We develop a framework for indirect discovery in the Standard Model Effective Field Theory (SMEFT) based on Bayesian model selection over operator subsets. We argue that SMEFT should be understood as a structured space of competing hypotheses rather than a single high-dimensional model, with each operator subset corresponding to a physically distinct low-energy realisation of new dynamics. Bayesian inference is applied at the level of model space itself, assigning posterior probabilities to operator subsets and marginal inclusion probabilities to individual operators. A genetic algorithm efficiently navigates the high-dimensional discrete model space, concentrating evaluations in the high-posterior region, while the Bayesian Information Criterion provides a tractable approximation to the Bayesian evidence. We apply this framework to a dataset comprising electroweak precision observables from LEP and Higgs, top-quark, and diboson measurements from LHC Run 2, at both linear and quadratic order in the Wilson coefficients, with one-loop renormalisation group evolution systematically included. The analysis finds no statistically significant evidence for any departure from the SM, and demonstrates that Bayesian Model Average posteriors on Wilson coefficients carry substantially improved characterisation potential compared to traditional global fits. The operator correlation matrix encodes the relational structure of the model posterior, identifying operator pairs that co-appear in high-posterior models and flat directions where additional measurements would be most valuable. The sensitivity of all results to the choice of matching scale $\textit{μ}$ is assessed, and its promotion to a continuous parameter of inference is identified as a natural extension of the framework.

Spain

Luca Mantani

Exploring the SMEFT landscape: Bayesian model selection for indirect discovery

We present a method to obtain analytic results in terms of multiple polylogarithms for one-loop triangle, box and pentagon integrals depending on an arbitrary number of scales and to any desired order in the Laurent expansion in the dimensional regulator $\textit{ε}$. Our method leverages the fact that for $\textit{ε}$ = 0 one-loop integrals compute volumes of simplices in hyperbolic spaces, which can always be evaluated in terms of polylogarithms using an algorithm recently introduced in pure mathematics. The higher orders in $\textit{ε}$ can then be expressed as a one-fold integral involving the result for $\textit{ε}$ = 0. Remarkably, we find that for up to five external legs, all integrals can be evaluated algorithmically in terms of polylogarithms using direct integration techniques, which, in particular, requires us to rationalise all appearing square roots. We also discuss how we can use the connection to hyperbolic geometry to perform the analytic continuation from the Euclidean region to other kinematic regions.

Germany

Claude Duhr

Paul Mork

Analytic results for one-loop integrals in dimensional regularisation

In the present study, we extend our previous analysis of the proton electromagnetic form factors (FFs) extracted from exclusive photon leptoproduction (EP) measurements in kinematic regions where the Bethe-Heitler (BH) process dominates the cross section by including all currently available high-precision EP data from CLAS and Hall A Collaborations. Using the same phenomenological framework, we investigate the consistency among the different datasets, determine the proton electromagnetic FFs within several fitting scenarios, and extract the corresponding charge and magnetic radii. A significant tension is found between the CLAS 2018 measurements and the remaining EP data, with the low-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><mi>t</mi><mo stretchy="false">|</mo></math> region playing a dominant role in this tension. We systematically investigate this behavior through <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><mi>t</mi><mo stretchy="false">|</mo></math>-cut scans and assess its impact on the extracted FFs and radii. For all analyses, the extracted proton charge radius is smaller than the Particle Data Group average and most determinations based on elastic electron-proton scattering. However, the results are consistent, within uncertainties, with the PRad measurement and muonic hydrogen spectroscopy. In contrast, the magnetic radius is found to be compatible with the current world average. These results demonstrate that BH-dominated EP measurements provide an independent and complementary approach to determine the electromagnetic structure of the proton and offer additional support for the small-radius solution of the proton charge-radius puzzle.

Iran

Muhammad Goharipour

Anoushiravan Moradi

Türkiye

K. Azizi

Implications of exclusive photon leptoproduction measurements for the proton charge-radius puzzle

Quantum correlation functions in supersymmetric field theories can be encoded in the Nicolai map. The infinitesimal inverse map provides their response to a change in a coupling constant through a “flow equation”. We investigate the flow in the gravitational constant $\textit{κ}$ for four-dimensional Poincaré supergravity via its superconformal formulation. By expressing the full superconformal off-shell action as a supervariation we derive a “flow operator” in the effective vierbein theory, whose exponentiation yields the gauge-invariant part of an all-order (inverse) Nicolai map for supergravity. Alas, the BRST gauge fixing adds to this functional differential flow operator a multiplicative term, which ruins its derivational property and therefore jeopardizes its connection with the Nicolai map. We argue and present an example, however, that such multiplicative flow contributions might be rewritable as derivational ones with the help of Wick’s theorem in the free effective theory where the Nicolai-transformed correlators are ultimately evaluated. At least in the Landau gauge, the supergravity flow equation is shown to be regular at $\textit{κ}$=0, allowing for a perturbative expansion around Minkowski geometry. Therewith, we have overcome two of the three obstacles met in an earlier attempt towards a Nicolai map for Poincaré supergravity. Finally, we compare with the direct on-shell construction of a Nicolai map to leading order in $\textit{κ}$.

Federico Arrighi

Saurish Khandelwal

Olaf Lechtenfeld

The coupling flow for supergravity

We present the first experimental search for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>-naturalness tower of neutrinos using a global analysis of publicly available neutrino data. As a potential solution to the hierarchy problem, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>-naturalness model employs a varying Higgs mass parameter among <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> dark sectors and encodes the required fine-tuning of the placement of the sectors in a parameter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>r</mi></math>. We report exclusion limits on the parameter space (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>r</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>), for normal and inverted ordering and in case the neutrino is Majorana or Dirac. In the case of a Majorana neutrino, we can rule out <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>≤</mo><msup><mn>10</mn><mn>4</mn></msup></math> sectors with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>r</mi><mo>≥</mo><mn>0.1</mn></math>. This is particularly exciting as it shows that a gauge and gravitational unification around <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>M</mi><mi>GUT</mi></msub></math>, which is a benchmark scenario of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>-naturalness framework with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><msup><mn>10</mn><mn>4</mn></msup></math> without fine-tuning, is ruled out by neutrino experiments.

Sofia Lonardi

France

Manuel Ettengruber

Philipp Eller

Searching for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>-naturalness tower of neutrinos

In this work, we apply topic modeling to detect new physics in proton-proton collisions at the LHC in an unsupervised way. We investigate three new physics scenarios where fully leptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi><mover accent="true"><mi>t</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">→</mo><mi>b</mi><mover accent="true"><mi>b</mi><mo stretchy="false">¯</mo></mover><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mo>ℓ</mo></msub></math> is the main source of background without relying on jet substructure variables. We demonstrate that the algorithm remains effective even in this low-particle multiplicity framework, complementing jet tagging studies, where it is typically employed. Moreover, we demonstrate that the performance of topic modeling is competitive or even better than well-known semisupervised outlier detectors, such as isolation forest and variational autoencoders, and unsupervised algorithms like Gaussian mixture models and k-means clustering with moderate and high-background pollution in almost all new physics scenarios considered.

Brazil

Alexandre Alves

Eduardo da Silva Almeida

Douglas Roberto de Matos Pimentel

Topic modeling in new physics detection

The black hole horizon can induce chaotic motion of particles around the black hole. The original integrable motion of particles can transit to the chaotic motion when approaching black hole horizon. In this work, we consider the black hole background where quantum conformal anomaly correction is taken into account. We use Poincare section and Lyapunov exponent as representative probes to illustrate chaos. We investigate the effect of anomaly coefficient on the chaos of particles and for both probes, we find that quantum anomaly generally enhances the chaos of particle motions. As the chaotic orbits of particles can leave an imprint on the gravitational wave signals of the extreme mass ratio inspirals, our results pave the way to detect conformal anomaly effect in actual observations.

China

Yu-Sen An

Wei-Hao Zhang

Probing quantum anomaly corrections on black hole physics through chaos

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

We derive the expressions for the one-point energy correlator (OPEC) in deep inelastic scattering in the high-energy (small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>) limit within the Color Glass Condensate (CGC) framework. The OPEC is computed as a function of the angle between the energy flow and the target proton or nucleus, enabling a systematic exploration of different momentum scales in the scattering process. Owing to the momentum sum rule, the dependence on fragmentation functions cancels, leaving the dipole amplitude as the only nonperturbative input. As a result, the OPEC provides a sensitive and promising probe of gluon saturation dynamics at small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>. We present numerical results for representative kinematic configurations relevant to the future Electron-Ion Collider, demonstrating sizable nuclear suppression effects within the CGC framework and highlighting the consistency of this observable with predictions from gluon saturation.

United States

Zhong-Bo Kang

Robert Kao

Meijian Li

Jani Penttala

One-point energy correlator for deep inelastic scattering at small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>x</mi></mrow></math>

Neutrino momentum reconstruction at hadron colliders is intrinsically ambiguous because the longitudinal momentum is not directly observed. We study this problem in semileptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi><mover accent="true"><mi>t</mi><mo stretchy="false">¯</mo></mover></math> events using mixture of neutrino solutions with transformer event representation (monster), a mixture density network that predicts a multivariate normal mixture for the conditional distribution of neutrino momentum from reconstructed event objects. The model uses a transformer-based event encoder and yields a sampling-free point estimate of the neutrino momentum from the closed-form density. On the public benchmark introduced with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ν</mi></math>-flows, monster reduces the 68th percentile of the three-momentum residual by 5% and the 95th percentile by 6% relative to the empirical-mode <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ν</mi></math>-flows baseline, with per-variable root-mean-square errors smaller by 2 to 9% at comparable bias, while running 2 to 8.5 times faster at inference, depending on the device and batch size. These results indicate that mixture density networks are a competitive alternative to normalizing flows for neutrino reconstruction.