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 investigate the direct $\rm CP $ violation in the decay $ D^\pm \to \pi^\pm \pi^+ \pi^- $ incorporating the $ a_0^0(980) $ - $ f_0(980) $ mixing mechanism. The integrated mixing intensities $ \overline \xi_{fa} $ and $ \overline \xi_{af} $ are calculated using meson masses and coupling constants extracted from various theoretical models and experimental data, yielding values of appreciable magnitude. We find that when the invariant mass of the $ \pi^+\pi^- $ pair lies near the $ f_0(980) $ resonance, this isospin-breaking mechanism can enhance the $\rm CP $ asymmetry. The enhancement is particularly pronounced when the $ f_0(980) $ carries a significant $ n\bar{n} $ quark component and the $ f_0(980) $ and $ \sigma(600) $ mixing angle is approximately $ 26^\circ $ . After accounting for non-factorizable effects, we find these corrections tend to partially cancel the leading-order contributions, resulting in a suppression of the $\rm CP $ violations relative to the naive factorization predictions. It is emphasized that the $ a_0^0(980) $ - $ f_0(980) $ mixing mechanism should be taken into account in both theoretical and experimental studies of $\rm CP $ violation in $\textit{B}$ or $\textit{D}$ meson decays.

Shi-Ji Cao

Jing-Juan Qi

Yi-Fan Zhao

Chao Wang

Zhen-Yang Wang

Xin-Heng Guo

Direct CP violation in ${ {\boldsymbol D}^{\bf\pm }\to {\boldsymbol\pi}^{\bf\pm} {\boldsymbol\pi}^{\bf +} {\boldsymbol\pi}^{\bf -}} $ with ${{\boldsymbol a}_{\bf 0}^{\bf 0}{\bf (980)-}{\boldsymbol f}_{\bf 0}{\bf (980)}} $ mixing * Supported by the National Natural Science Foundation of China (12405115, 12105149, 11805153, 12275024), and the High-Level Scientific Research Fund of Ningbo University (GJPY2026032)

We constructed a four-Higgs-doublet model (4HDM) invariant under $\textit{D}$ $_{5}$ symmetry and investigated its complete neutral vacuum structure in detail. Assuming explicit CP conservation in the scalar potential, we examined whether CP symmetry can be spontaneously broken. We provided a complete list of all possible real and complex vacua, along with the constraints on the potential parameters required for each vacuum solution to exist. We also discussed the positive-definiteness conditions that the Hessian must satisfy for each vacuum to be a local minimum of the potential. The results show that, after spontaneous symmetry breaking, some complex vacua lead to spontaneous CP violation in the potential, whereas the remaining complex vacua still preserve CP conservation. Among these CP-violating complex vacua, one can be regarded as the most general form. Furthermore, we discussed the relationship between real and complex vacua.

Dong-Ping Fu

Michihisa Takeuchi

Spontaneous CP violation in the $\textit{D}$ $_{5}$-symmetric four-Higgs-doublet models * Supported by the Fundamental Research Funds for the Central Universities, the One Hundred Talent Program of Sun Yat-sen University, China, and the Guangdong Natural Science Foundation (2026A1515012641)

<p>We present a systematic study of the effects of ultralight dark matter (ULDM) on neutrino oscillations using the latest long-baseline data from the T2K and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>NO</mi><mi>ν</mi><mi mathvariant="normal">A</mi></math> experiments. Our analysis covers both flavor-universal and flavor-general scalar interactions as well as vector interactions associated with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>L</mi><mi>e</mi></msub><mo>−</mo><msub><mi>L</mi><mi>μ</mi></msub></math> and <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> gauge symmetries. Importantly, we explicitly consider the coherence properties of the ULDM by incorporating the resulting stochastic fluctuations into our statistical analysis. We find that in the low-mass regime, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>ϕ</mi></msub><mo>≲</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>17</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>eV</mi></math>, where the stochastic effects are maximal, the constraints on the ULDM couplings are relaxed by roughly an order of magnitude compared to those in the high-mass regime, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>ϕ</mi></msub><mo>≳</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>15</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>eV</mi></math>, where such fluctuations are effectively averaged out. While the combined T2K and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>NO</mi><mi>ν</mi><mi mathvariant="normal">A</mi></math> datasets impose nontrivial exclusion limits on the ULDM interactions, we do not find statistically significant evidence that these effects can alleviate the current tension in determining the charge-parity (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>) violating phase <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> between the two experiments. Therefore, it will be essential for future high-precision facilities to further probe the ULDM scenarios and achieve a definitive measurement of <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>.</p>

Xin-Qiang Li

Hai-Xing Lin

Jian Tang

Sweden

Sampsa Vihonen

Ultralight dark matter in long-baseline accelerator neutrino oscillations

<p>We investigate the finite-temperature SU(2) Savvidy model under an imaginary angular velocity. Employing the background-field method, we derive the one-loop effective potential and analyze both its real and imaginary parts. We demonstrate that imaginary rotation modifies the chromomagnetic condensate and the Polyakov loop, and can partially suppress the Nielsen-Olesen instability of the chromomagnetic background. Moreover, a high-temperature expansion shows that imaginary rotation strengthens the effective coupling and that the chromomagnetic field induces a negative contribution to the moment of inertia.</p>

Hao-Lei Chen

Xu-Guang Huang

Chromomagnetic condensate in finite-temperature SU(2) Yang-Mills theory under an imaginary rotation

This article presents a detailed study of an Ayón–Beato–García–de Sitter black hole surrounded by a quintessential field and cloud of strings. We begin by observing the metric and examining how different parameter choices impact the spacetime structure. Specifically, we study scenarios with positive (1/2) $$\Lambda $$ and changing other parameters. We then study particle geodesic motion, examining the effect of the modified spacetime on neighboring massive and massless particles, where we also discuss the stability for timelike geodesics. We then calculate the expression for the energy corresponding to circular orbits, examine the Lyapunov exponent and geodesic precession frequency for various values, and demonstrate how different parameters impact the evolution. Lastly, we utilize the null geodesics of photons to investigate the gravitational lensing properties of a black hole enveloped by quintessence and a cloud of strings by employing finite-distance formalism. The overall effort will allow us to understand the dynamical and stability properties of spacetime with small perturbations. In conclusion, a comprehensive study of the impacts of de-Sitter black holes on particle dynamics and motion in curved geometry has been provided in this article by considering additional fields.

Saudi Arabia

I. Shakir

Pakistan

Z. Yousaf

A. Farhat

Türkiye

I. Siddique

Azerbaijan

M. Bhatti

Geodesic dynamics of an Ayón–Beato–García–de Sitter black hole in the presence of quintessence and a cloud of strings

We conjecture a precise relation between the superconformal indices of two theories defined in different spacetime dimensions. The first is the three-dimensional ABJM theory describing the worldvolume of parallel M2-branes in M-theory on $\textit{ℝ}$ . The second is the $$ \mathcal{N} $$ = (2, 0) theory in six dimensions which describes the worldvolume of parallel M5-branes in the same background. As we review, the existence of such a duality is closely related to Imamura’s proposal for the giant graviton expansion of the three-dimensional index. We check our conjecture against various results for the two indices available in the literature. Using an existing proposal of Hristov for the ABJM superconformal index, we verify our conjecture to the first three orders in an expansion around the six-dimensional Cardy limit.

Taiwan

Heng-Yu Chen

United Kingdom

Nick Dorey

Japan

Sanefumi Moriyama

Rishi Mouland

Czechia

Canberk Şanlı

An M2/M5 duality from the giant graviton expansion

We present an exact analytical model describing a complete gravitational collapse of matter from horizonless initial conditions to black hole formation, tracing the full evolution of the horizon $\textit{H}$($\textit{t}$) from its formation at microscopic scales to macroscopic stabilization. The solution reveals two main stages: (i) a dynamical horizon growth, where an apparent horizon $\textit{H}$($\textit{t}$) emerges at a critical time $$t_b$$ until reaching its final size $$h=2\mathcal{M}$$ , demonstrating how trapped surfaces form dynamically in finite time, and (ii) a naked-singularity resolution, where an integrable Ricci curvature singularity ( $$R^\mu {}_\nu \sim r^{-2}$$ ) develops at $$r=0$$ , but remains causally hidden by the horizon growth, preserving weak cosmic censorship without exotic matter. The model could offer a framework to study the quantum-to-classical transition ( $$H(t) \sim \ell _\textrm{Planck}$$ ).

Sinya Aoki

Chile

Jorge Ovalle

An analytic model for a total process of gravitational collapse: from star to Schwarzschild black hole

We give an extensive discussion of the displaced signals of heavy Majorana neutrino production at future electron-positron colliders operating at various proposed energies in the context of the Left-Right symmetric model. A comprehensive collection of channels is taken into account, ranging from those featuring $\textit{W}$ and $\textit{W}$ mediation to those induced by scalar mixing and gauge/scalar boson fusion, with connections to the mechanism of neutrino mass origin. The emerging signatures feature possibly multiple displaced heavy neutrinos that are in some cases accompanied by prompt activity and forward leptons. We derive the corresponding total production rates and differential distributions, which allow us to differentiate the channels and have analytical estimates of the signal yield. We then develop realistic estimates of the selection efficiencies using a dedicated vertexing algorithm which establishes the displaced decay positions and supplies a reliable proxy for reconstructing the full four-momenta of long-lived particles. This allows us to determine the realistic reaches in the parameter space of the Left-Right symmetric model across the various channels, and we show that these can strongly surpass the LHC ones, demonstrating that future lepton colliders are sensitive to left-right symmetry breaking scales in the deep multi-TeV regime.

France

Benjamin Fuks

Slovenia

Jonathan Kriewald

Miha Nemevšek

Italy

Fabrizio Nesti

Long-lived left-right signals at the FCC-ee

We study the equation of state (EoS) of QCD matter in a bottom-up holographic setup that combines an Einstein-Maxwell-dilaton (EMD) sector with an improved Karch-Katz-Son-Stephanov (KKSS) flavor action. In the probe approximation, we perform an inverse reconstruction of the model functions by parameterizing them with neural networks and solving the EMD equations via a differentiable ODE solver (a neural ODE framework), calibrating the model to a reference thermodynamic table for $(2+1)$ -flavor QCD at finite temperature and finite baryon chemical potential. The reconstructed model functions are then parameterized and kept fixed across thermodynamic states. Next, viewing the EMD sector as an effective description of pure Yang-Mills theory, we fix its parameters by fitting the $\mu_B=0$ lattice pure-glue EoS using a hybrid optimization strategy. Finally, we go beyond the probe limit and solve the coupled EMD+KKSS equations with back-reaction, using the pure-glue-calibrated EMD sector as a fixed input and varying the KKSS couplings to compare with the $\mu_B=0$ two-flavor lattice EoS. We find a visible mismatch and a high-temperature behavior in which the back-reacted dimensionless ratios approach a nearly $\beta_1$ -insensitive plateau close to the pure-glue baseline, providing a simple structural diagnostic for the present flavor-sector truncation.

Yutian Deng

Mei Huang

Lin Zhang

Holographic QCD equation of state constrained by lattice QCD: neural-ODE for probe-limit and a back-reaction test * Start-up funding from Sun Yat-sen University (SYSU) (Y. Deng and L. Zhang); National Natural Science Foundation of China (NSFC) (12235016) (L. Zhang and M. Huang) and 12221005 (M. Huang)