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 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

We explore an unusual symmetry in a field theory on a specific (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional curved spacetime, which has an interesting interpretation as an approximate asymptotic Weyl symmetry. Unlike the conventional Weyl symmetry, the boundary term under the variation plays a crucial role in understanding for its anomaly. After converting a two-dimensional field theory on curved spacetime to an inhomogeneous field theory, we obtain the vacuum expectation value of the energy-momentum tensor. Then, we show the existence of an Unruh-like effect in the bubble wall expansion at the zero temperature.

O-Kab Kwon

Jeongwon Ho

Sang-Heon Yi

Sang-A Park

Asymptotic Weyl symmetry and its anomaly in a curved spacetime

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

We investigate cosmological and astrophysical constraints on dark photons with masses <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo>∼</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mtext>−</mtext><msup><mrow><mn>10</mn></mrow><mrow><mn>3</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>. These dark photons can be copiously produced either in the early Universe or during core-collapse supernovae, potentially leaving distinct observational signatures. First, we derive updated constraints from cosmological and astrophysical observables that rely on the thermal relic abundance of dark photons, including the cosmic microwave background spectrum, primordial light element abundances, and Galactic/extragalactic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math>-ray flux. We consider the minimal reheating temperature possible, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>RH</mi></mrow></msub><mrow><mo>=</mo><mn>6</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></mrow></math>, such that our constraints are conservative, but unavoidable within the minimal dark photon model. Then, for supernova-sourced dark photons, we systematically examine all relevant observational bounds, revisit the standard cooling argument and derive limits from other arguments such as fireball formation, low energy supernovae and Galactic positron injection.

Andrea Caputo

Jaeyoung Park

Seokhoon Yun

Heavy dark photon handbook: Cosmological and astrophysical bounds

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 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

In models of strongly interacting dark sectors, the production of dark quarks at accelerators can give rise to dark showers with multiple dark mesons in the final state. If some of these dark mesons are sufficiently light and long-lived, they can be detected with searches for displaced vertices at beam-dump experiments and electron-positron colliders. In this work we focus on the case that dark quark production proceeds via effective operators, while the dark sector analog of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>ρ</mi><mn>0</mn></msup></math> meson can decay via kinetic mixing. We evaluate current constraints from NA62 and BABAR as well as sensitivity projections for SHiP and Belle II. We find that there exists a sizeable parameter region where SHiP may detect several displaced vertices in a single event and thus obtain valuable information about the structure of the dark sector.

Elias Bernreuther

Nicoline Hemme

Felix Kahlhoefer

Suchita Kulkarni

Maksym Ovchynnikov

Sub-GeV dark matter and multidecay signatures from dark showers at beam-dump experiments

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.