The weak decays of charmonium states such as $ J/\psi $ and $ \psi(2S) $ are instrumental in probing both nonperturbative QCD dynamics and the flavor structure of the Standard Model (SM). The extreme rarity of charmonium weak decays renders them highly sensitive to physics beyond the SM, particularly in channels that are heavily suppressed in the SM, such as flavor-changing neutral-current (FCNC) decays. This review highlights the critical role of the BESIII experiment, which leverages an unprecedented data sample of over $ 10^{10} $ $ J/\psi $ and $ 2.7\times10^{9} $ $ \psi(2S) $ events to achieve leading sensitivity in searches for charmonium weak decays. We present the latest and most stringent upper limits established by BESIII on various semileptonic, nonleptonic, and FCNC charmonium weak decay channels.

China

Xu-Ze Li

Kai-Xin Fan

Zheng-Yun You

Yu Zhang

Minggang Zhao

Mini-review of charmonium weak decays at BESIII * Supported in part by the National Key R&D Program of China (2023YFA1606000); the National Natural Science Foundation of China (NSFC) (12035009, 12175321, U1932101), and the National College Students' Science and Technology Innovation Project of Sun Yat-sen University

We present an exact analysis of black hole (BH) solutions in the two-dimensional (2D) dilaton gravity model with action <math altimg='si55.svg'><mrow><mi>I</mi><mo linebreak='goodbreak'>=</mo><mrow><mo>(</mo><mn>1</mn><mo linebreak='badbreak'>/</mo><mn>2</mn><mi>G</mi><mo>)</mo></mrow><mo>&#8747;</mo><msup><mi>d</mi><mn>2</mn></msup><mi>x</mi><mspace width='0.16em' /><msqrt><mrow><mo>&#8722;</mo><mi>g</mi></mrow></msqrt><mspace width='0.16em' /><mrow><mo>(</mo><mstyle mathvariant='normal'><mi>&#934;</mi></mstyle><mi>R</mi><mo linebreak='badbreak'>&#8722;</mo><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle><msup><mstyle mathvariant='normal'><mi>&#934;</mi></mstyle><mn>2</mn></msup><mo>)</mo></mrow></mrow></math>. Identifying the dilaton as the radial coordinate, we obtain the metric function <math altimg='si1.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mrow><mo>(</mo><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle><mo linebreak='badbreak'>/</mo><mn>3</mn><mo>)</mo></mrow><mspace width='0.16em' /><msup><mi>x</mi><mn>3</mn></msup><mo linebreak='goodbreak'>&#8722;</mo><mn>2</mn><mi>G</mi><mi>M</mi></mrow></math> and derive closed-form expressions for the mass, Wald entropy, Hawking temperature, heat capacity, and Helmholtz free energy. For &#923;&#8239;&lt;&#8239;0 and <italic>M</italic>&#8239;&gt;&#8239;0 the solution admits a single non-degenerate horizon with <math altimg='si46.svg'><mrow><mi>C</mi><mo linebreak='goodbreak'>=</mo><mi>S</mi><mo linebreak='goodbreak'>/</mo><mn>2</mn><mo linebreak='goodbreak'>&gt;</mo><mn>0</mn></mrow></math>, globally negative free energy, and no phase transitions. A nonperturbative exponential entropy correction preserves stability for <italic>&#951;&#947;</italic>&#8239;&lt;&#8239;1 but triggers a temperature divergence and negative heat capacity for <italic>&#951;&#947;</italic>&#8239;&gt;&#8239;1. The topological analysis of the off-shell free-energy landscape yields a total topological charge <math altimg='si29.svg'><mrow><mi>W</mi><mo linebreak='goodbreak'>=</mo><mo>+</mo><mn>1</mn></mrow></math> in the classical regime, while strong corrections drive a transition to <math altimg='si56.svg'><mrow><mi>W</mi><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math>, signaling an additional unstable branch. We derive the quasinormal mode (QNM) master equation for probe-scalar perturbations and compute the cavity spectrum, confirming the universal scaling |Im( <italic>&#969;</italic>)|&#8733; <italic>T</italic> and a quality factor <math altimg='si52.svg'><mrow><mi mathvariant='script'>Q</mi><mo>&#8776;</mo><mn>0.43</mn></mrow></math>&#8211;0.48. Because 2D dilaton gravity arises from the spherical reduction of four-dimensional Einstein&#8211;Maxwell theory and governs near-extremal BH throats, our results establish the <math altimg='si54.svg'><mrow><mstyle mathvariant='normal'><mi>&#934;</mi></mstyle><mi>R</mi><mo linebreak='goodbreak'>&#8722;</mo><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle><msup><mstyle mathvariant='normal'><mi>&#934;</mi></mstyle><mn>2</mn></msup></mrow></math> model as a transparent laboratory for exact BH thermodynamics, quantum corrections, topological classification, and dynamical response.

Iraq

Aram Bahroz Brzo

Peshwaz Abdulkareem Abdoul

Azerbaijan

Iran

Behnam Pourhassan

Saeed Noori Gashti

Türkiye

İzzet Sakallı

Exact black-hole solutions in <math altimg='si54.svg'><mrow><mstyle mathvariant='normal'><mi>&#934;</mi></mstyle><mi>R</mi><mo linebreak='goodbreak'>&#8722;</mo><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle><msup><mstyle mathvariant='normal'><mi>&#934;</mi></mstyle><mn>2</mn></msup></mrow></math> dilaton gravity: Thermodynamics, stability, topology, and dynamical probes

By introducing an extra stack of D6-branes to standard $$ \mathcal{N} $$ = 1 supersymmetric Pati-Salam models, we extend the landscape of its complete search. In this construction, the $\textit{d}$-stack of D6-branes is introduced besides the standard $\textit{a}$, $\textit{b}$, $\textit{c}$-stacks. More intersections from the extra stacks of D6-branes appear, and thus Higgs/Higgs-like particles arise from more origins. Among these models, we complete with 28 classes of $$ \mathcal{N} $$ = 1 supersymmetric Pati-Salam models under gauge symmetries $\textit{SU}$ (4) × $\textit{SU}$ (2) × $$ SU{(2)}_{R_1} $$ × $$ SU{(2)}_{R_2} $$ and $\textit{SU}$ (4) × $$ SU{(2)}_{L_1} $$ × $\textit{SU}$ (2) × $$ SU{(2)}_{L_2} $$ , where $\textit{d}$-stack of D6-branes carries the gauge symmetries $$ SU{(2)}_{R_2} $$ and $$ SU{(2)}_{L_2} $$ , respectively. The $$ SU{(2)}_{L_1/{R}_1} $$ × $$ SU{(2)}_{L_2/{R}_2} $$ can be broken down to the diagonal $\textit{SU}$ (2) gauge symmetry via bifundamental Higgs fields. In such a way, we for the first time successfully constructed three-family supersymmetric Pati-Salam models from non-rigid D6-branes with extra $\textit{d}$-stacks of D6-branes as visible sectors. Interestingly, by introducing extra stack of D6-branes to the standard supersymmetric Pati-Salam models, the number of filler brane reduces in general, and eventually the models without any $\textit{USp}$($\textit{N}$) gauge symmetry present. This reduces the exotic particles from filler brane intersection yet provides more vector-like particles from $$ \mathcal{N} $$ = 2 subsector that are useful in renormalization group equation evolution as an advantage. Moreover, interesting degeneracy behavior with the same gauge coupling ratio exists in certain class of models.

Haotian Huangfu

Tianjun Li

Qi Sun

Rui Sun

The $$ \mathcal{N} $$ = 1 supersymmetric Pati-Salam models with extra $$ SU{(2)}_{L_2/{R}_2} $$ gauge symmetry from intersecting D6-branes

We develop a local reconstruction framework between $$\Phi (R,\phi ,X)$$ theories with linear dependence on $$X$$ and generalized hybrid metric-Palatini gravity. The construction is formulated in vacuum in the Einstein frame, where both formulations can be written as two-scalar theories with the same field-space geometry. The framework provides a practical method for finding $$\Phi (R,\phi ,X)$$ and $$f(R,\mathcal {R})$$ functions that describe the same regular Einstein-frame two-scalar sector. Starting from a given $$\Phi (R,\phi ,X)$$ model, we derive the equation that determines the compatible hybrid functions $$f(R,\mathcal {R})$$ and show that it has a Clairaut-type structure. We also show that the inverse reconstruction is not unique: a regular hybrid Einstein-frame potential determines a family of compatible $$\Phi (R,\phi ,X)$$ theories, parametrized by the kinetic coupling. Explicit examples illustrate the reconstruction procedure, its domain of validity, and the translation of model parameters between the $$\Phi (R,\phi ,X)$$ and $$f(R,\mathcal {R})$$ formulations.

Brazil

Jonathan Ramírez

Reconstruction between generalized hybrid metric-Palatini gravity and $$\Phi (R,\phi ,X)$$ theories

We ask whether two classical time-machine geometries, the Ori (2005) compact-vacuum-core metric and the Ahmed (2018) four-dimensional generalisation of Misner space, remain admissible exact solutions when the gravitational sector is enlarged to the recently proposed $$f(R,\mathcal {L}_{m},\Phi ,X)$$ class, an extension of $$f(R,\mathcal {L}_{m})$$ that couples curvature, the matter Lagrangian density, a scalar field $$\Phi $$ , and its kinetic invariant $$X = g^{\mu \nu }\nabla _{\mu }\Phi \nabla _{\nu }\Phi $$ . Working with the explicit model $$f = R + \mathcal {L}_{m} + (\lambda /2)\,X$$ and a vanishing scalar potential, we compute the curvature invariants, the modified field equations, and the effective stress-energy components produced by the harmonic scalar profile $$\Phi (x,y) = a(x^{2}-y^{2})/2$$ in both backgrounds. The Ricci scalar vanishes for the Ori metric and obeys $$R = e^{f}(f_{,xx}+f_{,yy})$$ for the Ahmed metric; the kinetic invariant takes the explicit forms $$X = a^{2}(x^{2}+y^{2})$$ and $$X = a^{2}e^{f}(x^{2}+y^{2})$$ , respectively. Both metrics solve the field equations of the modified theory with anisotropic matter sources, and the chronology-violating regions $$g_{zz}<0$$ (Ori) and $$g_{\psi \psi }<0$$ (Ahmed) survive the modification. Energy-density profiles measured by a closed-timelike-curve observer match those measured by a static observer outside the chronology horizon, so the additional scalar degree of freedom in $$f(R,\mathcal {L}_{m},\Phi ,X)$$ gravity does not enforce a chronology-protection mechanism in either background. The conclusion mirrors the parallel result for the Li time-machine and supplies a consistency test for scalar-extended modified gravity in non-globally-hyperbolic settings.

India

Faizuddin Ahmed

Jordan

Ahmad Al-Badawi

Are Petrov type-N and D spacetimes admitting CTCs valid in $$f(R,\mathcal {L}_m,\Phi ,X)$$ gravity?

In this study, within the framework of <math altimg='si3.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> modified gravity, we investigate the influence of coupling parameter ( <italic>&#955;</italic>), magnetic field and anisotropy parameter on the neutron star structure. This work employs an accurate equation of state (EoS), derived from realistic microscopic calculations based on the AV18 nucleon-nucleon potential, to compute the structure of this compact object. Here, determination of Schwarzschild radius, compactness, gravitational surface redshift and Kretschmann scalar within the <math altimg='si3.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> gravity, confirms that our theoretical results are consistent with the observational constraints. While established physical EoSs within the framework of Einstein gravity have successfully characterized a broad range of compact objects, they remain inadequate in explaining certain massive objects residing within the mass gap ( <math altimg='si82.svg'><mrow><mn>2.5</mn><mo linebreak='goodbreak'>&#8722;</mo><mn>5</mn><msub><mi>M</mi><mo>&#8857;</mo></msub></mrow></math>). We show that some compact objects residing in the mass gap can be interpreted as candidates of neutron stars within the framework of <math altimg='si3.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> gravity. Motivated by the observation of objects within this mass range, we employ a framework that simultaneously incorporates <math altimg='si83.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>R</mi><mo>,</mo><mi>T</mi><mo>)</mo><mo>=</mo><mi mathvariant='script'>R</mi><mo linebreak='goodbreak'>+</mo><mn>2</mn><mi>&#955;</mi><mi>T</mi></mrow></math> gravity and Bowers-Liang anisotropy model. Our study concludes that an increase in the star&#8217;s surface magnetic field (which dominates the softening of the EoS) leads to a reduction in the maximum masses and corresponding radii. Furthermore, at a fixed <italic>&#955;</italic>, larger values of the anisotropy parameter <italic>&#946;</italic> result in increased masses and radii. Conversely, for fixed <italic>&#946;</italic>, a decrease in <italic>&#955;</italic> yields an increasing trend in both masses and radii. Finally, we compare our results with the observational data from LIGO/Virgo/KAGRA and NICER, setting the parameters of the <math altimg='si3.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> theory and anisotropy to successfully reproduce the masses and radii of the GW170817, PSR J0952-0607 and PSR J0740+6620 and the masses of the secondary components of GW190814 ( <math altimg='si84.svg'><mrow><msub><mi>m</mi><mn>2</mn></msub><mo linebreak='goodbreak'>=</mo><mn>2</mn><mo>.</mo><msubsup><mn>59</mn><mrow><mo>&#8722;</mo><mn>0.09</mn></mrow><mrow><mo>+</mo><mn>0.08</mn></mrow></msubsup><msub><mi>M</mi><mo>&#8857;</mo></msub></mrow></math>) and GW200210-092254 ( <math altimg='si85.svg'><mrow><msub><mi>m</mi><mn>2</mn></msub><mo linebreak='goodbreak'>=</mo><mn>2</mn><mo>.</mo><msubsup><mn>83</mn><mrow><mo>&#8722;</mo><mn>0.42</mn></mrow><mrow><mo>+</mo><mn>0.47</mn></mrow></msubsup><msub><mi>M</mi><mo>&#8857;</mo></msub></mrow></math>).

M. Savari

G.H. Bordbar

J. Sedaghat

A. Sheykhi

Structure of anisotropic magnetized neutron stars in <math altimg='si3.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> gravity with realistic equation of state

We investigate the interplay of the Weak Gravity Conjecture (WGC) and the Weak Cosmic Censorship Conjecture (WCCC) in $\textit{F}$($\textit{R}$)-Euler-Heisenberg black holes in Anti-de Sitter and de Sitter backgrounds. The solution is characterized by the electric charge $\textit{q}$, the $\textit{F}$($\textit{R}$) deviation $$ {f}_{R_0} $$ , the Euler-Heisenberg coupling $\textit{λ}$, and the constant scalar curvature $\textit{R}$ . We establish a universal entropy-extremality relation that provides thermodynamic evidence for the WGC independently of $$ {f}_{R_0} $$ and $\textit{R}$ . Photon sphere analysis from both geodesic and topological perspectives confirms the simultaneous compatibility of the WGC and WCCC, with the Euler-Heisenberg coupling restoring photon spheres in the naked singularity regime. Gravitational lensing in the strong- and weak-deflection limits reveals that the photon sphere radius is independent of the cosmological background while the critical impact parameter nearly doubles in de Sitter. Black hole shadow images under isotropic accretion are constructed. Within the Barrow entropy framework, we uncover van der Waals-type phase transitions and analyze Joule-Thomson expansion, identifying the small black hole phase as the WGC-compatible thermodynamic regime accessible via isenthalpic cooling.

Erdem Sucu

Mohammad Alipour

Ankit Anand

Mohammad Afshar

Jafar Sadeghi

Testing the weak gravity conjecture via gravitational lensing, black hole shadows, and Barrow thermodynamics in F(R)-Euler-Heisenberg (A)dS black holes

<p>We study neutrino nonstandard interactions (NSI) induced by the trilinear <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>L</mi><mi>i</mi></msub><msub><mi>L</mi><mi>j</mi></msub><msubsup><mi>E</mi><mi>k</mi><mi>c</mi></msubsup></math> (LLE) couplings in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math>-parity-violating supersymmetry in a split-family spectrum where third-generation sleptons can be comparatively light. We systematically classify the relevant coupling patterns, derive the corresponding effective interactions and NSI parameters, and confront the resulting parameter space with a broad set of experimental constraints. We find that percent-level NSI can be realized in selected channels, with the largest magnitudes reaching <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ϵ</mi><mrow><mi>e</mi><mi>e</mi></mrow></msub><mo>≃</mo><mn>8</mn><mo>%</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ϵ</mi><mrow><mi>μ</mi><mi>μ</mi></mrow></msub><mo>≃</mo><mn>3.8</mn><mo>%</mo></math>, while other entries are typically restricted to the subpercent level (including <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ϵ</mi><mrow><mi>μ</mi><mi>τ</mi></mrow></msub><mo>≃</mo><mo>−</mo><mn>0.3</mn><mo>%</mo></math> in the viable off-diagonal case). We also highlight the structural origin of the different constraint patterns between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>τ</mi><mo stretchy="false">˜</mo></mover><mi>R</mi></msub></math>- and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>τ</mi><mo stretchy="false">˜</mo></mover><mi>L</mi></msub></math>-mediated scenarios and comment on the relation to the Zee model.</p>

United States

Fang Xu

Neutrino nonstandard interactions from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi><mi>L</mi><mi>E</mi></math>-type <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math>-parity violation

Egypt

Tahia Dabash

Moataz Emam

Germany

Lukas Schöppner

Reply to “Comment on: Symmetry and conserved quantities in $\textit{f}$($\textit{R}$)-gravity: Mei vs. Noether approaches”

In this work, two analytical solutions are proposed to characterize compact star configurations containing an effective negative-pressure fluid in the <italic>f</italic>( <italic>R, T</italic>) gravity paradigm that admit spherically symmetric geometry. We derive a system of modified field equations by taking into account a static interior spacetime, which consists of both negative-pressure fluid and ordinary matter sources. In order to investigate the interactions between the fluid components, we solve the field equations using two different equations of state. As the gravitational equations still contain more unknowns, we further use the Finch-Skea and Tolman IV spacetimes which lead us to two distinct models. The junction conditions are also applied to compute the constants associated with these solutions. Afterwards, our developed models&#8217; feasibility is explored by contrasting them with the observed characteristics of two particular stars, SAX J1808.4&#8211;3658 and Her X-1. Under certain parametric values, our results demonstrate that both the developed fluid configurations are physically realistic in this minimally coupled gravity framework.

Pakistan

M. Sharif

Tayyab Naseer

Aqsa Bashir

Examining the behavior of exotic compact stars within the <italic>f</italic>( <italic>R, T</italic>) gravity under Finch-Skea and Tolman IV spacetimes