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.

China

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)

In the present work, the strong decays of the discovered $ P_c(4380) $ , $ P_c(4440) $ , $ P_c(4457) $ and their possible isospin cousins are systematically studied via the assignment that they are meson-baryon molecular states. In detail, the strong decay constants and partial decay widths of their decay channels are calculated under the framework of QCD sum rules. The decay widths of the discovered $ P_c(4380) $ , $ P_c(4440) $ , and $ P_c(4457) $ are in good agreement with the experiments. The predictions of the decays of these three related possible isospin cousins are presented, which would shed light on their findings in experiments. In return, this may testify to the assignments of the discovered $ P_c $ states.

Xiu-Wu Wang

Xin Li

Zhi-Gang Wang

Systematic study of the strong decays of the $\textit{P}$ $\textit{c}$ states and their possible isospin cousins via the QCD sum rules * Supported by the National Natural Science Foundation of China (12575083) and the Natural Science Foundation of Hebei Province (A2024502002)

The exploration of symmetry laws stands as a cutting-edge direction in modern physics research. This study delves into the examination of $\textit{P}$ and $\rm CP$ symmetry properties within the charm quark system by analyzing asymmetry parameters in the two-body decay process of $ \Omega_c $ . By accounting for the polarization effects of electron and positron beams and employing the helicity formalism, we systematically analyze the decay characteristics of $ \Omega_c $ and its subsequent hyperon decays through specific asymmetry parameters. A comprehensive formulation of the angular distribution for these decay processes has been developed. The research assesses the detection sensitivity of asymmetry parameters in the $ \Omega_c\rightarrow \Omega^-\pi^+ $ decay mode across different experimental conditions, including varying data sample sizes and beam polarization configurations. These results contribute to enriching a theoretical foundation for forthcoming experimental endeavors at the STCF, offering significant implications for symmetry studies in the charm sector.

Yunlu Wang

Yunlong Xiao

Pengcheng Hong

Phenomenological study of Ω $\textit{c}$ → Ω$^{−}$ $\textit{π}$ $^{+}$ at polarized electron-positron collider

Hadron-hadron interactions, being nonperturbative in nature, play a significant role in addressing phenomenological questions in particle physics. Femtoscopy is a powerful tool in heavy-ion collision experiments, enabling the extraction of hadron-hadron interactions via momentum-correlation functions (CFs). These CFs are typically expressed as a convolution of source functions and hadron-hadron wave functions, with the latter encoding information about the interactions. However, source functions remain poorly constrained and are commonly approximated by a Gaussian form. Reconstructing source functions from experimental correlation data constitutes an 'inverse problem.' To address this, we propose a toy model based on Tikhonov regularization. Using a square-well potential with four distinct strengths, we calculate the CFs for inputs of single Gaussian source functions and mixed Gaussian source functions. The resulting CFs are then used to reconstruct the source functions via Tikhonov regularization. Our results show that the Gaussian source function can be successfully reconstructed, highlighting the potential of this approach for extracting realistic source functions from hadron pairs of interest.

Ao-Sheng Xiong

Qi-Wei Yuan

Ming-Zhu Liu

Fu-Sheng Yu

Zhi-Wei Liu

Li-Sheng Geng

Solving the inverse source problem in femtoscopy with a toy model * Supported in part by the Fundamental and Interdisciplinary Disciplines Breakthrough Plan of the Ministry of Education of China (JYB2025XDXM204) and the National Natural Science Foundation of China (W2543006, 12435007). Ming-Zhu Liu acknowledges support from the National Natural Science Foundation of China (12575086). Zhi-Wei Liu acknowledges support from the National Natural Science Foundation of China (12405133) and from the Shenzhen Science and Technology Program (ZDSYS20230626091501002). Fu-Sheng Yu and Ao-Sheng Xiong acknowledge support from the Scientific Research Innovation Capability Support Project for Young Faculty (ZYGXQNJSKYCXNLZCXM-P2) and from the Fundamental Research Funds for the Central Universities (lzujbky-2023-stlt01, lzujbky-2024-oy02, lzujbky-2025-eyt01)

We continue the approach of [$\textit{JHEP}$ (2023) 167] to attempt to reproduce the classical electromagnetic current of the $$ \sqrt{\mathrm{Kerr}} $$ solution from the infinite-spin limit of a three-point amplitude with two higher-spin string states and a massless vector. We review the infinite-spin limit of three-point amplitudes along the leading Regge trajectory, which differ from $$ \sqrt{\mathrm{Kerr}} $$ , and we provide evidence that any sub-leading trajectory parallel to the leading one give the same result. We extend the above investigation to the simplest sub-leading trajectory not parallel to the leading one, containing physical states with the first two harmonics. We compute all three-point amplitudes involving two such states and a massless vector, using both covariant and DDF formalism, and we extract the associated classical infinite-spin limit. Inspired by the leading Regge case, where this limit reproduces the classical electromagnetic current sourced by a rigid rotating string, we derive new classical string solutions containing the first two harmonics and compare the currents they source to the infinite-spin amplitude of the two-harmonic state. We do not see a matching between the two approaches, and we find that the classical behaviour is instead reproduced by the amplitude involving coherent string states. We conclude this paper by discussing common patterns between the different amplitudes we considered, and we conjecture how they can be generalised to reproduce $$ \sqrt{\mathrm{Kerr}} $$ .

Italy

F. Alessio

Denmark

Sweden

P. Vecchia

Greece

M. Firrotta

United Kingdom

P. Pichini

Searching for Kerr in string amplitudes

It is well known that all physically relevant states of gauge theories lie in the sectors of the Hilbert space which satisfy the Gauss law. On the lattice, the manifeslty gauge invariant subspace is known to be exactly spanned by gauged tensor networks. In this work, we demonstrate that the continuum limit of certain types of gauged tensor networks is well defined and leads to a novel class of states.

Israel

Gertian Roose

Erez Zohar

Continuum limit of gauged tensor network states

We study the interaction of a kaon with the $$f_1(1285)$$ resonance, assuming that the $$f_1(1285)$$ is a molecular state generated by the $$K \bar{K}^*, \bar{K} K^*$$ interaction, evaluating the scattering amplitude, the scattering length and effective range of the $$K f_1$$ system. The scattering amplitude develops a resonant structure approximately 56 MeV below the $$K f_1$$ threshold, with a width of around 123 MeV. The corresponding correlation function has the distinctive shape of a system with a bound state close to threshold. We also show that the interaction of the $$K f_1$$ system differs significantly from the one obtained assuming that the $$f_1(1285)$$ is an ordinary, non-molecular, particle. This provides motivation to continue the search for these observables, already initiated by the measurement of the $$p f_1(1285)$$ correlation function by the ALICE collaboration.

Wen-Hao Jia

Jing Song

Wei-Hong Liang

Spain

Eulogio Oset

Scattering data and correlation function for the $$K f_1(1285)$$ interaction

The $$B_c$$ meson constitutes a unique system for investigating heavy-hadron dynamics, since it exhibits quarkonium-like bound-state structure while decaying predominantly through weak interactions. In this work, we present a unified study of $$B_c$$ -meson spectroscopy, decay constants, weak decays, radiative transitions, and Regge trajectories within a single framework. The mass spectrum is computed in a screened potential model including relativistic kinetic-energy corrections and spin-dependent interactions, from which we obtain both spin-averaged and spin-resolved states together with the corresponding pseudoscalar and vector decay constants. Using these spectroscopic inputs, we then analyze weak decays within a mass-updated three-point QCD sum-rule framework for transitions to $\textit{S}$-, $\textit{P}$-, and $\textit{D}$-wave charmonium states, as well as to final states containing charmonium and $$D^{(*)}_{(s)}$$ mesons. In this part of the analysis, the hadronic thresholds, Borel-window prescriptions, Lorentz decompositions, and decay-width expressions of the underlying sum-rule formulations are retained, while the heavy-quark masses are updated to $$m_c=1.48~\textrm{GeV}$$ and $$m_b=4.90~\textrm{GeV}$$ , leading to a controlled refit of the overall normalization rather than a full rederivation of all perturbative and condensate contributions. We further investigate purely leptonic decay widths and radiative $\textit{E}$1 and $\textit{M}$1 transitions, and examine the Regge behavior of the resulting spectrum. The present study therefore provides a coherent description of the $$B_c$$ meson in which the spectroscopic wave functions determine the short-distance couplings that enter both weak and electromagnetic observables, while the Regge analysis serves as a complementary global consistency test of the same dynamical picture.

India

Vikas Patel

Chetan Lodha

Raghav Chaturvedi

A. Rai

A unified study of the $$B_c$$ meson: from spectrum and form factors to weak and radiative decays

Recent analyses combining DESI DR2 BAO measurements with CMB and supernova data have suggested a preference for dynamical dark energy, particularly when using the DES-SN5Y and DES-SN5Y $$(z>0.1)$$ supernova samples. With the revision of this dataset into the DES-Dovekie compilation, it is important to reassess the robustness of this result. In this work, we analyze a broad class of dark energy parametrizations, including $\textit{w}$CDM, $$w_0w_a$$ CDM, BA, JBP, Efstathiou, and GEDE models, using DESI DR2 BAO, a compressed CMB likelihood, and supernova data. We find that the DES-SN5Y dataset consistently yields a stronger preference for deviations from $$\Lambda $$ CDM compared to DES-Dovekie. In particular, redshift-dependent parametrizations favor the region $$w_0 > -1$$ and $$w_a < 0$$ , corresponding to a Quintom-B–type evolution with phantom crossing. This behavior is observed across multiple models, indicating that it is not specific to a single parametrization. We find that the DES-SN5Y $$(z>0.1)$$ sample also preserves the same qualitative behavior, although the deviations from the $$\Lambda $$ CDM limit become significantly weaker compared to the full DES-SN5Y sample. However, when DES-Dovekie is used, the statistical preference for dynamical dark energy is significantly reduced. The improvement over $$\Lambda $$ CDM drops to below the $$1\sigma $$ level for most models, and the Bayesian evidence weakens from moderate to weak or inconclusive. Similarly, for the DES-SN5Y $$(z>0.1)$$ sample, the preference for dynamical dark energy becomes intermediate between the DES-SN5Y and DES-Dovekie cases, with mostly weak or inconclusive evidence. Overall, the DES-Dovekie and DES-SN5Y $$(z>0.1)$$ datasets weaken the preference for dynamical dark energy compared to the full DES-SN5Y dataset.

Nepal

Anil Kandel

Uzbekistan

Azerbaijan

Farruh Atamurotov

Türkiye

Ertan Güdekli

Thailand

Phongpichit Channuie

Gulzoda Rakhimova

Revisiting the evidence for dynamical dark energy: from DES-SN5Y to DES-Dovekie

We present a comprehensive and self-contained formulation of Chrono-Grid Dynamics (CGD), a theory in which spacetime and general relativity emerge from a discrete, unitary evolution of a quantum spin network on a spatial lattice. The fundamental postulate is a universal quantum of proper time $$\tau $$ (the Takt), which drives the unitary step $$|\psi _{n+1}\rangle = e^{-i\hat{H}\tau }|\psi _n\rangle $$ . Starting from a 3D cubic or tetrahedral lattice with spin-1/2 degrees of freedom on sites and dynamical $\textit{SU}$(2) link variables, we construct a local Hamiltonian that generates the dynamics. In the continuum limit, the link variables become the Ashtekar connection and their conjugate momenta become the densitised triad, leading to the canonical formulation of general relativity and the fundamental relation $$8\pi G\beta = \tau ^2$$ . We define the Gauss, diffeomorphism and Hamiltonian constraints on the lattice and show that their algebra closes, reproducing the Dirac algebra in the continuum. Edge modes appear on boundaries and carry topological degrees of freedom. Upon quantization we obtain discrete spectra for area, volume and length operators, expressed in terms of $$\tau $$ and spin labels. The 6$\textit{j}$ symbol of $\textit{SU}$(2) emerges as the central object describing the quantum geometry of a tetrahedron, linking CGD to spin-foam models and the Ponzano–Regge asymptotic. When a cosmological constant is introduced, the curvature constraint regularizes to the quantum group $$SU_q(2)$$ , connecting CGD to topological field theories such as the Turaev–Viro model. The discrete time step automatically provides a natural ultraviolet cutoff, and the lattice dispersion relation yields a minimal length of order the Planck scale. This work provides the mathematical foundation for the CGD program and paves the way for applications in quantum cosmology and numerical studies of lattice quantum gravity.

Serbia

Nebojša Jovanović

Chrono-Grid Dynamics: a discrete unitary framework for emergent gravity