Search

We study the potential of symbolic regression (SR) to derive compact and precise analytic expressions that can improve the accuracy and simplicity of phenomenological analyses at the Large Hadron Collider (LHC). As a benchmark, we apply SR to equation recovery in quantum electrodynamics (QED), where established analytical results from quantum field theory provide a reliable framework for evaluation. This benchmark serves to validate the performance and reliability of SR before extending its application to structure functions in the Drell-Yan process mediated by virtual photons, which lack analytic representations from first principles. By combining the simplicity of analytic expressions with the predictive power of machine learning techniques, SR offers a useful tool for facilitating phenomenological analyses in high energy physics., Comment: 7 pages, 7 figures, 3 tables. Accepted for the Machine Learning and the Physical Sciences Workshop NeurIPS 2024

We discuss how the two existing approximate N$^3$LO (aN$^3$LO) sets of parton distributions (PDFs) from the MSHT20 and NNPDF4.0 series can be combined for LHC phenomenology, both in the pure QCD case and for the QCD$\otimes$QED sets that include the photon PDF. Using the resulting combinations, we present predictions for the total inclusive cross-section for Higgs production in gluon fusion, vector boson fusion, and associated production at the LHC Run-3. For the gluon fusion and vector boson fusion channels, the corrections that arise when using correctly matched aN$^3$LO PDFs with N$^3$LO cross section calculations, compared to using NNLO PDFs, are significant, in many cases larger than the PDF uncertainty, and generally larger than the differences between the two aN$^3$LO PDF sets entering the combination. The combined aN$^3$LO PDF sets, MSHT20xNNPDF40_an3lo and MSHT20xNNPDF40_an3lo_qed, are made publicly available in the LHAPDF format and can be readily used for LHC phenomenology., Comment: 22 pages, 11 figures, LHAPDF grids available from https://zenodo.org/records/13843626

Recent studies suggest that global fits of Parton Distribution Functions (PDFs) might inadvertently 'fit away' signs of new physics in the high-energy tails of the distributions measured at the high luminosity programme of the LHC (HL-LHC). This could lead to spurious effects that might conceal key BSM signatures and hinder the success of indirect searches for new physics. In this letter, we demonstrate that future deep-inelastic scattering (DIS) measurements at the Electron-Ion Collider (EIC), and at CERN via FASER$\nu$ and SND@LHC at LHC Run III, and the future neutrino experiments to be hosted at the proposed Forward Physics Facility (FPF) at the HL-LHC, provide complementary constraints on large-$x$ sea quarks. These constraints are crucial to mitigate the risk of missing key BSM signals, by enabling precise constraints on large-$x$ PDFs through a 'BSM-safe' integration of both high- and low-energy data, which is essential for a robust interpretation of the high-energy measurements., Comment: 11 pages, 6 figures, 5 tables

The unprecedented precision of experimental measurements at the Large Hadron Collider (LHC) and the increased statistics that will be reached in the High-Luminosity phase of the LHC (HL-LHC) are pushing the phenomenology community to a new precision frontier, in which new challenges present themselves and new questions arise. A key ingredients of theoretical predictions at hadron colliders are the Parton Distribution Functions (PDFs) of the proton. This contribution highlights some of the new developments in the determination of PDFs from a global set of experimental data, from approximate N3LO PDFs and the inclusion of theory uncertainties in PDF fits, to the realisation of the non trivial interplay between parton densities at large-x and possible signals of New Physics in high energy tails of the distributions, which highlights the synergy between high energy and low energy experimental programs., Comment: Contribution to the Proceedings of the XXX Cracow Epiphany Conference on Precision Physics at High Energy Colliders, dedicated to the memory of Staszek Jadach

Due to the pseudo-scalar nature of the axion-like particle (ALP), the CP- conserving production of two Higgs bosons via the ALP necessarily involves an additional Z or $\gamma$ boson. We examine the existing constraints from di-Higgs searches at Run 2 of the LHC and find that, despite the presence of extra objects in the final state, these searches are sensitive to a combination of ALP couplings to gluons and three-bosons in the TeV scale range. Additionally, we propose a specialized search strategy incorporating an energetic leptonic Z boson. This refined ALP-induced production process would allow for the identification of the h h $\rightarrow$ 4 b-jet final state and could potentially probe the TeV scale using data from Run 2 of the LHC. This production process can also occur through a coupling between the top quark and the ALP. We translate the current constraints on di-Higgs production into new limits on the ALP-top coupling., Comment: 19 pages, 9 figures

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 (aN$^3$LO). We construct an approximation to the N$^3$LO 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 N$^3$LO corrections to deep-inelastic scattering structure functions and extend the FONLL general-mass scheme to $\mathcal{O}\left( \alpha_s^3\right)$ accuracy. We determine a set of aN$^3$LO PDFs by accounting both for the uncertainty on splitting functions due to the incomplete knowledge of N$^3$LO 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 aN$^3$LO PDFs from the MSHT group. We examine the phenomenological impact of aN$^3$LO corrections on parton luminosities at the LHC, and give a first assessment of the impact of aN$^3$LO PDFs on the Higgs and Drell-Yan total production cross-sections. We find that the aN$^3$LO 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., Comment: 63 pages, 41 figures. Final version, as published in EPJC. Various clarifications added. Fig 2.9 and Tab. 4.6, 5.1 and 5.2 added. In particular, comparison to approximate YR4 estimate of PDF uncertainties added (Tab 4.1, 4.2 and associate discussion in sect. 5)

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., Comment: 28 pages, 11 figures, full code documentation at https://hep-pbsp.github.io/SIMUnet/ and public code at https://github.com/HEP-PBSP/SIMUnet

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 with an ensuing moderate reduction of PDF uncertainties at NNLO., Comment: 23 pages, 6 figures. Final version, as published in EPJC. Several small improvements; expanded discussion of the phi indicator in sect 4.2

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 O(alpha), O(alpha alphas) and O(alpha^2) 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., Comment: 32 pages, 19 figures. Final; version, as published on EPJC. Pheno discussion in Sect 4.2 improved, a few typos corrected

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., Comment: 50 pages, 23 figures. v2: version accepted for publication in JHEP

The main requirements for 5G and beyond connectivity include a uniform high quality of service, which can be attained in crowded scenarios by extra-large MIMO (XL-MIMO) systems. Another requirement is to support increasing connected users in (over)crowded machine-type communication (mMTC). In such scenarios, pilot assignment (PA) becomes paramount to reduce pilot contamination and consequently improve spectral efficiency (SE). We propose a novel quasi-optimal low-complexity iterative pilot assignment strategy for XL-MIMO systems based on a genetic algorithm (GA). The proposed GA-based PA procedure turns the quality of service more uniform, taking into account the normalized mean-square error (NMSE) of channel estimation from each candidate of the population. The simulations reveal that the proposed iterative procedure minimizes the channel estimation NMSE averaged over the UEs. The second procedure is the subarray (SA) selection. In XL-MIMO systems, commonly, a UE is close to a SA antenna subset such that a sufficient data rate can be achieved if only a specific SA serves that UE. Thus, a SA selection procedure is investigated to make the system scalable by defining the maximum number of UEs each SA can help. Hence, the SA clusters are formatted based on the PA decision. Furthermore, we introduce an appropriate channel model for XL-MIMO, which considers a deterministic LoS component with a distance-dependent probability of existence combined with a stochastic spatially correlated Rayleigh NLoS fading component. The developed simulations and analyses rely on this suitable channel model under realistic assumptions of pilot contamination and correlated channels., Comment: 29 pages, 6 figures, 2 tables, In Press

In this paper we explore the coupling of a light axion-like particle (ALP) to top quarks. We use high-energy LHC probes, and examine both the direct probe to this coupling in associated production of a top-pair with an ALP, and the indirect probe through loop-induced gluon fusion to an ALP leading to top pairs. Using the latest LHC Run II data, we provide the best limit on this coupling. We also compare these limits with those obtained from loop-induced couplings in diboson final states, finding that the $t\bar t$+MET channel is the best current handle on this coupling., Comment: 41 pages, 18 figures

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 calculations, resulting in bounds on 25 Wilson coefficients modifying top quark interactions. Subsequently, we integrate the two analyses within the SIMUnet approach to realise a simultaneous 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., Comment: 60 pages, 22 figures

We respond to the criticism raised by Courtoy et al., in which the faithfulness of the NNPDF4.0 sampling is questioned and an under-estimate of the NNPDF4.0 PDF uncertainties is implied. We list, correct, and clarify in detail a number of inaccurate or misleading claims that are made in this Reference. Specifically, we explain and explicitly demonstrate why the central value of the PDF distribution does not generally coincide with the absolute minimum of the $\chi^{2}$ to the data. We examine some PDFs that have been constructed in the above study and claimed to be "good solutions": we show that similar PDFs are found with the NNPDF methodology, but with very low probability., Comment: 18 pages, 12 figures

This report was prepared on behalf of three Energy Frontier Topical Groups of the Snowmass 2021 Community Planning Exercise. It summarizes the status and implications of studies of strong interactions in high-energy experiments and QCD theory. We emphasize the rich landscape and broad impact of these studies in the decade ahead. Hadronic interactions play a central role in the high-luminosity Large Hadron Collider (LHC) physics program, and strong synergies exist between the (HL-)LHC and planned or proposed experiments at the U.S. Electron-Ion Collider, CERN forward physics experiments, high-intensity facilities, and future TeV-range lepton and hadron colliders. Prospects for precision determinations of the strong coupling and a variety of nonperturbative distribution and fragmentation functions are examined. We also review the potential of envisioned tests of new dynamical regimes of QCD in high-energy and high-density scattering processes with nucleon, ion, and photon initial states. The important role of the high-energy heavy-ion program in studies of nuclear structure and the nuclear medium, and its connections with QCD involving nucleons are summarized. We address ongoing and future theoretical advancements in multi-loop QCD computations, lattice QCD, jet substructure, and event generators. Cross-cutting connections between experimental measurements, theoretical predictions, large-scale data analysis, and high-performance computing are emphasized., Comment: 95 pages (bibliography 30 pages), 28 figures; v.2: minor changes, authors and references added

We compute the perturbative component of the fragmentation function of the $b$ quark to the best of the present theoretical knowledge. The fixed-order calculation to order $\alpha_s^2$ of the fragmentation function at the initial scale is matched with soft-emission logarithm resummation to next-to-next-to-leading logarithmic accuracy, so that order-$\alpha_s^2$ corrections are accounted for exactly, and logarithmically enhanced contributions from loops of $b$ quarks are included. This requires the calculation of the Mellin transform of the order-$\alpha_s^2$ result in the whole complex plane for the Mellin variable, which we provide for the first time for all the fragmenting partons. Evolution is performed to next-to-next- to-leading log accuracy, and mixing with the gluon fragmentation function is taken into account. The perturbative fragmentation functions are made available via LHAPDF grids., Comment: 25 pages, 4 figures

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., Comment: 41 pages, 12 figures

An overwhelming number of theoretical predictions for hadron colliders require parton distribution functions (PDFs), which are an important ingredient of theory infrastructure for the next generation of high-energy experiments. This whitepaper summarizes the status and future prospects for determination of high-precision PDFs applicable in a wide range of energies and experiments, in particular in precision tests of the Standard Model and in new physics searches at the high-luminosity Large Hadron Collider and Electron-Ion Collider. We discuss the envisioned advancements in experimental measurements, QCD theory, global analysis methodology, and computing that are necessary to bring unpolarized PDFs in the nucleon to the N2LO and N3LO accuracy in the QCD coupling strength. Special attention is given to the new tasks that emerge in the era of the precision PDF analysis, such as those focusing on the robust control of systematic factors both in experimental measurements and theoretical computations. Various synergies between experimental and theoretical studies of the hadron structure are explored, including opportunities for studying PDFs for nuclear and meson targets, PDFs with electroweak contributions or dependence on the transverse momentum, for incisive comparisons between phenomenological models for the PDFs and computations on discrete lattice, and for cross-fertilization with machine learning/AI approaches. [Submitted to the US Community Study on the Future of Particle Physics (Snowmass 2021).], Comment: 83 pages, 27 figures, contribution to Snowmass 2021; v.3: journal version

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., Comment: 30 pages, 11 figures

We present a new methodology that is able to yield a simultaneous determination of the Parton Distribution Functions (PDFs) of the proton alongside any set of parameters that determine the theory predictions; whether within the Standard Model (SM) or beyond it. The SIMUnet methodology is based on an extension of the NNPDF4.0 neural network architecture, which allows the addition of an extra layer to simultaneously determine PDFs alongside an arbitrary number of such parameters. We illustrate its capabilities by simultaneously fitting PDFs with a subset of Wilson coefficients within the Standard Model Effective Field Theory framework and show how the methodology extends naturally to larger subsets of Wilson coefficients and to other SM precision parameters, such as the strong coupling constant or the heavy quark masses., Comment: 38 pages, 18 figures

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., Comment: 14 pages, 4 figures. A companion paper describes the NNPDF4.0 PDFs

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 optimisation, 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., Comment: 139 pages, more than 60 figures. A companion paper describes the open-source NNPDF code. Figs 9.1 and 9.3 replaced after correction of a plotting bug (thanks to J.Huston and G.Salam for spotting it). A few more typos corrected and a reference updated. Final published version. References updated, several typos corrected, 72 issues raised by the referee addressed

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 $(\hat W, \hat Y)$ 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., Comment: 64 pages, 29 figures

Massive multiple-input-multiple-output (M-MIMO) is a key technology for 5G networks. Within this research area, new types of deployment are arising, such as the extremely-large regime (XL- MIMO), where the antenna array at the base station (BS) has extreme dimensions. As a consequence, spatial non-stationary properties appear as the users see only a portion of the antenna array, which is called visibility region (VR). In this challenging transmission-reception scenario, an algorithm to select the appropriate antenna-elements for processing the received signal of a given user in the uplink (UL), as well as to transmit the signal of this user during downlink (DL) is proposed. The advantage of not using all the available antenna-elements at the BS is the computational burden and circuit power consumption reduction, improving the energy efficiency (EE) substantially. Numerical results demonstrate that one can increase the EE without compromising considerably the spectral efficiency (SE). Under few active users scenario, the performance of the XL-MIMO system shows that the EE is maximized using less than 20% of the antenna-elements of the array, without compromising the SE severely., Comment: 25 pages, 8 figures, 4 tables, published paper

We present an improved determination of the strange quark and anti-quark parton distribution functions of the proton by means of a global QCD analysis that takes into account a comprehensive set of strangeness-sensitive measurements: charm-tagged cross sections for fixed-target neutrino-nucleus deep-inelastic scattering, and cross sections for inclusive gauge-boson production and $W$-boson production in association with light jets or charm quarks at hadron colliders. Our analysis is accurate to next-to-next-to leading order in perturbative QCD where available, and specifically includes charm-quark mass corrections to neutrino-nucleus structure functions. We find that a good overall description of the input dataset can be achieved and that a strangeness moderately suppressed in comparison to the rest of the light sea quarks is strongly favored by the global analysis., Comment: Version accepted for publication in EPJC. PDF sets available from http://nnpdf.mi.infn.it/nnpdf3-1strangeness/. v3: fixed typos

We study the impact of recent LHC $t$-channel single top-quark and top-antiquark measurements at centre-of-mass energies of 7, 8 and 13 TeV on the parton distribution functions (PDFs) of the proton. We consider, namely, total cross sections, top-antitop cross section ratios, and differential distributions. We present a critical appraisal of the data, studying in particular how their description is affected by the theoretical details that enter the computation of the corresponding observables: QCD and electroweak higher-order corrections, the flavour scheme, and the value of the bottom-quark threshold. We perform a series of fits to the data within the NNPDF3.1 framework, whereby next-to-next-to-leading order QCD corrections are applied to single top measurements in a systematic way. We find that there exists an optimal combination of data that maximises consistency with the rest of the dataset, and efficiency in constraining the up, down and, partially, gluon PDFs., Comment: 42 pages, 19 figures, 7 tables. Version accepted for publication in JHEP

Processes involving heavy quarks are a crucial component of the LHC physics program, both by themselves and as backgrounds for Higgs physics and new physics searches. In this work, we critically reconsider the validity of the widely-adopted approximation in which heavy quarks are generated at the matrix-element level, with special emphasis on the impact of the collinear logarithms associated with final-state heavy quark and gluon splittings. Our study, based on a perturbative fragmentation-function approach, explicitly shows that neglecting the resummation of collinear logarithms may yield inaccurate predictions, in particular when observables exclusive in the heavy quark degrees of freedom are considered. Our findings motivate the use of schemes which encompass the resummation of final-state collinear logarithms., Comment: 34 pages, 9 figures. v2: Minor revision suggested by JHEP implemented