In gravitational lensing under the weak-field approximation, the usual viewpoint is that light bending measures how a ray deviates from a straight line in Euclidean space. In this work, we take the opposite perspective: we ask how a straight line bends in a curved space, such as optical geometry–that is, how it deviates from geodesics. Using the Gauss–Bonnet theorem, we show that, at leading order, the deflection angle can be written as the integral of the geodesic curvature of a straight line in curved space. This reformulation emphasizes the global, coordinate-independent nature of the deflection angle and provides a complementary way of understanding the classical Gibbons–Werner method. To illustrate the idea, we apply it to three familiar spacetimes–Schwarzschild, Reissner–Nordström, and Kerr–and recover the well-known results. Furthermore, we extend the method to massive particles using the Jacobi metric, and illustrate it with the Reissner–Nordström spacetime.

China

Zonghai Li

Xiao-Jun Gao

The bending of a straight line

This work presents a universal and revisited formalism for the entropy of the apparent horizon in modified gravity to investigate the validity of the Generalized Second Law (GSL) of thermodynamics. This revisited horizon entropy is constructed directly from the modified Friedmann equations in a Friedmann–Robertson–Walker (FRW) universe. The resulting entropy relation contains, beside the standard Bekenstein–Hawking term, an additional integral contribution that encodes the effective energy density and pressure generated by deviations from general relativity. Using this universal entropy formula, a compact expression for the GSL is derived. This formalism is then applied to some viable $\textit{f}$($\textit{T}$) and $\textit{f}$($\textit{R}$) gravity models, in order to re-evaluate the validity of the GSL as a function of redshift. The analysis demonstrates that including the integral term in the revisited entropy can relatively improve the late-time validity of the GSL for some of these models while living others unchanged, thereby reinforcing the profound connection between thermodynamics and gravity.

Iran

Soma Heydari

Parastoo Askari

Kayoomars Karami

Revisited apparent horizon entropy and GSL in modified gravity

For axions present during inflation, it has been shown that a nonminimal coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ξ</mi><mi>σ</mi></msub></math> of the inflaton to gravity worsens isocurvature bounds [arXiv:2504.02952], while a nonminimal coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ξ</mi><mi>ρ</mi></msub></math> of the radial Peccei-Quinn field can alleviate them [Revisiting isocurvature bounds on the minimal QCD axion, <a href="http://dx.doi.org/10.1007/JHEP12(2025)028">J. High Energy Phys. 12 (2025) 028</a>.]. We analyze the simultaneous presence of both couplings and determine when one effect dominates the other, in both the metric and Palatini formulations of gravity. The two tendencies interpolate smoothly, but introducing a nonminimal inflaton coupling reduces the viable interval of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ξ</mi><mi>ρ</mi></msub></math> in which isocurvature bounds can be alleviated while avoiding backreaction on the inflationary dynamics. We illustrate our findings in Palatini Higgs inflation and Starobinsky inflation.

United Kingdom

Claire Rigouzzo

Germany

Sebastian Zell

Nonminimal couplings to gravity and axion isocurvature bounds

Motivated by the recently reported resonant structure <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>2300</mn><mo stretchy="false">)</mo></math>, a strong candidate for a fully strange tetraquark with positive parity, we perform a systematic study of fully strange tetra- and pentaquark systems within a chiral quark model. Low-lying <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave configurations of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi><mi>s</mi><mi>s</mi><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math> systems are investigated using the Gaussian expansion method combined with the complex scaling method, which allow for a unified treatment of bound, resonant, and scattering states. For tetraquarks, all possible configurations: meson-meson, diquark-antidiquark, and K-type structures, with complete color bases, are incorporated, while baryon-meson and diquark-diquark-antiquark configurations are considered for pentaquarks. Several weakly bound states and narrow resonances are identified in both sectors. In particular, a compact fully strange tetraquark with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mn>1</mn><mrow><mo>+</mo><mo>−</mo></mrow></msup></math> is found near 2.3 GeV, providing a natural interpretation of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>2300</mn><mo stretchy="false">)</mo></math> resonance. Additional exotic states with dominant hidden-color and K-type components are predicted in the mass ranges 1.6–3.1 GeV for tetraquarks and 2.6–3.2 GeV for pentaquarks. The internal structure of these states is analyzed through their sizes, magnetic moments, and wave-function compositions, highlighting the essential role of channel coupling and exotic color configurations. Finally, promising two-body strong decay channels are proposed to facilitate future experimental searches.

Gang Yang

Jialun Ping

Spain

Jorge Segovia

Fully strange tetra- and pentaquarks in a chiral quark model

We propose HoloNet, a neural-network framework that unifies lattice QCD (LQCD) thermodynamics and holographic Einstein-Maxwell-Dilaton (EMD) theory within a data-to-holography pipeline. Instead of assuming specific functional forms, HoloNet learns the metric profile <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>A</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo></math> and the gauge-dilaton coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>f</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo></math> directly from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>-flavor LQCD data at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi><mo>=</mo><mn>0</mn></math>. These learned functions are embedded into the EMD equations, enabling the model to reproduce the lattice equation of state and baryon number fluctuations with high fidelity. Once trained, HoloNet provides a fully data-driven holographic description of QCD that extends naturally to finite density, allowing us to map the phase diagram and estimate the location of the critical end point. The reconstructed potential <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi><mo stretchy="false">(</mo><mi>ϕ</mi><mo stretchy="false">)</mo></math> and coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>f</mi><mo stretchy="false">(</mo><mi>ϕ</mi><mo stretchy="false">)</mo></math> agree quantitatively with those obtained from holographic renormalization, demonstrating that HoloNet can consistently bridge different holographic models.

Hong-An Zeng

Japan

Lingxiao Wang

Mei Huang

Toward a unified Einstein-Maxwell-dilaton framework of QCD

We present a study using the distillation method to analyze the spectra of nucleon, nucleon-pion, and nucleon-pion-pion states in the positive-parity sector, as well as nucleon and nucleon-pion states in the negative-parity sector. The study uses seven domain-wall fermion ensembles with varying pion masses (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>π</mi></mrow></msub><mo>=</mo><mn>139</mn><mi>–</mi><mn>279</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>), lattice spacings (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>a</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>=</mo><mn>1.730</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>a</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>=</mo><mn>2.359</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>) and volumes (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><mi>L</mi><mo>=</mo><mn>3.8</mn><mi>–</mi><mn>7.5</mn></math>). To address the large number of contractions in this project, we implemented an algorithm to automate the contraction of nucleon-pion correlation functions that contain an arbitrary number of pions. In the positive-parity sector, we extrapolate the nucleon mass to the physical point. This study demonstrates the effectiveness of the distillation method for baryonic quantities with a focus on multihadronic states and establishes a foundation for future work.

A. Hackl

C. Lehner

Spectral analysis for nucleon-pion and nucleon-pion-pion states in both parity sectors using distillation with domain-wall fermions

Hadronic electromagnetic form factors and radiative decay properties offer a crucial window into the nonperturbative dynamics of quantum chromodynamics (QCD). In this work, we employ the light-cone sum rules (LCSR) method to systematically investigate the M1 radiative decay of vector mesons. Our study covers processes including <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mrow><mo>*</mo><mo>−</mo></mrow></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>−</mo></msup><mi>γ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><mo stretchy="false">→</mo><mi>D</mi><mi>γ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>*</mo></msup><mo stretchy="false">→</mo><mi>B</mi><mi>γ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mrow><mo>*</mo><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mi>γ</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>s</mi><mo>*</mo></msubsup><mo stretchy="false">→</mo><msub><mi>B</mi><mi>s</mi></msub><mi>γ</mi></math>, and further extends to the excited charmonium state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math>. Our calculations yield decay widths for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> that are in excellent agreement with experimental data. For the charm and bottom meson decays, where precise measurements are lacking, we provide theoretical predictions and compare them with other theoretical approaches. Most notably, our analysis reveals a universal linear dependence of the decay width on a function A(x) in the logarithmic coordinate system, which originates from the two-body decay dynamics and the ratio of the initial and final state decay constants. This relationship holds for the ground state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi><mo stretchy="false">→</mo><mi>P</mi><mi>γ</mi></math> processes here and suggests a broader applicability to radiative decays of ground-state vector mesons.

Zhi Jun Wang

Russia

Di Gao

Kai Kai Zhang

Yuan Yuan Ma

Yan Jun Sun

Radiative decays of vector mesons with light-cone sum rules

In this work, we compute the graviton mediated scattering amplitude of a massive spin-2 Fierz-Pauli field with various other massive spin fields, and in the nonrelativistic limit, find out the corresponding two-body gravitational potentials. The massive spin-2 field does not represent gravity here. The theory of gravity is taken to be the usual massless general relativity, and the massive spin-2 field is taken as a test quantum field coupled to gravity via the standard minimal prescription. We first compute the tree level 2-2 scattering of a massive spin-2 field with massive scalar, spin-1, and spin-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math> fields with one graviton exchange. Leading Newton potential, as well as the subleading spin or polarization dependent terms at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mi>G</mi><mo stretchy="false">)</mo></math> have been computed. We also consider the next to the leading order [<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mi>G</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math>] scattering of the massive spin-2 field with a massive scalar, and demonstrate the spin independent, spherically symmetric leading part of the two body gravitational potential. The present paper can be considered as an attempt to compute the gravitational potential in the context of a higher spin field theory.

India

Avijit Sen Majumder

Sourav Bhattacharya

Scattering of massive spin-2 field via graviton exchanges with different spin fields and the long range gravitational potential

We generalize the nature of the so-called beam-dump “ceiling” beyond which the improvement on the sensitivity reach in the search for fast-decaying mediators dramatically slows down, and we point out its experimental implications that motivate tabletop-sized beam-dump experiments for the search. Light (bosonic) mediators are well-motivated new-physics particles, as they can appear in dark-sector portal scenarios and models to explain various laboratory-based anomalies. Due to their low mass and feebly interacting nature, beam-dump-type experiments, utilizing high-intensity particle beams, can play a crucial role in probing the parameter space of such visibly decaying mediators—in particular, the “prompt decay” region, where the mediators feature relatively large coupling and mass. We present a general and semianalytic proof that the ceiling effectively arises in the prompt-decay region of an experiment and show its insensitivity to data statistics, background estimates, and systematic uncertainties, considering a concrete example, the search for axion-like particles interacting with ordinary photons at three benchmark beam facilities: PIP-II at FNAL, and SPS and LHC-dump at CERN. We then identify optimal criteria to perform a cost-effective and short-term experiment to reach the ceiling, demonstrating that very short-baseline compact experiments enable access to the parameter space unreachable thus far.

United States

Doojin Kim

Jaehoon Yu

South Korea

Jong-Chul Park

Hyunyong Kim

Beam-dump ceiling and its experimental implications: The case of a portable experiment

This study presents a comparative analysis of a light dark matter (DM) scenario in the minimal supersymmetric Standard Model (MSSM), the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>3</mn></msub></math>-symmetric next-to-minimal supersymmetric Standard Model, and the general next-to-minimal supersymmetric Standard Model (GNMSSM), incorporating constraints from DM relic density, the LUX-ZEPLIN 2024 experiment, Higgs data, and the Large Hadron Collider (LHC). The results suggest that, among the three frameworks, only GNMSSM can naturally accommodate light DM with a mass below 100 GeV. As such, the viable supersymmetry candidate is primarily Singlino-like. One key advantage of the GNMSSM is the effective decoupling between interactions that establish the relic density and those that control direct detection, allowing the model to satisfy all current experimental bounds simultaneously. We further explore two characteristic mass hierarchies in the GNMSSM parameter space, each exhibiting distinct phenomenological behaviors. The first hierarchy, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>S</mi><mo stretchy="false">˜</mo></mover><mo>&lt;</mo><mover accent="true"><mi>B</mi><mo stretchy="false">˜</mo></mover><mo>&lt;</mo><mover accent="true"><mi>H</mi><mo stretchy="false">˜</mo></mover></math> (Singlino-Bino-Higgsino), involves a relatively light Bino and allows the Higgsino mass parameter, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>μ</mi><mi>tot</mi></msub></math>, to be as low as about 200 GeV, naturally yielding light DM at tens of GeV. The dominant annihilation channels are then <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mover accent="true"><mi>χ</mi><mo stretchy="false">˜</mo></mover><mn>1</mn><mn>0</mn></msubsup><msubsup><mover accent="true"><mi>χ</mi><mo stretchy="false">˜</mo></mover><mn>1</mn><mn>0</mn></msubsup><mo stretchy="false">→</mo><msub><mi>A</mi><mi>s</mi></msub><msub><mi>A</mi><mi>s</mi></msub></math> in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mn>1</mn></msub></math> scenario and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mover accent="true"><mi>χ</mi><mo stretchy="false">˜</mo></mover><mn>1</mn><mn>0</mn></msubsup><msubsup><mover accent="true"><mi>χ</mi><mo stretchy="false">˜</mo></mover><mn>1</mn><mn>0</mn></msubsup><mo stretchy="false">→</mo><msub><mi>h</mi><mi>s</mi></msub><msub><mi>A</mi><mi>s</mi></msub></math> in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mn>2</mn></msub></math> scenario, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mi>s</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>A</mi><mi>s</mi></msub></math> denote singlet-dominated <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-even and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-odd Higgs bosons, respectively. The second hierarchy, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>S</mi><mo stretchy="false">˜</mo></mover><mo>&lt;</mo><mover accent="true"><mi>H</mi><mo stretchy="false">˜</mo></mover><mo>&lt;</mo><mover accent="true"><mi>B</mi><mo stretchy="false">˜</mo></mover></math>, corresponds to a heavy Bino. In this case, although the DM phenomenology remains qualitatively similar, LHC constraints require <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>μ</mi><mi>tot</mi></msub><mo>≳</mo><mn>900</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, implying a significant degree of fine-tuning in reproducing the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math>-boson mass.

Fei Li

Junjie Cao

Natural realization of tens-of-GeV dark matter in the general NMSSM