In this work, we investigate the relativistic structure of white dwarfs (WDs) within the framework of modified gravity theory <math altimg='si3.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>,</mo><msub><mi>L</mi><mi>m</mi></msub><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mi>R</mi><mo linebreak='goodbreak'>+</mo><mi>&#945;</mi><mi>T</mi><msub><mi>L</mi><mi>m</mi></msub></mrow></math>, which introduces a non-minimal coupling between matter and curvature. Using a realistic equation of state (EoS) that includes contributions from a relativistic degenerate electron gas and ionic lattice effects, we solve the modified Tolman-Oppenheimer-Volkoff (TOV) equations for two standard choices of the matter Lagrangian density: <math altimg='si9.svg'><mrow><msub><mi>L</mi><mi>m</mi></msub><mo linebreak='goodbreak'>=</mo><mi>p</mi></mrow></math> and <math altimg='si6.svg'><mrow><msub><mi>L</mi><mi>m</mi></msub><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mi>&#961;</mi></mrow></math>. We show that the extra <italic>&#945;TL<inf>m</inf></italic> term significantly alters the mass-radius relation of WDs, especially at high central densities <math altimg='si11.svg'><mrow><mo>(</mo><msub><mi>&#961;</mi><mi>c</mi></msub><mo>&#8819;</mo><msup><mn>10</mn><mn>8</mn></msup><mo linebreak='goodbreak'>&#8722;</mo><msup><mn>10</mn><mn>9</mn></msup><mspace width='0.16em' /><mrow><mi mathvariant='normal'>g</mi></mrow><mo linebreak='goodbreak'>/</mo><mi>c</mi><msup><mi>m</mi><mn>3</mn></msup><mo>)</mo></mrow></math>, allowing for stable super-Chandrasekhar configurations. In particular, depending on the sign and magnitude of the parameter <italic>&#945;</italic>, the maximum mass can increase or decrease, and in some regimes, the usual critical point indicating the transition from stability to instability disappears. Our findings suggest that <italic>f</italic>( <italic>R, T, L<inf>m</inf></italic>) gravity provides a viable framework to explain the existence of massive WDs beyond the classical Chandrasekhar limit. Using Bayesian inference with WD observational data, we further constrain the coupling parameter <italic>&#945;</italic> for the two choices of the Lagrangian density <italic>L<inf>m</inf></italic>.

Brazil

Edson Otoniel

Juan M.Z. Pretel

Clésio E. Mota

César O.V. Flores

Victor B.T. Alves

Germany

Franciele M. da Silva

White dwarf structure in <italic>f</italic>( <italic>R, T, L<inf>m</inf></italic>) gravity: Beyond the Chandrasekhar mass limit

Several possible excesses around $ 95 $ GeV hint at an additional light scalar beyond the Standard Model. We examine the capability of the Circular Electron-Positron Collider (CEPC) to test this hypothesis in the Higgs-strahlung channel $ e^{+}e^{-} \to ZS $ with $ Z \to\mu^{+}\mu^{-} $ and $ S \to\tau^{+}\tau^{-} $ . A full detector simulation shows that the optimal center-of-mass energy for studying the 95 GeV light scalar is 210 GeV. A deep neural network classifier reduces the luminosity required for discovery by half. At $ L = 20\; \mathrm{ab}^{-1} $ , the $ 5\sigma $ sensitivity of the CEPC to the signal strength $ \mu_{\tau\tau}^{ZS} $ reaches 0.016 and 0.020 for $ \sqrt{s} = 210 $ GeV and 240 GeV, respectively. The corresponding thresholds for a 5% precision measurement are $ \mu_{\tau\tau}^{ZS} \gt 0.10 $ and $ \gt 0.12 $ . At $ \sqrt{s}=210 $ GeV (240 GeV), the $ 5\sigma $ coverage of all N2HDM-Flipped samples with $ \chi^2_{h_{95}} \lt 7.82 $ requires $ L=800\ \mathrm{fb}^{-1} $ (1.22 $ \mathrm{ab}^{-1} $ ). These results establish a 210 GeV run, augmented by machine-learning selection, as the most efficient strategy to confirm or refute the 95 GeV excess at future lepton colliders.

China

Yabo Dong

Manqi Ruan

Kun Wang

Haijun Yang

Jingya Zhu

Testing a 95 GeV Scalar at the CEPC with Machine Learning * This work was supported by the National Natural Science Foundation of China under Grant No. 12275066 and by the startup research funds of Henan University. The work of K. Wang was also supported by the Open Project of the Shanghai Key Laboratory of Particle Physics and Cosmology under Grant No. 22DZ2229013-3. The work of M. Ruan was also supported by the National Key Program for S&T Research and Development under Contract No. 2024YFA1610603. The work of H. Yang was also supported by the National Natural Science Foundation of China under Grant No. W2441004.

We consider near-extremal membranes embedded in M-theory, consistently truncated to gauged $$ \mathcal{N} $$ = 2 supergravity in four dimensions on the coset space $\textit{M}$ . These are holographically dual to 2+1 dimensional superconformal gauge theory with U(1) × U(1) global symmetry. Turning on the chemical potential to either the $\textit{R}$-symmetry or the baryonic symmetry gives access to the quantum critical regime of the boundary gauge theory. We study perturbative stability of the extremal limit, and demonstrate that membranes with topological (baryonic) charge are free from all known instabilities. $\textit{R}$-charged membranes are free from the superconducting instabilities, but have unstable charge transport and instabilities associated with the condensation of the axions.

Canada

Alex Buchel

Switzerland

Ruben Monten

Near-extremal membranes in M-theory

Motivated by recent progress in the spurion analysis of non-invertible selection rules (NISRs) arising from near-group fusion algebras, we further generalize the framework to a class of NISRs obtained from $\textit{ℤ}$ orbifolding of a $\textit{ℤ}$ symmetry, denoted as $\textit{ℤ}$ /$\textit{ℤ}$ . Many structural features are carried over: for instance, our labeling scheme enables systematic tracking of all couplings when constructing composite amplitudes from simpler building blocks at arbitrary loop orders in perturbation theory. Our analysis provides a transparent understanding of both low-order and all-order zeros of couplings under radiative corrections. Furthermore, we examine the fate of low-order zeros when the fusion algebra is not faithfully realized — a situation not captured by the vanilla argument of “loop-induced groupification” — and formulate a conjecture on the related aspects of particle decoupling and effective theory. Finally, we discuss the low-order versus all-order zeros in Yukawa textures from the perspective of spurion analysis.

Italy

Motoo Suzuki

Ling-Xiao Xu

Spurion analysis of $\textit{ℤ}$ $\textit{M}$ /$\textit{ℤ}$ 2 non-invertible selection rules: low-order versus all-order zeros

Pulsars, with their extreme densities and precise measurements, offer an exceptional probe of matter under intense gravity. We examined compact star structures within the extended <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi mathvariant='script'>T</mi><mo>)</mo></mrow></math> gravity framework, incorporating the Ricci scalar, matter Lagrangian, and energy-momentum trace. Introducing coupling constants <italic>&#955;</italic> <inf>1</inf> and <italic>&#955;</italic> <inf>2</inf> enabled a realistic description beyond general relativity. Using the Durgapal-Bannerji-type metric, we derived modified field and TOV equations, obtaining expressions for energy density and anisotropic pressures. With the transformation <math altimg='si165.svg'><mrow><msup><mi>e</mi><mrow><mi mathvariant='script'>B</mi><mo>(</mo><mi>r</mi><mo>)</mo></mrow></msup><mo linebreak='goodbreak'>=</mo><msup><mstyle mathvariant='normal'><mi>&#934;</mi></mstyle><mn>2</mn></msup><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow></mrow></math> and a chosen anisotropy function &#916;( <italic>r</italic>), regular stellar models were integrated and matched smoothly to the exterior Schwarzschild-de Sitter spacetime. All physical conditions are satisfied: density and pressures are positive and finite; &#916;( <italic>r</italic>)&#8239;&gt;&#8239;0 implies an outward-directed force; sound speeds remain subluminal; and the adiabatic index &#915;&#8239;&gt;&#8239;4/3 ensures dynamical stability. The generalized TOV equation confirms equilibrium among gravitational, hydrostatic, anisotropic, and curvature-matter coupling forces. The <math altimg='si166.svg'><mrow><mi>M</mi><mo linebreak='goodbreak'>&#8722;</mo><mi>R</mi></mrow></math> relations exhibit clear trends. For <math altimg='si167.svg'><mrow><msub><mi>&#955;</mi><mn>1</mn></msub><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mn>4</mn><mo>,</mo><msub><mi>&#955;</mi><mn>2</mn></msub><mo linebreak='goodbreak'>=</mo><mn>0.4</mn></mrow></math>: PSR J2215+5135 (2.28, <italic>M</italic> <inf>&#8857;</inf>) has <math altimg='si168.svg'><mrow><mi>R</mi><mo linebreak='goodbreak'>=</mo><mn>13</mn><mo>.</mo><msubsup><mn>05</mn><mrow><mo>&#8722;</mo><mn>0.20</mn></mrow><mrow><mo>+</mo><mn>0.13</mn></mrow></msubsup></mrow></math> km (GR: 12.33&#8239;km); PSR J0740+6620 (2.08, <italic>M</italic> <inf>&#8857;</inf>): 12.68 &#8239;&#8594;&#8239; 13.32&#8239;km; PSR J0348+0432 (2.01, <italic>M</italic> <inf>&#8857;</inf>): 12.76 &#8239;&#8594;&#8239; 13.39&#8239;km; PSR J0030+0451 (1.44, <italic>M</italic> <inf>&#8857;</inf>): 13.19 &#8239;&#8594;&#8239; 13.77&#8239;km. Positive <italic>&#955;</italic> <inf>1</inf> compresses stars <math altimg='si169.svg'><mrow><mo>(</mo><mi>R</mi><mo linebreak='goodbreak'>=</mo><mn>11</mn><mo>.</mo><msup><mn>26</mn><mrow><mo>+</mo><mn>0.33</mn></mrow></msup></mrow></math> km for <math altimg='si170.svg'><mrow><msub><mi>&#955;</mi><mn>1</mn></msub><mrow><mo>=</mo><mn>5</mn><mo>)</mo></mrow></mrow></math>, while <math altimg='si171.svg'><mrow><msub><mi>&#955;</mi><mn>1</mn></msub><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mn>5</mn></mrow></math> expands to <math altimg='si27.svg'><mrow><mn>13</mn><mo>.</mo><msubsup><mn>07</mn><mrow><mo>&#8722;</mo><mn>0.20</mn></mrow><mrow><mo>+</mo><mn>0.14</mn></mrow></msubsup></mrow></math> km. At <math altimg='si5.svg'><mrow><msub><mi>&#955;</mi><mn>1</mn></msub><mo linebreak='goodbreak'>=</mo><mn>3</mn></mrow></math>, varying <italic>&#955;</italic> <inf>2</inf> shifts <italic>R</italic> from <math altimg='si86.svg'><mrow><mn>12</mn><mo>.</mo><msubsup><mn>32</mn><mrow><mo>&#8722;</mo><mn>0.29</mn></mrow><mrow><mo>+</mo><mn>0.18</mn></mrow></msubsup></mrow></math> km <math altimg='si172.svg'><mrow><mo>(</mo><msub><mi>&#955;</mi><mn>2</mn></msub><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mn>5</mn><mo>)</mo></mrow></math> to <math altimg='si173.svg'><mrow><mn>11</mn><mo>.</mo><msup><mn>23</mn><mrow><mo>+</mo><mn>0.35</mn></mrow></msup></mrow></math> km <math altimg='si174.svg'><mrow><mo>(</mo><msub><mi>&#955;</mi><mn>2</mn></msub><mo linebreak='goodbreak'>=</mo><mn>5</mn><mo>)</mo></mrow></math>. Overall, including <math altimg='si175.svg'><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub></math> or <math altimg='si176.svg'><mi mathvariant='script'>T</mi></math> slightly enlarges radii, showing that tuning <italic>&#955;</italic> <inf>1</inf>,&#8201; <italic>&#955;</italic> <inf>2</inf> precisely controls compactness and maximum mass&#8212;consistent with observations and testable by future data.

Oman

S.K. Maurya

South Africa

Azerbaijan

A. Errehymy

India

K.N. Singh

Kuwait

O. Donmez

Uzbekistan

J. Rayimbaev

S. Otaboyev

Y. Turaev

Constraining <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi mathvariant='script'>T</mi><mo>)</mo></mrow></math> gravity with millisecond pulsar observations

We present a non-singular, definition-level formulation of F-theory by replacing the traditional shrinking-fiber limit of M-theory with compactification on a tower-completed circle described using perfectoid geometry and condensed mathematics. This construction provides an intrinsic eleven-dimensional carrier for modular data and admits a canonical tilting and comparison procedure that yields elliptic geometry as an output rather than an auxiliary input. Using this framework, we establish a precise M-theory/Type IIB dictionary in the constant-coupling sector, showing how the physical axio-dilaton is fixed by eleven-dimensional geometric and topological data. The correspondence is tested at the level of the ten-dimensional bosonic effective action, including its topological couplings inherited from eleven dimensions. The tower-completed geometry naturally organizes global sectors in generalized cohomology, with charge data governed by K-theory and exhibiting a canonical prime-power torsion structure. We further show how this framework extends to varying-coupling backgrounds and duality defects, admits a natural adelic completion with prime-independence, and generalizes to higher-rank and U-duality geometries. We also discuss holographic aspects and the anomaly-refined extension of the duality group beyond the bosonic truncation. Together, these results provide a coherent, non-singular foundation for F-theory and its extensions.

Arshid Shabir

Indonesia

Bobby Eka Gunara

United Kingdom

Belgium

Mir Faizal

A perfectoid duality between M-theory and F-theory

We use equivariant localization and holography to study four-dimensional $$ \mathcal{N}=1 $$ superconformal field theories arising from M5-branes wrapped on a punctured Riemann surface. We explain how, given a Riemann surface with marked points, one can glue in a “puncture geometry” locally around each point. Using equivariant localization we show that the central charge consists of a bulk contribution plus localized puncture contributions. We recover and generalize the known results for locally $$ \mathcal{N}=2 $$ preserving punctures, and derive new results for genuinely locally $$ \mathcal{N}=1 $$ preserving punctures.

Christopher Couzens

Alice Lüscher

James Sparks

Localizing punctures in M-theory

The Galactic Center excess (GCE) of GeV <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math> rays may hint at dark matter (DM), yet its origin remains debated. Motivated by this, we survey weakly interacting massive particle (WIMP) models that can fit the GCE while satisfying relic-density, direct-detection (DD), and indirect-detection (ID) bounds. We group candidates into hadronic (Higgs portals; simplified scalar/vector mediators), leptonic [<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><mrow><msub><mi>L</mi><mi>i</mi></msub><mo>−</mo><msub><mi>L</mi><mi>j</mi></msub></mrow></msub></math>], and mixed [<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><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math>-portal] classes. Across all cases, present DD and dwarf-spheroidal <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math>-ray limits exclude wide regions, leaving mainly narrow resonant funnels with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mrow><mi>DM</mi></mrow></msub><mo>≃</mo><msub><mi>m</mi><mrow><mi>med</mi></mrow></msub><mo>/</mo><mn>2</mn></math> and portal couplings <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>≪</mo><mn>1</mn></math>. In hadronic setups, scalar and vector Higgs portals survive only in a thin strip near <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>h</mi></msub><mo>/</mo><mn>2</mn><mo>≃</mo><mn>62.5</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> with portal couplings <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, while the Dirac Higgs and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> portals are essentially excluded. The UV-complete vector Higgs portal retains resonant bands whose viable portal strength depends on the mixing angle. Simplified scalars allow small windows for complex-scalar or vector DM; Dirac DM is strongly disfavored, whereas a pseudoscalar with Dirac DM remains viable over a broader parameter range. For a simplified <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> mediator, a pure vector coupling leaves only a marginal region, while pure axial is excluded by DD/ID bounds. In leptonic scenarios, inverse-Compton emission is essential: <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>e</mi></msub></math> (and, to a lesser extent, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo>−</mo><mi>L</mi></math>) fits the GCE with near-thermal cross sections, while <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> is disfavored. Overall, viable WIMP explanations are constrained to the finely tuned resonant regime, with leptophilic vectors and pseudoscalar portals emerging as the most robust options.

United States

Chuiyang Kong

Mattia Di Mauro

Comprehensive study of WIMP models explaining the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>F</mi><mi>e</mi><mi>r</mi><mi>m</mi><mi>i</mi></math>-LAT Galactic Center excess

We study the decomposition of 4d $$ \mathcal{N}=1 $$ gauge theories with Lie algebras of type $$ \mathfrak{su}(N) $$ , $$ \mathfrak{so}(2N) $$ , and $$ {\mathfrak{e}}_6 $$ , realized via M-theory geometric engineering. These theories, together with their novel decomposition structure, arise from quotienting the Bryant-Salamon spin bundle over the 3-sphere by special finite subgroups acting simultaneously on both the fiber and base. We show that these gauge theories admit both inner and outer automorphisms, enabling sequences of gauge theory breaking. In particular, outer automorphisms extend the decomposition structure to theories with $$ \mathfrak{so}\left(2N+1\right) $$ , $$ \mathfrak{sp}(2N) $$ , $$ {\mathfrak{f}}_4 $$ , and $$ {\mathfrak{g}}_2 $$ gauge algebras. For these theories, including both simply-laced and non-simply-laced cases, we analyze their $\textit{p}$-form symmetries, including (−1)-form symmetries, derive the corresponding SymTFTs, and identify the M-theoretic origin of their symmetry topological operators and defects. Finally, we demonstrate that these gauge theories exhibit modified instanton sums and higher 4-group structures, and we derive the associated topological sector directly from M-theory.

Osama Khlaif

Marwan Najjar

Aspects of 4d $$ \mathcal{N}=1 $$ $\textit{ADE}$ gauge theories from M-theory: decomposition, automorphisms, and generalised symmetries

Motivated by the recently obtained Hadrons to Atomic nuclei from Lattice QCD potentials for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi><mtext>−</mtext><mi>ϕ</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi><mtext>−</mtext><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi><mtext>−</mtext><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math> interactions, we investigate the structure of the exotic nuclei <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>Be</mi></mrow><mprescripts></mprescripts><mrow><mi>ϕ</mi></mrow><mrow><mn>8</mn></mrow></mmultiscripts></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mmultiscripts><mrow><mi>Be</mi></mrow><mprescripts></mprescripts><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow><mrow><mn>8</mn></mrow></mmultiscripts></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>Be</mi></mrow><mprescripts></mprescripts><msub><mi>η</mi><mi>c</mi></msub><mrow><mn>8</mn></mrow></mmultiscripts></mrow></math> as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi><mo>+</mo><mi>α</mi><mo>+</mo><mi>M</mi></math> three-body systems (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>M</mi></math> denotes the meson). The bound and resonant states are calculated consistently using the Gaussian expansion method, with resonances identified via the complex scaling method. For the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi><mi>ϕ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi></math>-charmonium interactions, a folding potential is constructed based on the Hadrons to Atomic nuclei from Lattice (HAL) QCD potentials and fitted to a Woods-Saxon form. We find that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math> meson exhibits a strong “gluelike” effect, binding the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mn>0</mn><mn>1</mn><mo>+</mo></msubsup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mn>2</mn><mn>1</mn><mo>+</mo></msubsup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mn>4</mn><mn>1</mn><mo>+</mo></msubsup></math> resonant states of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>Be</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>8</mn></mrow></mmultiscripts></mrow></math> into stable states and significantly reducing the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>α</mi><mtext>−</mtext><mi>α</mi></mrow></math> distance. In contrast, the interactions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub></math> with the nucleus are weaker, forming only shallow bound states with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mn>0</mn><mn>1</mn><mo>+</mo></msubsup></math> state of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>Be</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>8</mn></mrow></mmultiscripts></mrow></math> and even increasing the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>α</mi><mtext>−</mtext><mi>α</mi></mrow></math> separation. Notably, our analysis predicts weakly bound <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>α</mi><mtext>−</mtext><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> states in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mmultiscripts><mrow><mi>S</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>4</mn></mrow></mmultiscripts></mrow><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mmultiscripts><mrow><mi>S</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>2</mn></mrow></mmultiscripts></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></math> channels, a result not reported in prior studies, which suggests that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mmultiscripts><mrow><mi>Be</mi></mrow><mprescripts></mprescripts><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow><mrow><mn>8</mn></mrow></mmultiscripts></math> may not be a Borromean nucleus. The sensitivity of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>Be</mi></mrow><mprescripts></mprescripts><mrow><mi>ϕ</mi></mrow><mrow><mn>8</mn></mrow></mmultiscripts></mrow><mo stretchy="false">(</mo><msubsup><mn>4</mn><mn>1</mn><mo>+</mo></msubsup><mo stretchy="false">)</mo></math> state—transitioning from bound to resonant depending on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi></math>-particle radius—highlights the subtle dynamics at play. These results provide a systematic theoretical comparison of how different vector mesons modify nuclear clustering, offering critical predictions for future experimental searches of such exotic hadron-nucleus systems.

Hao Zhou

Xiang Liu

Three-body resonances of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi><mi>α</mi><mi>M</mi></math> clusters (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>M</mi><mo>=</mo><mi>ϕ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub></math>) in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>Be</mi></mrow><mprescripts></mprescripts><mrow><mi>M</mi></mrow><mrow><mn>8</mn></mrow></mmultiscripts></mrow></math> nuclei