’s rainbow, we obtain power-law solutions for these equations. We also identify the decoupling temperature and the ratio of baryonic number to entropy density in this model, depending on the model’s parameters. First, we discuss the acceptable intervals of the model’s parameters which are defined by constraints on the background quantity. We note that the decoupling temperature and the ratio of baryon-to-entropy in these models depend on the value of the rainbow function. We compare the predictions of this model with the existing observational data. Our results suggest that $\textit{F}$($\textit{R}$) gravity’s rainbow provides a novel mechanism for gravitational baryogenesis, potentially explaining the observed baryon asymmetry in the universe while incorporating quantum gravity corrections.

Iran

Parviz Goodarzi

Gravitational baryogenesis in $\textit{F}$($\textit{R}$) gravity’s rainbow

The one-loop correction to eleven-dimensional supergravity involves a cubically divergent term $\textit{t}$ $\textit{t}$ $\textit{R}$ , with four Riemann tensors. A similar term (with finite coefficient) has been argued to be present in the M-theory effective action. It is expected to reduce to a similar one-loop term present in the type IIA effective action. This has previously been verified in the NSNS sector at the 4-point level. Here we extend this result to couplings of NSNS and RR fields, which have been computed using the pure spinor formalism. In particular, we check all couplings of RR fields to the dilaton as well as all couplings involving the metric and RR three-form. Correcting some minor mistakes in the literature we find complete agreement. We also give a complete analysis of 4-point terms in eleven dimensions computed previously from superparticle amplitudes and present a very simple form for these.

Czechia

Aviral Aggarwal

Subhroneel Chakrabarti

Steven Hsia

Bangladesh

Ahmed Kamal

Linus Wulff

One loop in $\textit{D}$ = 11 vs $\textit{D}$ = 10: 4-point check