We uncover surprising hidden simplicity in Mellin amplitudes for tree-level anti–de Sitter (AdS) holographic correlators for AdS “gluon” (spin-1) operators. We define Mellin amplitudes with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi></math> spinning operators via the so-called scaffolding of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>n</mi></math>-scalar ones with specific projection operators for each spin state, which are rational functions of Mellin variables of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>n</mi></math> scalars generalizing flat-space scaffolding amplitudes. We classify possible three-point structures with spin 1, which take the same form as massive three-point amplitudes in flat space, and match them with special solutions such as those extracted from 6-scalar ones in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>5</mn></mrow></msub><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></math>. Focusing on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>5</mn></mrow></msub></mrow></math> gluons, we directly bootstrap spinning amplitudes in scaffolding form up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi><mo>=</mo><mn>6</mn></math> gluons (which amounts to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>n</mi><mo>=</mo><mn>12</mn></math> scalars) using factorizations, multilinearity, and flat-space limit. The results take a remarkably simple form in analogy with flat-space amplitudes, which can be constructed from familiar 3- and 4-vertices as well as propagators of massive spin-1 particles. Surprisingly, we find that vertices with any descendant levels are proportional to the primary ones with nice combinatorial coefficients, which makes manifest the correct flat-space limit in the simplest possible way.

China

Song He

Xiang Li

Yuyu Mo

Dongyu Yang

Hidden Simplicity in AdS Spinning Mellin Amplitudes via Scaffolding

Recent discoveries of exotic hadrons, which cannot be classified within the conventional quark model of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math> mesons and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>q</mi><mi>q</mi></math> baryons, strongly imply the existence of dynamically generated hadronic molecules. Some of these hadron-hadron interactions are accompanied by coupled-channel effects, which remain challenging to quantitatively determine. In this work, we demonstrate that femtoscopy provides a sensitive probe of such coupled-channel dynamics. We calculate correlation functions for the double-strangeness pentaquark candidates <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mrow><mi>c</mi><mi>s</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4493</mn><mo stretchy="false">)</mo></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math>) and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mrow><mi>c</mi><mi>s</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4633</mn><mo stretchy="false">)</mo></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math>), revealing clear signatures of the attractive interactions that can form bound states. The results are markedly different from those obtained in scenarios that neglect off-diagonal transitions, highlighting the importance of coupled-channel effects for understanding the structure of these hadrons.

Zheng-Ting Lai

Jun-Xu Lu

Zhi-Wei Liu

Brazil

A. Martínez Torres

K.P. Khemchandani

Li-Sheng Geng

Revealing the nature of double-strangeness pentaquark states via femtoscopic correlation functions

We present an extension of the Standard Model based upon the gauged <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>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></mrow></msub></math> symmetry, featuring an ultralight vector boson that couples to the difference of muon and tau lepton numbers. This anomaly-free construction, whilst historically motivated by the muon’s anomalous magnetic moment, is here employed as an independent phenomenological framework for solar neutrino physics. Through kinetic mixing with the photon, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> boson generates an effective matter potential within the solar interior, thereby modifying neutrino flavor oscillations via the Mikheyev-Smirnov-Wolfenstein mechanism. Utilizing recent solar neutrino measurements from Borexino, SNO, and Super-Kamiokande, together with an up-to-date solar standard model, we constrain the boson mass to be below <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>5.7</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>17</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>eV</mi></math>, positioning it as a potential ultralight dark matter candidate. The optimal model, corresponding to a coupling parameter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>o</mi></msub><mo>≈</mo><mo>−</mo><mn>2</mn></math>, yields <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>χ</mi><mi>ν</mi><mn>2</mn></msubsup><mo>=</mo><mn>2.7</mn></math>, which compares favorably with the standard three-flavor scenario (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>χ</mi><mi>ν</mi><mn>2</mn></msubsup><mo>=</mo><mn>3.1</mn></math>). This best-fit configuration corresponds to an effective four-fermion coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>g</mi><msup><mi>Z</mi><mo>′</mo></msup><mn>2</mn></msubsup><mi>ϵ</mi><mo>/</mo><msubsup><mi>m</mi><msup><mi>Z</mi><mo>′</mo></msup><mn>2</mn></msubsup><mo>≈</mo><mn>6.6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>23</mn></mrow></msup><mtext> </mtext><mtext> </mtext><msup><mrow><mi>eV</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup></math>, approximately 5.7 times the Fermi constant, which for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϵ</mi><mo>≈</mo><mn>1</mn></math> and a reference mediator mass of 1 eV is equivalent to a gauge coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><msup><mi>Z</mi><mo>′</mo></msup></msub><mo>≈</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>12</mn></mrow></msup></math>. We furthermore present projections for forthcoming experiments. The Jiangmen Underground Neutrino Observatory (JUNO), which commenced operations in August 2025 and has already achieved world-leading precision in oscillation parameter measurements, together with the XLZD consortium, should substantially refine these constraints. Such ultralight particles may address long-standing discrepancies in galaxy simulations within the cold dark matter paradigm, and recent theoretical developments demonstrate their compatibility with nonthermal dark matter production mechanisms. Additionally, terrestrial long-baseline neutrino experiments provide complementary probes of this parameter space.

Portugal

Ilídio Lopes

Constraining ultralight vector bosons via solar neutrino oscillations: The gauged <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> model and prospects for JUNO and XLZD

Evaluating quantum loop corrections to curvature perturbations in non-attractor inflation presents theoretical ambiguities. A crucial aspect of this challenge arises from unconstrained finite contributions to renormalization counterterms and from regularization-scheme dependence. In this work, we derive Ward identities via the path integral formalism based on the large gauge symmetry of the background-perturbation split. These identities are shown to impose nontrivial, model-independent constraints on the renormalization procedure. Provided the ultraviolet completion respects this symmetry, the Ward identities constrain the infrared evolution of the power spectrum and fix the residual finite ambiguity. This symmetry-based framework offers a systematic criterion for addressing recent theoretical discrepancies concerning one-loop corrections in ultra-slow-roll inflation.

Cheng-Jun Fang

Zong-Kuan Guo

Fixing the renormalization of inflationary loops via Ward identities

Vector-like leptons (VLLs) are well-motivated candidates for physics beyond the standard model. We investigate the sensitivity of the 6 TeV muon collider to the neutral doublet VLL (denoted by $\textit{N}$) via its pair production in an SU(2) $$_L$$ doublet model with hypercharge $$Y=-\frac{1}{2}$$ . Assuming mixing with muons, we study the subsequent decay $$N\rightarrow W^+ \mu ^-$$ and analyze two representative signals, namely $$4j2\mu $$ and $$2\ell 2\mu E\hspace{-5.83328pt}/$$ , arising from the hadronic and leptonic decays of the $\textit{W}$ boson, respectively. The signal and background events are simulated within a Monte Carlo framework, and a cut-based analysis is performed at the 6 TeV muon collider with an integrated luminosity $$\mathcal {L}=4$$ ab $$^{-1}$$ for the unpolarized and polarized beam configurations, $$(P_{\mu ^+},P_{\mu ^-})=(0,0)$$ and $$(P_{\mu ^+},P_{\mu ^-})=(-1,1)$$ . We consider VLL masses in the range of $$1300{-}2980$$ GeV and evaluate the corresponding search sensitivity. Our results show that the 6 TeV muon collider could provide strong sensitivity to neutral doublet VLLs through the $$4j2\mu $$ and $$2\ell 2\mu E\hspace{-5.83328pt}/$$ signals, particularly for the idealized fully polarized beam configuration, under the detector, polarization, luminosity and background assumptions adopted in this analysis.

Chong-Xing Yue

Mei-Shu-Yu Wang

Xin-Yang Li

Si-Yu Zhang

Prospects for probing neutral vector-like leptons via pair production at a muon collider

Yang Yu

Guan-Sen Wang

Bo Zhang

Tian-Peng Tang

Bing-Yu Su

Lei Feng

Correction: New constraints on cosmic-ray boosted sub-Gev dark matter via light mediators

We present a theory-constrained hierarchical Bayesian analysis of primordial black holes (PBHs) generated by inflationary perturbations in <italic>f</italic>( <italic>Q, T</italic>) gravity, and confront the resulting PBH population with the gravitational-wave catalog GWTC-3. In this framework, the parameters ( <italic>&#945;, &#946;, &#955;</italic>) characterize the effective inflationary dynamics, with <italic>&#945;</italic> and <italic>&#946;</italic> specifying the adopted <italic>f</italic>( <italic>Q, T</italic>) gravitational sector and <italic>&#955;</italic> parameterizing the local behavior of the specified inflaton potential near its quasi-inflection-point region. Starting from the modified background dynamics in <italic>f</italic>( <italic>Q, T</italic>) gravity, we compute the curvature power spectrum and determine the resulting PBH mass distribution through gravitational collapse at horizon re-entry. Within the adopted analytic approximation and Gaussian-modulated potential, the inflationary dynamics determine the PBH mass-function parameters through the background evolution and the curvature power spectrum. Using posterior samples of detected binary black-hole events, we construct a theory-constrained hierarchical likelihood and explore the corresponding hyperparameter space with Markov Chain Monte Carlo, obtaining constraints on the effective inflationary parameters of the adopted model. Our analysis demonstrates how gravitational-wave population data can be used to constrain an inflationary modified-gravity model through its predicted PBH population. This provides a statistical framework linking early-Universe modified gravity to late-time compact-binary observations and offers a new observational probe of the inflationary sector of alternative gravity theories.

Iran

S. Davood Sadatian

S. Mohamad Reza Hosseini

Theory-constrained hierarchical inference of primordial black holes in <italic>f</italic>( <italic>Q, T</italic>) gravity with GWTC-3

We study the phenomenology of the scalar leptoquark (sLQ) <math altimg='si1.svg'><msub><mover accent='true'><mrow><mi>R</mi></mrow><mo stretchy='true'>&#732;</mo></mover><mn>2</mn></msub></math> coupled to right-handed neutrinos (RHNs) at the High-Luminosity Large Hadron Collider (HL-LHC), focusing on signatures beyond those targeted in conventional sLQ searches. In the regime where the sLQ is heavier than the RHN and the Yukawa couplings are <math altimg='si13.svg'><mrow><mi mathvariant='script'>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></math>, the decay <math altimg='si14.svg'><mrow><msub><mover accent='true'><mrow><mi>R</mi></mrow><mo stretchy='true'>&#732;</mo></mover><mn>2</mn></msub><mo>&#8594;</mo><mi>N</mi><mi>j</mi></mrow></math> can dominate, leading to distinctive same-sign dimuon and multijet final states. This lepton-number-violating signature is weakly constrained by existing searches, benefits from low Standard Model backgrounds, and provides a direct probe of the Majorana nature of the RHN. We perform a comprehensive analysis by combining sLQ pair and single production at <math altimg='si15.svg'><mrow><msqrt><mi>s</mi></msqrt><mo linebreak='goodbreak'>=</mo><mn>14</mn><mspace width='0.33em' /><mtext>TeV</mtext></mrow></math>, and evaluate the HL-LHC sensitivity over a wide range of masses and Yukawa couplings. We find that pair production dominates at the TeV scale, while single production becomes increasingly important at higher masses, significantly extending the accessible parameter space beyond current direct and indirect limits. Our results demonstrate the strong complementarity between production modes and highlight the potential of the HL-LHC to probe sLQ scenarios with Majorana RHNs.

India

Subham Saha

Arvind Bhaskar

Manimala Mitra

Exploring <math altimg='si1.svg'><msub><mover accent='true'><mrow><mi>R</mi></mrow><mo stretchy='true'>&#732;</mo></mover><mn>2</mn></msub></math> leptoquarks and Majorana neutrinos via same-sign dimuons at the HL-LHC

It was proposed that there exists an $\textit{E}$ -invariant formulation of eleven-dimensional supergravity in which the propagating fields of the theory are realised through an infinite tower of higher duals. We show how to derive the propagating equations of the higher dual fields within $\textit{E}$ exceptional field theory at the linearised level. Starting from the pseudo-Lagrangian, we construct parent actions for all higher gradient dual fields that are associated with the three-form, the six-form, and the dual graviton. We show that the resulting Euler-Lagrange equations constrain the Stückelberg fields to be pure curls, ensuring that the higher duals propagate the same physical degrees of freedom as the original supergravity fields. The additional Stückelberg fields, which are not predicted by the tensor hierarchy algebra, are shown to play a specific role as sources for the Labastida tensors of the higher dual fields.

France

Guillaume Bossard

Belgium

Nicolas Boulanger

Josh O’Connor

Higher dualities in $\textit{E}$ 11 exceptional field theory

The prospects for observing small departures from Lorentz invariance are studied using effective interactions of the Higgs boson with photons. A single operator of mass-dimension five suffices to describe all leading signatures of Lorentz violation in the diphoton decay channel. Comparison of the theoretical modified decay rates with observed signal strengths measured by the ATLAS and CMS Collaborations at the Large Hadron Collider indicates an estimated attainable sensitivity to the corresponding coefficients for Lorentz violation of order <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mrow><msup><mrow><mi>GeV</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math>.