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

The Moore–Penrose algorithm provides a generalized notion of an inverse, applicable to degenerate matrices. In this paper, we introduce a covariant extension of the Moore–Penrose method that permits to deal with general relativity involving complex non-invertible metrics. Unlike the standard technique, this approach guarantees the uniqueness of the pseudoinverse metric through the fulfillment of a set of covariant relations, and it allows for the proper definition of a covariant derivative operator and curvature-related tensors. Remarkably, the degenerate nature of the metric can be given a geometrical representation in terms of a torsion tensor, which vanishes only in special cases. Applications of the new scheme to complex black hole geometries and cosmological models are also investigated, and a generalized concept of geodesics that exploits the notion of autoparallel and extremal curves is presented. Relevance of our findings to quantum gravity and quantum cosmology is finally discussed.

France

Arthur Garnier

Italy

Emmanuele Battista

Complex degenerate metrics in general relativity: a covariant extension of the Moore–Penrose algorithm

<p>Dark matter particles with a mass around 1 eV can decay into near-infrared photons. Utilizing available public blank sky observations from the NIRSpec IFU on the James Webb Space Telescope (JWST), we search for a narrow emission line due to decaying dark matter and derive leading constraints in the mass range 0.8–3 eV on the decay rate to photons, and more specifically, on the axion-photon coupling for the case of axionlike particles. We exclude <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi><mo>&lt;</mo><mn>3.5</mn><mo>×</mo><msup><mn>10</mn><mn>26</mn></msup><mtext> </mtext><mtext> </mtext><mi mathvariant="normal">s</mi></math> at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>DM</mi></mrow></msub><mo>≃</mo><mn>0.8</mn><mtext> </mtext><mtext> </mtext><mi>eV</mi></mrow></math> and, in the case of axions, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>g</mi></mrow><mrow><mi>a</mi><mi>γ</mi><mi>γ</mi></mrow></msub><mo>&gt;</mo><mn>1.3</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>11</mn></mrow></msup><mtext> </mtext><mtext> </mtext><msup><mrow><mi>GeV</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>a</mi></mrow></msub><mo>≃</mo><mn>2.2</mn><mtext> </mtext><mtext> </mtext><mi>eV</mi></mrow></math>. Our results do not rely on dedicated observations, rather we use blank sky observations intended for sky subtraction, and thus our reach may be automatically strengthened as JWST continues to observe.</p>

United States

Ryan Janish

Elena Pinetti

Hunting Dark Matter Lines in the Infrared Background with the James Webb Space Telescope

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 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

The interpretation of LHC data, and the assessment of possible hints of new physics, require the precise knowledge of the proton structure in terms of parton distribution functions (PDFs). We present a systematic methodology designed to determine whether and how global PDF fits might inadvertently ‘fit away’ signs of new physics in the high-energy tails of the distributions. We showcase a scenario for the High-Luminosity LHC, in which the PDFs may completely absorb such signs of new physics, thus biasing theoretical predictions and interpretations. We discuss strategies to single out the effects in this scenario, and disentangle the inconsistencies that stem from them. Our study brings to light the synergy between the high luminosity programme at the LHC and future low-energy non-LHC measurements of large-x sea quark distributions. The analysis code used in this work is made public so that any users can test the robustness of the signal associated to a given BSM model against absorption by the PDFs.

CERN

Michelangelo Mangano

Manuel Alvarado

Hide and seek: how PDFs can conceal new physics

We assess the impact of top quark production at the LHC on global analyses of parton distributions (PDFs) and of Wilson coefficients in the SMEFT, both separately and in the framework of a joint interpretation. We consider the broadest top quark dataset to date containing all available measurements based on the full Run II luminosity. First, we determine the constraints that this dataset provides on the large-x gluon PDF and study its consistency with other gluon-sensitive measurements. Second, we carry out a SMEFT interpretation of the same dataset using state-of-the-art SM and EFT theory cal- culations, resulting in bounds on 25 Wilson coefficients modifying top quark interactions. Subsequently, we integrate the two analyses within the SIMUnet approach to realise a simul- taneous determination of the SMEFT PDFs and the EFT coefficients and identify regions in the parameter space where their interplay is most phenomenologically relevant. We also demonstrate how to separate eventual BSM signals from QCD effects in the interpretation of top quark measurements at the LHC.

Netherlands

Juan Rojo

The top quark legacy of the LHC Run II for PDF and SMEFT analyses

We study the sensitivity of the High-Luminosity LHC to a light baryonic dark photon B, primarily coupled to quarks, as a constituent of the proton. This is achieved by allowing for a dark photon parton distribution function (PDF) in the PDF evolution equations. Depending on the mass and coupling of the dark photon, the evolution of standard quark and gluon PDFs is distorted to varying degrees. By analysing the effect of the dark photon on the tails of Drell-Yan invariant mass distributions, we demonstrate the potential of the LHC in determining competitive bounds on dark photon parameter space.

Matthew McCullough

The dark side of the proton

The high-energy tails of charged- and neutral-current Drell-Yan processes provide important constraints on the light quark and anti-quark parton distribution functions (PDFs) in the large-x region. At the same time, short-distance new physics effects such as those encoded by the Standard Model Effective Field Theory (SMEFT) would induce smooth distortions to the same high-energy Drell-Yan tails. In this work, we assess for the first time the interplay between PDFs and EFT effects for high-mass Drell-Yan processes at the LHC and quantify the impact that the consistent joint determination of PDFs and Wilson coefficients has on the bounds derived for the latter. We consider two well-motivated new physics scenarios: 1) electroweak oblique corrections (  <math> <mover> <mi>W</mi> <mo>̂</mo> </mover> <mo>,</mo> <mover> <mi>Y</mi> <mo>̂</mo> </mover> </math>  $$ \hat{W},\hat{Y} $$ ) and 2) four-fermion interactions potentially related to the LHCb anomalies in R(K (*)). We account for available Drell-Yan data, both from unfolded cross sections and from searches, and carry out dedicated projections for the High-Luminosity LHC. Our main finding is that, while the interplay between PDFs and EFT effects remains moderate for the current dataset, it will become a significant challenge for EFT analyses at the HL-LHC.