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.

United Kingdom

Mark Costantini

Elie Hammou

Zahari Kassabov

Germany

Maeve Madigan

Luca Mantani

Manuel Morales-Alvarado

James Moore

Maria Ubiali

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

We extend the existing leading (LO), next-to-leading (NLO), and next-to-next-to-leading order (NNLO) NNPDF4.0 sets of parton distribution functions (PDFs) to approximate next-to-next-to-next-to-leading order ( $$\hbox {aN}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>aN</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>  ). We construct an approximation to the  $$\hbox {N}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>N</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   splitting functions that includes all available partial information from both fixed-order computations and from small and large x resummation, and estimate the uncertainty on this approximation by varying the set of basis functions used to construct the approximation. We include known  $$\hbox {N}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>N</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   corrections to deep-inelastic scattering structure functions and extend the FONLL general-mass scheme to  $$\mathcal {O}\left( \alpha _s^3\right) $$  <math> <mrow> <mi>O</mi> <mfenced> <msubsup> <mi>α</mi> <mi>s</mi> <mn>3</mn> </msubsup> </mfenced> </mrow> </math>   accuracy. We determine a set of  $$\hbox {aN}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>aN</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   PDFs by accounting both for the uncertainty on splitting functions due to the incomplete knowledge of  $$\hbox {N}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>N</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   terms, and to the uncertainty related to missing higher corrections (MHOU), estimated by scale variation, through a theory covariance matrix formalism. We assess the perturbative stability of the resulting PDFs, we study the impact of MHOUs on them, and we compare our results to the  $$\hbox {aN}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>aN</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   PDFs from the MSHT group. We examine the phenomenological impact of  $$\hbox {aN}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>aN</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   corrections on parton luminosities at the LHC, and give a first assessment of the impact of  $$\hbox {aN}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>aN</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   PDFs on the Higgs and Drell–Yan total production cross-sections. We find that the  $$\hbox {aN}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>aN</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   NNPDF4.0 PDFs are consistent within uncertainties with their NNLO counterparts, that they improve the description of the global dataset and the perturbative convergence of Higgs and Drell–Yan cross-sections, and that MHOUs on PDFs decrease substantially with the increase of perturbative order.

Richard Ball

Italy

Andrea Barontini

CERN

Alessandro Candido

Stefano Carrazza

Juan Cruz-Martinez

Luigi Del Debbio

Stefano Forte

Netherlands

Tommaso Giani

Finland

Felix Hekhorn

Niccolò Laurenti

Giacomo Magni

Emanuele Nocera

Tanjona Rabemananjara

Juan Rojo

Christopher Schwan

Roy Stegeman

The path to  $$\hbox {N}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>N</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   parton distributions

We construct a set of parton distribution functions (PDFs), based on the recent NNPDF4.0 PDF set, that also include a photon PDF. The photon PDF is constructed using the LuxQED formalism, while QED evolution accounting for  $${\mathcal {O}}\left( \alpha \right) $$  <math> <mrow> <mi>O</mi> <mfenced> <mi>α</mi> </mfenced> </mrow> </math>  ,  $${\mathcal {O}}\left( \alpha \alpha _s\right) $$  <math> <mrow> <mi>O</mi> <mfenced> <mi>α</mi> <msub> <mi>α</mi> <mi>s</mi> </msub> </mfenced> </mrow> </math>  , and  $${\mathcal {O}}\left( \alpha ^2\right) $$  <math> <mrow> <mi>O</mi> <mfenced> <msup> <mi>α</mi> <mn>2</mn> </msup> </mfenced> </mrow> </math>   corrections is implemented and benchmarked by means of the EKO code. We investigate the impact of QED effects on NNPDF4.0, and compare our results both to our previous NNPDF3.1QED PDF set and to other recent PDF sets that include the photon. We assess the impact of photon-initiated processes and electroweak corrections on a variety of representative LHC processes, and find that they can reach the 5% level in vector boson pair production at large invariant mass.

Photons in the proton: implications for the LHC

We include uncertainties due to missing higher order corrections to QCD computations (MHOU) used in the determination of parton distributions (PDFs) in the recent NNPDF4.0 set of PDFs. We use our previously published methodology, based on the treatment of MHOUs and their full correlations through a theory covariance matrix determined by scale variation, now fully incorporated in the new NNPDF theory pipeline. We assess the impact of the inclusion of MHOUs on the NNPDF4.0 central values and uncertainties, and specifically show that they lead to improved consistency of the PDF determination. PDF uncertainties on physical predictions in the data region are consequently either unchanged or moderately reduced by the inclusion of MHOUs.

Determination of the theory uncertainties from missing higher orders on NNLO parton distributions with percent accuracy

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.

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.

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

We present the MCscales approach for incorporating scale uncertainties in parton distribution functions (PDFs). The new methodology builds on the Monte Carlo sampling for propagating experimental uncertainties into the PDF space that underlies the NNPDF approach, but it extends it to the space of factorisation and renomalisation scales. A prior probability is assigned to each scale combinations set in the theoretical predictions used to obtain each PDF replica in the Monte Carlo ensemble and a posterior probability is obtained by selecting replicas that satisfy fit-quality criteria. Our approach allows one to exactly match the scale variations in the PDFs with those in the computation of the partonic cross sections, thus accounting for the full correlations between the two. We illustrate the opportunities for phenomenological exploration made possible by our methodology for a variety of LHC observables. Sets of PDFs enriched with scale information are provided, along with a set of tools to use them.

Cameron Voisey

Parton distributions with scale uncertainties: a Monte Carlo sampling approach

We show how an inaccurate determination of experimental uncertainty correlations in high-precision LHC measurements may undermine the reliability of the associated  $$\chi ^2$$  <math> <msup> <mi>χ</mi> <mn>2</mn> </msup> </math>  . We formulate the problem rigorously, and devise a regularisation procedure that increases the stability of the  $$\chi ^2$$  <math> <msup> <mi>χ</mi> <mn>2</mn> </msup> </math>   by altering the covariance matrix of the measurement as little as possible. We apply the procedure to the NNPDF4.0 global analysis of parton distribution functions that utilises a large amount of LHC measurements. We find that the regularised  $$\chi ^2$$  <math> <msup> <mi>χ</mi> <mn>2</mn> </msup> </math>   of the NNPDF4.0 determination is lowered by about  $$3\sigma $$  <math> <mrow> <mn>3</mn> <mi>σ</mi> </mrow> </math>  , without significantly altering the resulting PDFs upon refitting.

Michael Wilson

Regularising experimental correlations in LHC data: theory and application to a global analysis of parton distributions

We present a new set of parton distribution functions (PDFs) based on a fully global dataset and machine learning techniques: NNPDF4.0. We expand the NNPDF3.1 determination with 44 new datasets, mostly from the LHC. We derive a novel methodology through hyperparameter optimization, leading to an efficient fitting algorithm built upon stochastic gradient descent. We use NNLO QCD calculations and account for NLO electroweak corrections and nuclear uncertainties. Theoretical improvements in the PDF description include a systematic implementation of positivity constraints and integrability of sum rules. We validate our methodology by means of closure tests and “future tests” (i.e. tests of backward and forward data compatibility), and assess its stability, specifically upon changes of PDF parametrization basis. We study the internal compatibility of our dataset, and investigate the dependence of results both upon the choice of input dataset and of fitting methodology. We perform a first study of the phenomenological implications of NNPDF4.0 on representative LHC processes. The software framework used to produce NNPDF4.0 is made available as an open-source package together with documentation and examples.

Shayan Iranipour

United Arab Emirates

Singapore

Spain

Jose Latorre

Rosalyn Pearson

The path to proton structure at 1% accuracy

We present the software framework underlying the NNPDF4.0 global determination of parton distribution functions (PDFs). The code is released under an open source licence and is accompanied by extensive documentation and examples. The code base is composed by a PDF fitting package, tools to handle experimental data and to efficiently compare it to theoretical predictions, and a versatile analysis framework. In addition to ensuring the reproducibility of the NNPDF4.0 (and subsequent) determination, the public release of the NNPDF fitting framework enables a number of phenomenological applications and the production of PDF fits under user-defined data and theory assumptions.

An open-source machine learning framework for global analyses of parton distributions