We solve the radical-square reflection residual of the symmetric elliptic free-fermion eight-vertex model in a minimal four-dimensional local coefficient algebra. Two parity-odd tangent channels generate an ordered product in the square of the radical, and the reflection equation fixes its parity-even completion within the trace-fixed sector whose radical-square term starts at order <italic>u</italic> 2. The resulting regular boundary object enters a double-row transfer construction. Its scalar quotient yields the open anisotropic XY Hamiltonian with diagonal boundary fields, while the full transfer object retains the non-semisimple boundary channels. Finite-chain audits through <math altimg='si1.svg'><mrow><mi>N</mi><mo linebreak='goodbreak'>=</mo><mn>12</mn></mrow></math> accompany the analytic construction.

China

Ze Tao

Hao Yan

Fujun Liu

Exact open anisotropic XY Hamiltonian from a non-semisimple boundary completion

We investigate <italic>X</italic>(6900) as a hadronic realization of a gluonic portal between a dark sector and QCD. The analysis is updated using the 2026 CMS observation of a family of all-charm structures and a recent combined LHCb&#8211;ATLAS&#8211;CMS analysis of the di- <italic>J</italic>/ <italic>&#968;</italic> spectrum. The CMS angular analysis favors <math altimg='si19.svg'><mrow><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo linebreak='goodbreak'>=</mo><msup><mn>2</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></mrow></math>, motivating a spin-two mediator rather than the scalar ansatz used in earlier versions of this study. The combined analysis also demonstrates that the extracted <italic>X</italic>(6900) mass and width are significantly model dependent because of interference. We therefore use <math altimg='si20.svg'><mrow><msub><mi>M</mi><mi>X</mi></msub><mo linebreak='goodbreak'>=</mo><mn>6.919</mn><mspace width='0.33em' /><mtext>GeV</mtext></mrow></math> and <math altimg='si21.svg'><mrow><msub><mstyle mathvariant='normal'><mi>&#915;</mi></mstyle><mi>X</mi></msub><mo linebreak='goodbreak'>=</mo><mn>70.3</mn><mspace width='0.33em' /><mtext>MeV</mtext></mrow></math> as a reference benchmark, corresponding to the narrow-width, weak-interference Model I of the combined analysis, while treating the spread among interference models as a systematic theoretical uncertainty. The interaction is <display><formula id='ueq0001'><math altimg='si22.svg'><mrow><msub><mi mathvariant='script'>L</mi><mrow><mrow><mi mathvariant='normal'>i</mi></mrow><mi>n</mi><mi>t</mi></mrow></msub><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mfrac><msub><mi>c</mi><mi>&#967;</mi></msub><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle></mfrac><msub><mi>X</mi><mrow><mi>&#956;</mi><mi>&#957;</mi></mrow></msub><msubsup><mi>T</mi><mi>&#967;</mi><mrow><mi>&#956;</mi><mi>&#957;</mi></mrow></msubsup><mo linebreak='goodbreak'>&#8722;</mo><mfrac><msub><mi>c</mi><mi>g</mi></msub><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle></mfrac><msub><mi>X</mi><mrow><mi>&#956;</mi><mi>&#957;</mi></mrow></msub><msubsup><mi>T</mi><mi>g</mi><mrow><mi>&#956;</mi><mi>&#957;</mi></mrow></msubsup><mo>.</mo></mrow></math></formula></display>Using the standard spin-two normalization, <display><formula id='ueq0002'><math altimg='si23.svg'><mrow><mstyle mathvariant='normal'><mi>&#915;</mi></mstyle><mrow><mo>(</mo><mi>X</mi><mo>&#8594;</mo><mi>g</mi><mi>g</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mfrac><mrow><msubsup><mi>c</mi><mi>g</mi><mn>2</mn></msubsup><msubsup><mi>M</mi><mi>X</mi><mn>3</mn></msubsup></mrow><mrow><mn>10</mn><mi>&#960;</mi><msup><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle><mn>2</mn></msup></mrow></mfrac><mo>,</mo></mrow></math></formula></display>and the gluonic gravitational form factor <italic>A<inf>g</inf></italic>(0), the leading spin-independent nucleon cross section is <display><formula id='ueq0003'><math altimg='si24.svg'><mrow><msubsup><mi>&#963;</mi><mrow><mi>&#967;</mi><mi>N</mi></mrow><mrow><mrow><mi mathvariant='normal'>S</mi></mrow><mi>I</mi></mrow></msubsup><mo linebreak='goodbreak'>=</mo><mfrac><mrow><msubsup><mi>&#956;</mi><mrow><mi>&#967;</mi><mi>N</mi></mrow><mn>2</mn></msubsup><msubsup><mi>m</mi><mi>&#967;</mi><mn>2</mn></msubsup><msubsup><mi>m</mi><mi>N</mi><mn>2</mn></msubsup></mrow><mi>&#960;</mi></mfrac><msup><mrow><mo stretchy='true'>(</mo><mfrac><mrow><msub><mi>c</mi><mi>&#967;</mi></msub><msub><mi>c</mi><mi>g</mi></msub></mrow><mrow><msup><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle><mn>2</mn></msup><msubsup><mi>M</mi><mi>X</mi><mn>2</mn></msubsup></mrow></mfrac><mo stretchy='true'>)</mo></mrow><mn>2</mn></msup><msub><mi>A</mi><mi>g</mi></msub><msup><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mn>2</mn></msup><mo>.</mo></mrow></math></formula></display>For <math altimg='si2.svg'><mrow><msub><mi>A</mi><mi>g</mi></msub><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mn>0.42</mn></mrow></math>, <math altimg='si8.svg'><mrow><msub><mi>B</mi><mrow><mi>g</mi><mi>g</mi></mrow></msub><mo linebreak='goodbreak'>=</mo><mn>0.10</mn></mrow></math>, and <math altimg='si25.svg'><mrow><msub><mi>m</mi><mi>&#967;</mi></msub><mo linebreak='goodbreak'>=</mo><mn>100</mn><mspace width='0.33em' /><mtext>GeV</mtext></mrow></math>, the benchmark reference-scale estimate implies <math altimg='si26.svg'><mrow><msub><mi>c</mi><mi>&#967;</mi></msub><mo linebreak='goodbreak'>/</mo><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle><mo>&#8818;</mo><mn>1.87</mn><mo linebreak='goodbreak'>&#215;</mo><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>8</mn></mrow></msup><mspace width='0.33em' /><msup><mrow><mtext>GeV</mtext></mrow><mrow><mo>&#8722;</mo><mn>1</mn></mrow></msup></mrow></math> when the 90% C.L. XENONnT reference scale is imposed. The annihilation channel <math altimg='si4.svg'><mrow><mi>&#967;</mi><mover accent='true'><mi>&#967;</mi><mo>&#175;</mo></mover><mo>&#8594;</mo><msup><mi>X</mi><mo>*</mo></msup><mo>&#8594;</mo><mi>g</mi><mi>g</mi></mrow></math> is <italic>p</italic>-wave suppressed and resonantly enhanced at <math altimg='si27.svg'><mrow><msub><mi>m</mi><mi>&#967;</mi></msub><mo>&#8771;</mo><msub><mi>M</mi><mi>X</mi></msub><mo linebreak='goodbreak'>/</mo><mn>2</mn><mo linebreak='goodbreak'>=</mo><mn>3.46</mn><mspace width='0.33em' /><mtext>GeV</mtext></mrow></math>. We show that the most important phenomenological uncertainty is no longer the existence of <italic>X</italic>(6900), which is now highly significant, but the interpretation of its line shape and hence the extraction of its mass, width, and gluonic coupling. We argue that a small set of numerical figures is essential for a publication-quality presentation: the direct-detection exclusion plane, the resonance line shape, and the resonant annihilation line shape.

Iran

Majid Monemzadeh

<italic>X</italic>(6900) as a hadronic mediator of a gluonic dark-matter portal

We investigate the gravitational deflection of charged massive particles by a charged galactic wormhole supported by the Sofue dark matter density profile [56], <math altimg='si2.svg'><mrow><mi>&#961;</mi><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><msub><mi>&#961;</mi><mn>0</mn></msub><msup><mi>e</mi><mrow><mo>&#8722;</mo><mi>r</mi><mo>/</mo><msub><mi>r</mi><mn>0</mn></msub></mrow></msup><mo>,</mo></mrow></math> where <italic>&#961;</italic> <inf>0</inf> and <italic>r</italic> <inf>0</inf> denote the central dark matter density and the characteristic scale radius, respectively. This phenomenological profile models the dark matter distribution in galactic halos and acts as the matter source sustaining the wormhole geometry. Extending our previous investigation of light rays and neutral massive particles in this spacetime [57], we study the combined effects of gravitational and electromagnetic interactions on the motion of charged massive particles. The deflection angle is computed independently using the Rindler&#8211;Ishak method based on the Jacobi metric and the Gauss&#8211;Bonnet theorem, enabling a systematic comparison between the two approaches. We find that the predictions of the two methods become nearly indistinguishable in the relativistic regime, whereas the differences at lower velocities arise from the velocity-dependent correction terms proportional to <math altimg='si3.svg'><mrow><mo>(</mo><mn>1</mn><mo linebreak='goodbreak'>&#8722;</mo><msup><mi>v</mi><mn>2</mn></msup><mo>)</mo></mrow></math> in the trajectory equation. We further perform backward relativistic ray tracing of optically thin accretion flows around the charged galactic wormhole to investigate its shadow and photon-ring structure. Although the shadow remains circular because of the spacetime&#8217;s spherical symmetry, its radius, photon-ring structure, and intensity distribution exhibit a nontrivial dependence on the wormhole charge, providing potential observational signatures of charged galactic wormholes. These results provide new insights into the interplay between gravitational and electromagnetic interactions in charged wormhole spacetimes and their observational manifestations.

India

Md Khalid Hossain

Humaun Kabir Laskar

Farook Rahaman

Aritra Sanyal

Charged galactic wormholes: Shadow imaging, accretion disks, and charged-particle deflection

Two Higgs doublets models with a scalar potential that breaks electroweak symmetry spontaneously can have either one or two local minima. While potentials with one minimum can have a decoupling regime where all the new scalars are heavy, we show that, for potentials with <italic>two</italic> local minima, the masses of all the scalars are bounded if the dimensionless quartic couplings obey perturbativity constraints.

Spain

José M. Camacho

Italy

Carlos Miró

Miguel Nebot

Tomás Tobarra

On vacua and bounded masses in the general 2HDM

A stationary surface response is formulated for an isolated, settled disk galaxy as a possible endpoint of deformation memory. The response is described by a scalar field coupled to the projected baryonic density, with a positive quadratic Hamiltonian and a finite range Green function constructed from the modified Bessel function <italic>K</italic> <inf>0</inf>. SPARC selects the long range regime, where the additional circular support follows the enclosed projected mass. Its normalization is fixed by the baryonic Tully&#8211;Fisher relation through a single acceleration scale. For 153 primary SPARC galaxies, the model gives a median relative rotation curve residual of 0.166, compared with 0.159 for the radial acceleration relation and 0.081 for NFW fits with two parameters for each galaxy. The inferred acceleration scale agrees with the canonical galactic value. Bootstrap resampling places the response and radial acceleration relation within the same population interval. Their predictions separate through their dependences on baryonic concentration, source mass, surface brightness, and gas fraction. These relations provide observational tests of an enclosed mass response as a description of galactic dynamics.

Kazakhstan

Daulet Berkimbayev

A deformation memory model for galactic rotation curves

In this paper, we investigate the Krylov complexity of the massless scalar field in the massive Bañados-Teitelboim-Zanelli (BTZ) black hole with quantum fluctuation. This fluctuation is considered to be triggered by the Hawking radiation, which indeed influences the behavior of the time evolution of Krylov complexity. Our results show that Lanczos coefficients <italic>b<inf>n</inf></italic> exhibit a black hole mass <italic>M</italic>-dependent staggering, <math altimg='si7.svg'><mrow><mstyle mathvariant='normal'><mi>&#916;</mi></mstyle><mover><mrow><msub><mi>b</mi><mi>N</mi></msub></mrow><mo stretchy='true'>&#8254;</mo></mover><mo>&#8764;</mo><mi>M</mi></mrow></math>, inducing oscillatory complexity dynamics that intensify with lower mass black holes. Moreover, the graviton mass <italic>m</italic> is found to suppress the oscillations but accelerate the late-time exponential growth <math altimg='si8.svg'><mrow><mi>K</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>&#8764;</mo><msup><mi>e</mi><mrow><msub><mi>&#955;</mi><mi>K</mi></msub><mi>t</mi></mrow></msup></mrow></math>. This study indicates that the Krylov complexity could be a sensitive probe to distinguish massless and massive gravity via operator growth signatures.

Yu-Ting Zhou

Xiao-Mei Kuang

Krylov complexity of a massless scalar field in massive BTZ black hole with quantum fluctuation

We study a quantum-corrected version of the Oppenheimer–Snyder (OS) spacetime in which classical collapse is modified by a single effective parameter <italic>&#945;</italic>, representing small quantum gravitational effects in a phenomenologically rescaled form. Although the correction enters through a term proportional to <italic>&#945;M</italic> 2/ <italic>r</italic> 4, it produces noticeable changes in the strong-field region while leaving weak-field physics almost unchanged. One of the main results is the appearance of a minimum mass for horizon formation, <math altimg='si19.svg'><mrow><msub><mi>M</mi><mi>min</mi></msub><mo>&#8764;</mo><mrow><mo>(</mo><mn>0.5</mn><mo linebreak='badbreak'>&#8722;</mo><mn>1.2</mn><mo>)</mo></mrow><mspace width='0.16em' /><msub><mi>M</mi><mo>&#8857;</mo></msub></mrow></math> for the effective parameter <italic>&#945;</italic>&#8239;&#8776;&#8239;0.22. We emphasize that this <italic>M</italic> <inf>min</inf> is expressed in terms of the effective parameter <italic>&#945;</italic>; in terms of the bare loop quantum gravity (LQG) parameter, <math altimg='si20.svg'><mrow><msub><mi>M</mi><mi>min</mi></msub><mo>&#8764;</mo><msub><mi>M</mi><mtext>Pl</mtext></msub><mo>&#8764;</mo><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>5</mn></mrow></msup></mrow></math> g, consistent with the theoretical expectation. Orbital properties are also slightly modified, with the innermost stable circular orbit (ISCO) shifting to <math altimg='si21.svg'><mrow><msub><mi>r</mi><mrow><mrow><mi mathvariant='normal'>I</mi></mrow><mi>S</mi><mi>C</mi><mi>O</mi></mrow></msub><mo linebreak='goodbreak'>=</mo><mn>6</mn><mi>M</mi><mo linebreak='goodbreak'>&#8722;</mo><mi>&#945;</mi><mo linebreak='goodbreak'>/</mo><mrow><mo>(</mo><mn>12</mn><mi>M</mi><mo>)</mo></mrow></mrow></math>, giving corrections of order <math altimg='si22.svg'><mrow><mo>&#8764;</mo><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>4</mn></mrow></msup></mrow></math> for stellar black holes and <math altimg='si23.svg'><mrow><mo>&#8764;</mo><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>10</mn></mrow></msup></mrow></math> for Sgr A*. In the same region, radial epicyclic frequencies change by about <math altimg='si24.svg'><mrow><mn>5</mn><mo>%</mo><mo>&#8722;</mo><mn>10</mn><mo>%</mo></mrow></math> near <italic>r</italic>&#8239;&#8764;&#8239;5 <italic>M</italic>, while vertical modes are less affected, leading to small but structured shifts in quasi-periodic oscillation (QPO) behavior. Using four X-ray binaries (GRS 1915+105, XTE J1550-564, XTE J1859+226, GRO J1655-40), we find a consistent range <math altimg='si18.svg'><mrow><mi>&#945;</mi><mo linebreak='goodbreak'>=</mo><mn>0.22</mn><mo>&#177;</mo><mn>0.10</mn></mrow></math>, with masses between <math altimg='si25.svg'><mrow><mn>5.4</mn><mo linebreak='goodbreak'>&#8722;</mo><mn>12.4</mn><mspace width='0.16em' /><msub><mi>M</mi><mo>&#8857;</mo></msub></mrow></math> and emission radii <math altimg='si26.svg'><mrow><mi>r</mi><mo linebreak='goodbreak'>/</mo><mi>M</mi><mo>&#8764;</mo><mn>5.5</mn><mo linebreak='goodbreak'>&#8722;</mo><mn>8.6</mn></mrow></math>. The observed QPO frequencies, lying in the range <math altimg='si27.svg'><mrow><mn>100</mn><mo linebreak='goodbreak'>&#8722;</mo><mn>450</mn></mrow></math> Hz, are well reproduced within this framework. Weak-field tests such as S2 and Mercury still allow <math altimg='si28.svg'><mrow><msub><mi>f</mi><mrow><mrow><mi mathvariant='normal'>s</mi></mrow><mi>p</mi></mrow></msub><mo linebreak='goodbreak'>=</mo><mn>1.10</mn><mo>&#177;</mo><mn>0.19</mn></mrow></math>, leaving room for these small strong-gravity corrections. This work demonstrates that while bare Planck-scale corrections are unobservable, effective rescaled parameters that encode the collective effect of quantum gravity can be constrained by current astrophysical observations.

South Africa

Azerbaijan

Jordan

A. Errehymy

Morocco

Y. Khedif

M. Daoud

Uzbekistan

B. Turimov

S. Usanov

F. Turaev

Z. Yasakov

Joint constraints on quantum Oppenheimer–Snyder black holes from high-frequency quasi-periodic oscillations in X-ray binary systems and the S2 star orbit

Multiple potential wells for massive test particles, allowing distinct families of bound orbits to coexist, are a characteristic feature of certain compact objects beyond the standard Einstein–Maxwell setting. Taking the dyonic black hole as a representative example, we demonstrate that such multi-well geometries can support multiple coexisting branches of bound orbits, in contrast to the single-branch behavior observed in the Schwarzschild spacetime. Crucially, the periodic orbits sharing identical rational rotation number and zoom number, and hence identical topological indices, can nevertheless produce <italic>radiatively distinct</italic> gravitational waves in a representative extreme-mass-ratio inspiral: their amplitude modulation and harmonic content differ because each branch spans different regions of spacetime curvature. These &#8220;topologically equivalent yet waveform-distinguishable&#8221; signatures identify multi-well orbital dynamics as a potential qualitative probe of strong-field spacetime structure beyond the Einstein&#8211;Maxwell paradigm.

Chao-Hui Wang

Shao-Wen Wei

Tao Zhu

Yu-Xiao Liu

Topologically equivalent yet radiatively distinct orbits in EMRI system

In the framework of modified teleparallel gravity, we study the neutrino flavor conversion. We show how the presence of spacetime torsion modifies both neutrino flavor oscillation and the matter-enhanced Mikheyev-Smirnov-Wolfenstein (MSW) resonance. Using data from solar neutrino experiments, we perform an analysis to place new bounds on the modified teleparallel model parameters and neutrino-torsion coupling. Our numerical results indicate that the resulting modifications to the neutrino survival probability may explain potential observational discrepancies in current and future observatories without invoking new physics or non-standard interactions.

H. Yazdani Ahmadabadi

H. Mohseni Sadjadi

Testing modified teleparallel gravity by neutrino oscillations

Inspired by the studies of Rahaman et al. [Eur. Phys. J. C (2018) 78, 948] and Chen et al. [Phys. Rev. D (2024) 109, 024010] which adopted dyon black hole and covariant loop quantum black hole solutions as effective descriptions of the solar exterior gravitational field and performed gravitational tests via Solar System planetary orbital motions, we adopt the exterior solution of a Schwarzschild black hole in modified gravity (MOG), which incorporates a dimensionless coupling parameter <italic>&#945;</italic>, to describe the gravitational field of spherical celestial bodies and constrain this key parameter. We calculate the first-order post-Newtonian periastron precession of a timelike particle in this spacetime. Using observational data from five binary pulsars and Solar System measurements, we obtain small-scale constraints on the MOG coupling parameter at the <math altimg='si19.svg'><mrow><mi>&#945;</mi><mo>&#8764;</mo><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>6</mn></mrow></msup><mo linebreak='goodbreak'>&#8722;</mo><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>5</mn></mrow></msup></mrow></math> level, which provide independent weak-field tests of the Schwarzschild&#8211;MOG spacetime complementary to large-scale galactic gravity probes.