We present a comprehensive study of secluded dark matter (DM) <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>χ</mi></math>, where the relic abundance is set by annihilations into lighter dark mediators <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math> that couple only feebly to the Standard Model (SM). In contrast to canonical weakly interacting massive particles (WIMPs), which are now strongly constrained by direct and indirect searches, secluded models still achieve the observed relic abundance via thermal freeze-out into hidden-sector mediators, while predicting highly suppressed present-day signals. We analyze three minimal models: (i) a <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><mi>X</mi></msub></math> gauge boson (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>A</mi><mo>′</mo></msup></math>) with kinetic mixing; (ii) a scalar DM candidate <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math> with a scalar mediator <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math> that has a trilinear vertex; and (iii) a Dirac fermion <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>χ</mi></math> whose mass arises from a Higgs–mixed singlet <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>H</mi><mi>p</mi></msub></math>. For each model we derive annihilation and scattering rates in both WIMP-like and secluded regimes, and solve the Boltzmann equations: a single-species equation for the WIMP case and a coupled <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>χ</mi><mo>−</mo><mi>ϕ</mi></math> system for the secluded case to account for possible early departure of the mediator from thermal equilibrium with the SM bath. In this regard, we provide explicit lower limits on the portal coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ε</mi></math> required to keep the mediator in thermal equilibrium with the SM bath and to ensure mediator decay before big bang nucleosynthesis. We show that for portal couplings <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>ε</mi><mo>≪</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math> the relic density is dominantly controlled by DM annihilation into mediator pairs, while spin-independent scattering lies well below current limits and remains viable even for future experiments approaching the irreducible neutrino background floor. Indirect constraints are typically weak due to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi></math>-wave suppression, off-resonance <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math>-channels, and cascade spectra controlled by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>ε</mi><mn>2</mn></msup></math>. Finally, we highlight the most promising collider tests, which remain sensitive despite tiny portal couplings.

Mattia Di Mauro

Yanhan Wang

Phenomenology of secluded dark matter in three minimal BSM scenarios

Quantifying the imprints of freeze-in dark matter (DM) on cosmological structures requires knowledge of its phase-space distribution. We investigate how variations in the cosmological history before nucleosynthesis, the “weather” of that epoch, give rise to distinct “seasons” in the DM momentum distribution that governs its warmness. Studying decay-driven production across diverse cosmological histories, we map how these conditions shape DM phase-space properties. Our study quantifies how the early Universe composition plays a key role in determining the mass bound on freeze-in DM.

Francesco D’Eramo

Alessandro Lenoci

Tommaso Sassi

Seasons of dark matter freeze-in shaped by the weather of the early Universe

We employ the Zubarev approach of the statistical operator to investigate the enhancement of the low-<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math> region of pion spectra, introducing an effective pion chemical potential, to describe the overpopulation of low-energy pion states. We test a corresponding freeze-out approach by analyzing the transverse-momentum spectra of identified particles measured recently with high precision by the ALICE Collaboration in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Pb</mi><mo>+</mo><mi>Pb</mi></mrow></math> collisions at CERN LHC. A blast-wave model and a blast-wave-based particle generator, coupled to a hadronic transport model, are utilized. Bayesian inference methods are applied to extract the most probable sets of thermodynamic parameters at the chemical freeze-out hypersurface. Both models for the overpopulated pion states, the hadronic transport model and the thermal model with a nonzero pion chemical potential, provide a satisfactory description of the observed pion spectra. However, both approaches contain approximations which can be improved within a systematic nonequilibrium approach. We demonstrate that the introduction of a nonequilibrium pion chemical potential offers an efficient alternative to the conventional explanation of the low-<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math> enhancement, typically attributed to resonance decays with subsequent thermalization. A similar discussion also holds for the kaon spectra.

Oleksandr Vitiuk

David Blaschke

Benjamin Dönigus

Gerd Röpke

Nonequilibrium phenomenology of identified particle spectra in heavy-ion collisions at energies available at the CERN Large Hadron Collider

The masses of exotic quantum-number <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup></math> compact tetraquark states are calculated in a constituent quark model, where a Cornell-like potential is employed as the central potential, spin-spin and spin-orbit coupling derived from the Breit-Fermi interaction are treated as hyperfine corrections, and model parameters are taken from previous works. The ground state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup></math> P-wave tetraquarks are predicted at 1.9, 4.2, and 6.6 GeV for the light, charmoniumlike, and fully charm sectors, respectively. The decay width ratios of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup></math> tetraquark states are calculated for two-body strong decay channels within the rearrangement mechanism, including <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi><msub><mi>h</mi><mn>1</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><msub><mi>f</mi><mn>1</mn></msub></math> for isospin <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>0</mn></math> light tetraquarks, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><msub><mi>h</mi><mn>1</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><msub><mi>f</mi><mn>1</mn></msub></math> for isospin <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>1</mn></math> light tetraquarks, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mo>/</mo><mi>η</mi><mo>+</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mo>/</mo><mi>ω</mi><mo>+</mo><msub><mi>h</mi><mi>c</mi></msub></math> for charmoniumlike tetraquarks, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><msub><mi>h</mi><mi>c</mi></msub></math> for fully charm tetraquarks. The theoretical results are compared with the observed exotic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup></math> states, and promising search channels for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup></math> tetraquarks are discussed. The work suggests that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1855</mn><mo stretchy="false">)</mo></math> is unlikely to be a compact tetraquark state.

Kai Xu

Zheng Zhao

Nattapat Tagsinsit

Attaphon Kaewsnod

Ayut Limphirat

Christoph Herold

Yupeng Yan

Systematic study of exotic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup></math> tetraquark spectroscopy

We present a comprehensive study of the axial-vector resonance <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>K</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1270</mn><mo stretchy="false">)</mo></math> within the unitarized chiral perturbation theory, focusing on its two-pole structure and manifestation in femtoscopic observables. By considering the dominant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mi>K</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup><mi>π</mi></math> coupled channels, we reproduce the well-established double-pole structure and trace the chiral evolution of both poles as functions of the pion mass, using the vector-meson mass trajectories fitted to lattice-QCD data and experimental values. The lower pole, dominantly coupled to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup><mi>π</mi></math>, evolves from an above-threshold resonance to a virtual or bound state with increasing pion mass. In comparison, the higher pole, dominantly coupled to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mi>K</mi></math>, moves downward in energy, reflecting the strengthening of the chiral attraction. The influence of the finite vector-meson widths is systematically examined, showing that their inclusion smooths the pole trajectories without altering their qualitative behavior. Furthermore, femtoscopic correlation functions are calculated for all relevant vector-pseudoscalar channels in both charged sectors. The results exhibit distinct resonance and bound-state features consistent with the two-pole dynamics. The weak impact of higher channels, such as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup><mi>η</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math>, confirms that the simplified two-channel treatment captures the essential dynamics of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>K</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1270</mn><mo stretchy="false">)</mo></math> resonance. This study demonstrates that combining chiral extrapolation and femtoscopic correlation analyses provides a powerful and complementary framework for connecting lattice-QCD calculations, chiral effective theory, and experimental measurements, offering new insights into the molecular nature and chiral origin of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>K</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1270</mn><mo stretchy="false">)</mo></math> resonance.

Jia-Ming Xie

Zhi-Wei Liu

Jun-Xu Lu

Haozhao Liang

Raquel Molina

Li-Sheng Geng

Chiral evolution and femtoscopic signatures of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1270</mn><mo stretchy="false">)</mo></mrow></math> resonance

This paper investigates the existence of cosmological black holes by analyzing the properties of trapping horizons in detail, based on Hayward’s formalism of future outer and past inner trapping horizons, in several dynamical spacetimes embedded in an expanding universe. Through a detailed examination of the McVittie, Culetu, and Sultana–Dyer metrics, as well as the generalized Glass–Mashhoon solution, we evaluate the existence and characteristics of trapping horizons and energy conditions. The Glass–Mashhoon solution provides an analytical model for spherical stellar collapse. However, it is shown that, as long as certain conditions are satisfied, it lacks suitable future outer trapping horizons, meaning it does not represent a cosmological black hole. As a result, the McVittie class of solutions also fails to describe a cosmological black hole. Conversely, the Culetu and Sultana–Dyer spacetimes can describe a cosmological black hole in the matter-dominated early universe, provided that the relevant energy conditions are satisfied.

Iran

Mahdi Esfandiar

Fatimah Shojai

Omid Jamshidi

Soran Zoorasna

Cosmological black hole candidates: a detailed analysis of McVittie, Culetu, Sultana–Dyer, and Glass–Mashhoon spacetimes

Recently, a theoretical framework was set up in Miramontes et al. (Eur Phys J C 85:1055, 2025), which allows for the symmetry-preserving inclusion of full quark-gluon vertices in the description of the meson dynamics. In the present work, we develop a special truncation within this approach, which leads to a tractable set of functional equations that satisfy the fundamental chiral Ward-Takahashi identities. Specifically, in the chiral limit that we consider, this truncation allows us to simplify considerably the quark-gluon Schwinger–Dyson equation, without significant loss of quantitative accuracy. Importantly, this implies a substantial reduction of complexity of the renormalized Bethe–Salpeter equation: it is composed by a pair of one-loop diagrams that contain the full quark-gluon vertex, and a single two-loop diagram that is instrumental for the masslessness of the pion in the chiral limit. A detailed numerical analysis reveals that the incorporation of the aforementioned two-loop diagram is instrumental for the corresponding eigenvalue to reach unity. The key relation between the quark mass function and the pion wave function is shown to be satisfied to within the numerical precision of the loop integrals, which is at the level of about one percent or better. The field-theoretic ingredients required for the extension of this analysis beyond the chiral limit are briefly discussed.

China

M. Ferreira

Spain

A. Miramontes

J. Morgado

J. Papavassiliou

Germany

J. Pawlowski

Pion physics with dressed quark-gluon vertices

Global analyses of particle physics data are integral for validating and scrutinizing published results of experiments. Global fits of anomalous oscillation data which search for one or more eV-scale sterile neutrinos are particularly challenging both to evaluate and to reconcile in the global picture. Fits (especially joint ones) to oscillation data suffer from significant computational burdens, such as likelihood intractability, making traditional Markov Chain-Monte Carlo all but impossible. Given evidence both supporting and challenging beyond Standard Model physics across neutrino experiments of various baselines, energies, and detection techniques, the global search for sterile neutrinos requires additional tools in order to determine whether sterile neutrinos remain a viable solution to unexplained anomalies. Furthermore, both a Bayesian and frequentist interpretation of sterile neutrino data is needed for a complete assessment of longstanding tensions in the field. Techniques from the machine learning subfield of simulation-based inference have a natural application to such a problem. In this contribution, we illustrate some of the outstanding questions of the global picture of light sterile neutrinos by focusing on experiments searching with the disappearance of electron (anti)neutrinos, and look to posterior density estimation strategies to craft answers, including comparisons to a machine-learning-based frequentist approach.

United States

Joshua Villarreal

Julia Woodward

John Hardin

Janet Conrad

Machine learning-informed 3+1 sterile neutrino global fits using posterior density estimation of electron disappearance data

We compute the effective action for covariantly constant gauge fields that are solutions of the sourceless Yang–Mills equation and have the form of magnetic flux tubes. They represent a superposition of infinite many alternating monopole/anti-monopole pairs situated at infinity, with each pair having a structure similar to the Nielsen–Olesen magnetic flux tube. The chromomagnetic flux tubes condensation is stable and indicates that the Yang–Mills vacuum state is highly degenerate.

Greece

George Savvidy

QCD effective lagrangian and condensation of chromomagnetic flux tubes

We investigate the bound-state equations (BSEs) in two-dimensional QCD in the $ N_{\rm{c}}\to \infty$ limit, viewed from both the infinite momentum frame (IMF) and the finite momentum frame (FMF). The BSE of a meson in the original 't Hooft model, $\textit{viz.}$, spinor QCD$_{2}$ containing only fermionc quarks, has been extensively studied in literature. In this work, we focus on the BSEs pertaining to two types of ''exotic'' hadrons, a ''tetraquark'' which is composed of a bosonic quark and bosonic antiquark, and a ''baryon'' which is composed of a bosonic antiquark and a fermionic quark. Utilizing the Hamiltonian approach, we derive the corresponding BSEs for both types of ''exotic'' hadrons, from the perspectives of the light-front and equal-time quantization, and confirm the known results. The recently available BSEs for ''tetraquark'' in FMF has also been recovered with the aid of the diagrammatic approach. For the first time we also present the BSEs of a ''baryon'' in FMF in the extended 't Hooft model. By solving various BSEs numerically, we obtain the mass spectra pertaining to ''tetraquark'' and ''baryon'' and the corresponding bound-state wave functions of the lowest-lying states. It is numerically demonstrated that, when a ''tetraquark'' or ''baryon'' is continuously boosted, the forward-moving component of the bound-state wave function approaches the corresponding light-cone wave function, while the backward-moving component fades away.

Xiaolin Li

Yu Jia

Ying Li

Zhewen Mo

Solving bound-state equations in QCD$_{2}$ with bosonic and fermionic quarks * Supported in part by the National Science Foundation of China (12475090, 11925506, 12435004) and the Natural Science Foundation of Shandong province (ZR2022ZD26). The work of Zhewen Mo is also supported in part by the National Natural Science Foundation of China (12347145, 12347105)