We evaluate discovery prospects for photophobic axion-like particles (ALPs) in the $\textit{WWjj}$ final state at the High-Luminosity LHC (HL-LHC; $\sqrt{s}=14\ {\rm{TeV}}$ , ${\cal{L}}=3\ {\rm{ab}}^{-1}$ ). In the photophobic limit ( $g_{a\gamma\gamma}=0$ ), ALPs couple to electroweak gauge bosons and are produced in association with two jets ( $ pp\to jj\ a $ ) via both $\textit{s}$-channel electroweak exchange and vector boson fusion (VBF)–like topologies, followed by $a\to W^+W^-$ decay. We target the different-flavour dilepton mode $W^+W^- \to e^\pm\mu^\mp\nu \bar{\nu}$ with two jets and moderate missing transverse momentum. The analysis employs a two-step strategy: initial preselection that defines the signal-like final state, followed by a multivariate analysis (MVA) trained on dijet and dileptonic-$\textit{WW}$ kinematics from both the $\textit{s}$-channel and VBF-like production mechanisms to separate signal from background; the MVA threshold is optimized independently at each $m_a$ . We present 2$\textit{σ}$ and 5$\textit{σ}$ discovery sensitivities for the ALP–$\textit{W}$ coupling $g_{aWW}$ across the 170–4000 GeV mass range. For $260\ {\rm{GeV}}\le m_a\le1500\ {\rm{GeV}}$ , the 2$\textit{σ}$ (5$\textit{σ}$) sensitivity is approximately flat around $ 0.61(0.76)\ {\rm{TeV}}^{-1}$ . At large masses/couplings, the mapping between an experimental rate and a single EFT parameter $g_{aWW}$ can become UV sensitive, and we treat the extreme high-mass/high-coupling corner as an extrapolation; therefore, we also report model-independent discovery thresholds for the fiducial quantity $ \sigma(pp\to jj\ a)\times\rm{Br}(a\to W^+W^-) $ over the same mass range to enable reinterpretation for other models. These results indicate that the $WWjj$ topology offers competitive and complementary sensitivity to heavy photophobic ALPs at the HL-LHC.

China

Jiaojiao Feng

Ying-nan Mao

Kechen Wang

Discovery prospects for photophobic axion-like particles in the $\textit{WWjj}$ final state at the High-Luminosity LHC * Jiaojiao Feng and Kechen Wang are supported by the National Natural Science Foundation of China (11905162), the Excellent Young Talents Program of the Wuhan University of Technology (40122102, 40122103) and the research program of the Wuhan University of Technology (2020IB024, 104972025KFYjc0101). Ying-nan Mao is supported by the National Natural Science Foundation of China (12205227). The simulation and analysis work of this article was completed with the computational cluster provided by the Theoretical Physics Group at the Department of Physics, School of Physics and Mechanics, Wuhan University of Technology

In the Cachazo-He-Yuan (CHY) representation, many tree-level scattering amplitudes are written as integrals localized by the scattering equations, where the CHY integrand encodes the theory and must reproduce the physical factorization pattern of Mandelstam singularities. The inverse CHY problem therefore asks for a rational integrand whose physical poles match a prescribed set of factorization channels, a task that becomes rapidly combinatorial at higher multiplicity. We present an algorithmic approach that makes the subset structure of pole data explicit by assigning each particle subset <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>A</mi></math> a generalized pole degree <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>K</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo></mrow></math>, realized as a signed internal-edge count in a colored integrand graph. Additivity under integrand multiplication and an elementary face recursion on the subset lattice imply that all higher-channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo></math> are linear functions of the two-particle integers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">{</mo><mi>K</mi><mo stretchy="false">(</mo><msub><mi>s</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">}</mo></math>, so the inverse step becomes a mixed-integer linear feasibility problem. The same subset lattice provides a fixed computation graph for exact constraint satisfaction: pole requirements and recursion identities are treated as hard constraints, updates are restricted to those that preserve feasibility, and whenever a proposed change would enter a fixed node its constraint residual is rerouted and redistributed through unfixed degrees of freedom so that all constraints remain satisfied throughout. After a factorial rescaling, every local propagation update is purely integral, keeping the entire procedure exact in integer arithmetic and avoiding a posteriori reconstruction from numerical evaluations. Since physical tree-level amplitudes must contain only simple factorization poles as dictated by unitarity and locality, we further organize generalized integrands by an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi></math>-regular grading under multiplication, where degree-zero factors act as Möbius-invariant insertions admitting a decomposition into products of four-point cross ratios, which guides efficient higher-order pole reduction. We illustrate the construction at six and eight points, including pole selection and higher-order pole reduction.

Simeng Li

Yaobo Zhang

Inverse Cachazo-He-Yuan integrand construction from factorization channels with exact integer constraint propagation

We study energy-energy correlators (EECs) in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> annihilation and deep inelastic lepton-hadron scattering (DIS), focusing on aspects of nonperturbative physics in these observables. We introduce the EEC jet functions and investigate the infrared behavior of both small-angle EECs and angle-integrated EECs by performing explicit one-loop calculations. The factorization and universality of the EECs in these processes are demonstrated. A matching scheme is proposed to smoothly connect kinematic regions where different scaling behaviors with jet energy are observed. In combination with the next-to-leading order correction, this matching provides a good description of the EEC data and pythia simulations in high-energy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> annihilation. Predictions for DIS processes for future electron-ion collider kinematics are also presented.

United States

Yuxun Guo

Germany

Werner Vogelsang

Feng Yuan

Wenbin Zhao

Energy-energy correlators in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> annihilation and deep inelastic scattering

We revisit the calculation of the next-to-leading order (NLO) corrections to dijet production in electron-ion collisions at small $\textit{x}$. We focus on the back-to-back configuration where the relative transverse momentum $\textit{P}$ of the measured jets is much larger than both their momentum imbalance $\textit{K}$ and the target saturation momentum $\textit{Q}$ ($\textit{x}$, $\textit{A}$). In this regime, we present for the first time a complete calculation of the real NLO corrections, associated with gluon emissions outside the jet cones, at leading power in 1/$\textit{P}$ . Our result exhibits TMD factorisation, with the same hard factor as at tree-level and a NLO correction to the Weiszäcker-Williams (WW) gluon transverse momentum dependent (TMD) distribution which involves four Wilson-line operators. By studying different kinematical regimes for $\textit{K}$ and for the radiated gluon, we recover all the quantum evolutions that were previously identified for this process at NLO: the B-JIMWLK high-energy evolution and the CSS evolution of the gluon WW TMD, and the DGLAP evolution of the gluon PDF. When both $\textit{K}$ and the transverse momentum transferred by the target are large compared to $\textit{Q}$ , all the Wilson-line operators boil down to the unintegrated gluon distribution and our NLO result for the gluon TMD can be used to isolate the transverse-momentum dependent gluon splitting function.

France

Paul Caucal

Edmond Iancu

Farid Salazar

Gluon splitting at small $\textit{x}$: a unified derivation for the JIMWLK, DGLAP and CSS equations

By utilizing the dihadron fragmentation formalism, we extend the previous factorization of near-side energy-energy correlators (EECs) in the collinear limit and derive an all order resummation in the Fourier transform <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>b</mi></mrow><mrow><mi>T</mi></mrow></msub></mrow></math>-space. A perfect matching is obtained when we compare to the fixed-order results. We further demonstrate the resummation effects for the EECs in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> annihilation and show that they will significantly improve the theoretical predictions at small angles.

Factorization and Resummation for the Near-Side Energy-Energy Correlators

We study the QCD scaling behavior of the small-angle energy-energy correlator (EEC), focusing on the transition between its perturbative preconfinement and nonperturbative postconfinement regimes. Applying the light-ray operator product expansion (OPE), we develop a formalism that describes the scaling of the EEC with the input energy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>Q</mi></mrow></math> in the transition and the postconfinement region, where the latter quantum scaling is determined by the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>=</mo><mn>5</mn></mrow></math> DGLAP anomalous dimension. A key result of our Letter is a novel connection between the light-ray OPE and the dihadron fragmentation function (DFF), where we show that the nonperturbative OPE coefficients correspond to moments of the DFF. This finding establishes a new paradigm for studying hadronization. Our theoretical predictions are validated against Monte Carlo simulations for both <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math> collisions, showing excellent agreement. The potential role of the quantum scaling in the precision determination of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></math> is also discussed.

Cyuan-Han Chang

Hao Chen

Xiaohui Liu

David Simmons-Duffin

Hua Xing Zhu

Quantum Scaling in Energy Correlators beyond the Confinement Transition

Within the Colour Glass Condensate effective theory, we demonstrate that back-to-back dijet correlations in dilute-dense collisions involving a small- <italic>x</italic> quark from the nuclear target can be factorised in terms of universal transverse momentum dependent distributions (TMDs) for the sea quarks. Two building blocks are needed to construct all these TMDs at the operator level: the sea quark TMD operator which appears in semi-inclusive Deep-Inelastic Scattering (SIDIS) or in the Drell-Yan process and the elastic <italic>S</italic>-matrix for a quark-antiquark dipole. Compared to SIDIS, the saturation effects are stronger for dijet production in forward proton-nucleus collisions, due to additional scattering in the initial and final state, effectively resulting in a larger value for the nuclear saturation momentum.

Marcos Guerrero Morales

Unveiling the sea: universality of the transverse momentum dependent quark distributions at small <italic>x</italic>

With Bayesian inference, we investigate the impact of recent near-threshold <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> production measurements by the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi><mn>007</mn></mrow></math> experiment and GlueX Collaboration on the extraction of proton gravitational form factors. We apply the generalized parton distribution framework at the next to leading order and demonstrate a stable expansion for the near-threshold kinematics. We find that the experimental constraints are in good agreement with the state-of-the-art lattice simulations, where negative <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>C</mi><mi>q</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi>g</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></math> are strongly preferred. This highlights a great potential to extract them from future high-precision experiments.

Bayesian Inferring Nucleon Gravitational Form Factors via Near-Threshold <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> Photoproduction

We study the forward-backward azimuthal angular correlations of hadrons in association with multiparticle production in the central rapidity region in proton-proton collisions at the LHC. We apply the nucleon energy-energy correlator framework, where the spinning gluon distribution introduces a nontrivial <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>cos</mi><mo stretchy="false">(</mo><mn>2</mn><mi>ϕ</mi><mo stretchy="false">)</mo></math> asymmetries. We will demonstrate that the fundamental helicity structure of quantym chromodynamics (QCD) amplitudes predicts a unique power counting rule: <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>cos</mi><mo stretchy="false">(</mo><mn>2</mn><mi>ϕ</mi><mo stretchy="false">)</mo></math> asymmetry starts at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msubsup><mi>α</mi><mi>s</mi><mn>2</mn></msubsup><mo stretchy="false">)</mo></math> order for dijet, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msub><mi>α</mi><mi>s</mi></msub><mo stretchy="false">)</mo></math> for three jet and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> for four (and more) jet productions. Our results will help us to understand the longstanding puzzle of nearside ridge behavior observed in high multiplicity events of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math> collisions at the LHC.

Long range energy-energy correlator at the LHC

We analyzed two-loop planar contributions to a three-body form factor at next-to-leading power in the high-energy limit, where the masses of the external particles are much smaller than their energies. Calculations were performed by exploiting differential equations for the expansion coefficients, both to facilitate linear relations among them and to derive their analytic expressions. The results are expressed in terms of generalized polylogarithms involving a few simple symbol letters. Our method can readily be applied to calculations of non-planar contributions as well. Our results provide crucial information for establishing sub-leading factorization theorems for massive scattering amplitudes in the high-energy limit.

Yishuai Guo

Zhi-Feng Liu

Mingming Lu

Tianya Xia

Li-Lin Yang

A three-body form factor at sub-leading power in the high-energy limit: planar contributions * Supported in part by the National Natural Science Foundation of China Sunder (12375097, 12347103) and the Fundamental Research Funds for the Central Universities. Zhi-Feng Liu was supported by the China Postdoctoral Science Foundation (2023M733123, 2023TQ0282) and the Postdoctoral Fellowship Program of China Postdoctoral Science Foundation