A robust uncertainty estimate in global analyses of Parton Distribution Functions (PDFs) is essential at the Large Hadron Collider (LHC), especially in view of the high-precision data anticipated by experimentalists in the High-Luminosity phase of the LHC. A Bayesian framework to determine PDFs provides a rigorous treatment of uncertainties and full control on the prior, though its practical implementation can be computationally demanding. To address these challenges, we introduce a novel approach to PDF determination tailored for Bayesian inference, based on the use of linear models. Unlike traditional parametrisations, our method represents PDFs as vectors in a functional space spanned by specially chosen bases, derived from the dimensional reduction of a neural network functional space, providing a compact yet versatile representation of PDFs. The low-dimensionality of the preferred models allows for particularly fast inference. The size of the bases can be systematically adjusted, allowing for transparent control over underfitting and overfitting, and facilitating principled model selection through Bayesian workflows. In this work, the methodology is applied to a fit of Deep Inelastic Scattering synthetic data, and thoroughly tested via multi-closure tests, thus paving the way to its application to global PDF fits.

United Kingdom

Mark Costantini

Spain

Luca Mantani

James Moore

Maria Ubiali

A linear PDF model for Bayesian inference

<p>We present a novel strategy to uncover indirect signs of new physics in collider data using the standard model effective field theory (SMEFT) framework, offering notably improved sensitivity compared to traditional global analyses. Our approach leverages genetic algorithms to efficiently navigate the high-dimensional space of operator subsets, identifying deformations that improve agreement with data without relying on prior ultraviolet (UV) assumptions. This enables the systematic detection of SMEFT scenarios that outperform the standard model in explaining observed deviations. We validate the approach on current large hadron collider and large electron-positron collider measurements, perform closure tests with injected UV signals, and assess performance under high-luminosity projections. The algorithm successfully recovers relevant operator subsets and highlights directions in parameter space where deviations are most likely to emerge. Our results demonstrate the potential of SMEFT-based discovery searches driven by model selection, providing a scalable framework for future data analyses.</p>

Martin Hirsch

Veronica Sanz

Data-Driven Discovery Strategy for Standard Model Effective Field Theory Searches

<p>Motivated by the updated high luminosity (HL)-LHC projections for Higgs pair production from ATLAS and CMS and by the release of the FCC-ee feasibility study, we critically revisit the sensitivity of the global standard model effective field theory (SMEFT) analysis to deformations of the Higgs self-coupling modifier <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>κ</mi><mn>3</mn></msub></math>. To this end, we quantify the impact of SMEFT operators modifying double Higgs production at the LHC and single Higgs production, including loop corrections, at the FCC-ee, and include renormalization group evolution throughout. We demonstrate that significantly improving on the legacy HL-LHC constraints on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>κ</mi><mn>3</mn></msub></math> at the FCC-ee is not possible without the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>365</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> run; that individual and marginalized determinations are similar at the HL-LHC while differing by up to a factor 3 at the FCC-ee; and that quadratic EFT corrections cannot be neglected, especially at the (HL-)LHC. This finding fundamentally alters the picture compared to strategic planning often based on one-parameter projections. Overall, the combination of HL-LHC and FCC-ee data offers unique potential to pin down the Higgs self-coupling with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><mn>15</mn><mo>%</mo></math> precision.</p>

Jaco ter Hoeve

Netherlands

Juan Rojo

Italy

Alejo N. Rossia

Eleni Vryonidou

Higgs trilinear coupling in the standard model effective field theory at the high luminosity LHC and the FCC-ee

The Standard Model Effective Field Theory (SMEFT) offers a systematic approach to study potential deviations from the Standard Model (SM) through higher-dimensional operators that encapsulate new physics effects. In this work, we analyze flavour-blind SMEFT contributions to flavour observables and assess their interplay with high-energy measurements from LEP and LHC. We perform global fits combining LEP precision data, flavour observables from rare B-meson decays, and LHC diboson measurements, revealing how the inclusion of different datasets breaks parameter degeneracies and enhances the sensitivity to SMEFT coefficients. Our study demonstrates that low-energy flavour observables provide reliable constraints even in flavour-blind scenarios, while high-energy measurements can be subject to EFT validity concerns due to kinematic growth. We investigate the impact of renormalization group evolution (RGE) and operator mixing across energy scales, highlighting the complementary nature of low- and high-energy datasets. The results emphasize the importance of flavour observables as robust probes of new physics and underline the necessity of global fits to avoid potential biases from limited datasets. Finally, we discuss the implications of our findings for the interpretation of global SMEFT analyses based on high-energy collider data, comparing UV models that contribute to SMEFT at tree- and loop-level.

Probing the flavour-blind SMEFT: EFT validity and the interplay of energy scales

Global interpretations of particle physics data within the framework of the Standard Model Effective Field Theory (SMEFT), including their matching to UV-complete models, involve energy scales potentially spanning several orders of magnitude. Relating these measurements among them in terms of a common energy scale is enabled by the Renormalisation Group Equations (RGEs). Here we present a systematic assessment of the impact of RGEs, accounting for QCD, electroweak, and Yukawa corrections, in a global SMEFT fit of LEP and LHC data where individual cross-sections are assigned a characteristic energy scale. We also quantify the impact of the RGE effects in projected global fits at the HL-LHC and the FCC-ee. Finally, we assess the role that RGEs play on the sensitivity at HL-LHC and FCC-ee to representative one-particle UV models matched onto SMEFT either at tree and one-loop level. Our study emphasizes the importance of a consistent treatment of energy scales to achieve the best precision and accuracy in indirect searches for heavy new physics through precision measurements.

Jaco Hoeve

Alejo Rossia

Connecting scales: RGE effects in the SMEFT at the LHC and future colliders

We present a detailed mathematical study of the Monte Carlo replica method as applied in the global fitting literature from the high-energy physics theory community. For the first time, we provide a rigorous derivation of the parameter distributions implied by the method, and show that, whilst they agree with Bayesian posteriors for linear models, they disagree otherwise. We proceed to numerically quantify the disagreement between the Monte Carlo replica method and the Bayesian method in the context of two phenomenologically relevant scenarios: fits of the SMEFT Wilson coefficients, and fits of PDFs (albeit in a toy scenario). In both scenarios, we find that uncertainty estimates of the quantities of interest are discrepant between the two approaches when non-linearity is relevant. Our findings motivate future investigation of Bayesian methodologies for global PDF fits, especially in the context of simultaneous determination of PDFs and SMEFT Wilson coefficients.

Germany

Maeve Madigan

A critical study of the Monte Carlo replica method

We present SMEFiT3.0, an updated global SMEFT analysis of Higgs, top quark, and diboson production data from the LHC complemented by electroweak precision observables (EWPOs) from LEP and SLD. We consider recent inclusive and differential measurements from the LHC Run II, alongside with a novel implementation of the EWPOs based on independent calculations of the relevant EFT contributions. We estimate the impact of HL-LHC measurements on the SMEFT parameter space when added on top of SMEFiT3.0, through dedicated projections extrapolating from Run II data. We quantify the significant constraints that measurements from two proposed high-energy circular e + e  −  colliders, the FCC-ee and the CEPC, would impose on both the SMEFT parameter space and on representative UV-complete models. Our analysis considers projections for the FCC-ee and the CEPC based on the latest running scenarios and includes Z-pole EWPOs, fermion-pair, Higgs, diboson, and top quark production, using optimal observables for both the W + W  −  and the   <math> <mi>t</mi> <mover> <mi>t</mi> <mo>¯</mo> </mover> </math>  $$ t\overline{t} $$  channels. The framework presented in this work may be extended to other future colliders and running scenarios, providing timely input to ongoing studies towards future high-energy particle physics facilities.

Eugenia Celada

Tommaso Giani

Marion Thomas

Mapping the SMEFT at high-energy colliders: from LEP and the (HL-)LHC to the FCC-ee

We present the open-source SIMUnet code, designed to fit Standard Model Effective Field Theory (SMEFT) Wilson coefficient alongside Parton Distribution Functions (PDFs) of the proton. SIMUnet can perform SMEFT global fits, as well as simultaneous fits of the PDFs and of an arbitrarily large number of SMEFT degrees of freedom, by including both PDF-dependent and PDF-independent observables. SIMUnet can also be used to determine whether the effects of any New Physics models can be fitted away in a global fit of PDFs. SIMUnet is built upon the open-source NNPDF code and is released together with documentation, and tutorials. To illustrate the functionalities of the new tool, we present a new global analysis of the SMEFT Wilson coefficients accounting for their interplay with the PDFs. We increment our previous analysis of the LHC Run II top quark data with both (i) the Higgs production and decay rates data from the LHC, and (ii) the precision electroweak and diboson measurements from LEP and the LHC.

Elie Hammou

Zahari Kassabov

Manuel Morales-Alvarado

SIMUnet: an open-source tool for simultaneous global fits of EFT Wilson coefficients and PDFs

CERN

Carlotta Accettura

Dean Adams

United States

Rohit Agarwal

Claudia Ahdida

Chiara Aimè

Nicola Amapane

David Amorim

Paolo Andreetto

Fabio Anulli

Robert Appleby

Artur Apresyan

Aram Apyan

France

Sergey Arsenyev

Pouya Asadi

Egypt

Mohammed Mahmoud

Aleksandr Azatov

John Back

Lorenzo Balconi

Laura Bandiera

Roger Barlow

Nazar Bartosik

Emanuela Barzi

Fabian Batsch

Matteo Bauce

J. Berg

Andrea Bersani

Alessandro Bertarelli

Alessandro Bertolin

Kevin Black

Fulvio Boattini

Alex Bogacz

Maurizio Bonesini

Bernardo Bordini

Salvatore Bottaro

Luca Bottura

Alessandro Braghieri

Marco Breschi

Natalie Bruhwiler

Xavier Buffat

Laura Buonincontri

Philip Burrows

Graeme Burt

Dario Buttazzo

Barbara Caiffi

Marco Calviani

Simone Calzaferri

Daniele Calzolari

Rodolfo Capdevilla

Christian Carli

Fausto Casaburo

Massimo Casarsa

Luca Castelli

Maria Catanesi

Lorenzo Cavallucci

Gianluca Cavoto

Francesco Celiberto

Luigi Celona

Alessandro Cerri

Gianmario Cesarini

Cari Cesarotti

Portugal

Grigorios Chachamis

Antoine Chance

Switzerland

Siyu Chen

Yang-Ting Chien

Mauro Chiesa

Anna Colaleo

Francesco Collamati

Gianmaria Collazuol

Marco Costa

Nathaniel Craig

Camilla Curatolo

Canada

David Curtin

Giacomo Molin

Magnus Dam

Heiko Damerau

Sridhara Dasu

Jorge Blas

Stefania Curtis

Ernesto Matteis

Stefania Rosa

Jean-Pierre Delahaye

Dmitri Denisov

Türkiye

Haluk Denizli

Christopher Densham

Radovan Dermisek

Luca Luzio

Elisa Meco

Biagio Micco

Keith Dienes

Eleonora Diociaiuti

Tommaso Dorigo

Alexey Dudarev

Robert Edgecock

Filippo Errico

Marco Fabbrichesi

Stefania Farinon

Anna Ferrari

Jose Somoza

Frank Filthaut

Davide Fiorina

Erratum: Towards a muon collider

We analyze six classes of <math><mi>t</mi></math>-channel dark matter simplified models in which the Standard Model field content is extended by a colored mediator and a dark matter state. The two new states are enforced to be odd under a new parity, while all Standard Model fields are taken even so that dark matter stability is guaranteed. We study several possibilities for the spin of the new particles and the self-conjugate property of the dark matter, and we focus on model configurations in which the dark matter couples to the right-handed up quark for simplicity. We investigate how the parameter spaces of the six models can be constrained by current and future cosmological, astrophysical and collider searches, and we highlight the strong complementary between those probes. Our results demonstrate that scenarios featuring a complex (non self-conjugate) dark matter field are excluded by cosmology and astrophysics alone, the only possibility to avoid these bounds being to invoke very weak couplings and mechanisms such as conversion-driven freeze-out. For models with self-conjugate dark matter, mediator and dark matter masses are pushed deep into the TeV regime, with the lower limits on the mediator mass reaching 3 to 4 TeV and those on the dark matter mass 1 to 2 TeV. In large parts of the parameter space these strong bounds are driven by same-sign mediator pair production, a channel so far not considered in the experimental analyses embedding <math><mi>t</mi></math>-channel dark matter model interpretations.

Belgium

Chiara Arina

Benjamin Fuks

Jan Heisig

Michael Krämer

Luca Panizzi

Comprehensive exploration of <math><mi>t</mi></math>-channel simplified models of dark matter