Analysis Of Parton Distribution Functions Research Articles

Accelerating Markov Chain Monte Carlo sampling with diffusion models

Global fits of physics models require efficient methods for exploring high-dimensional and/or multimodal posterior functions. We introduce a novel method for accelerating Markov Chain Monte Carlo (MCMC) sampling by pairing a Metropolis-Hastings algorithm with a diffusion model that can draw global samples with the aim of approximating the posterior. We briefly review diffusion models in the context of image synthesis before providing a streamlined diffusion model tailored towards low-dimensional data arrays. We then present our adapted Metropolis-Hastings algorithm which combines local proposals with global proposals taken from a diffusion model that is regularly trained on the samples produced during the MCMC run. Our approach leads to a significant reduction in the number of likelihood evaluations required to obtain an accurate representation of the Bayesian posterior across several analytic functions, as well as for a physical example based on a global analysis of parton distribution functions. Our method is extensible to other MCMC techniques, and we briefly compare our method to similar approaches based on normalizing flows. A code implementation can be found at https://github.com/NickHunt-Smith/MCMC-diffusion.

Impact of lattice strangeness asymmetry data in the CTEQ-TEA global analysis

We study the impact of lattice data on the determination of the strangeness asymmetry distribution ${s}_{\ensuremath{-}}(x)\ensuremath{\equiv}s(x)\ensuremath{-}\overline{s}(x)$ in the general CTEQ-TEA global analysis of parton distribution functions (PDFs) of the proton. Firstly, we find that allowing a nonvanishing ${s}_{\ensuremath{-}}(x)$, at the initial ${Q}_{0}=1.3\text{ }\text{ }\mathrm{GeV}$ scale, in a global PDF analysis leads to a CT18As fit with similar quality to CT18A. Secondly, including the lattice data in the CT18As_Lat fit greatly reduces the ${s}_{\ensuremath{-}}$-PDF error band size in the large-$x$ region. To further reduce its error would require more precise lattice data, extended to smaller $x$ values. We take ATLAS 7 TeV $W$ and $Z$ production data, SIDIS dimuon production data, ${F}_{3}$ structure function data, E866 NuSea data, and E906 SeaQuest data as examples to illustrate the implication of CT18As and CT18As_Lat fits. The parametrization dependence for PDF ratio $(s+\overline{s})/(\overline{u}+\overline{d})(x)$ is analyzed with CT18As2 and CT18As2_Lat fits as results.

Non-singlet quark helicity PDFs of the nucleon from pseudo-distributions

The non-singlet helicity quark parton distribution functions (PDFs) of the nucleon are determined from lattice QCD, by jointly leveraging pseudo-distributions and the distillation spatial smearing paradigm. A Lorentz decomposition of appropriately isolated space-like matrix elements reveals pseudo-distributions that contain information on the leading-twist helicity PDFs, as well as an invariant amplitude that induces an additional z2 contamination of the leading-twist signal. An analysis of the short-distance behavior of the space-like matrix elements using matching coefficients computed to next-to-leading order (NLO) exposes the desired PDF up to this additional z2 contamination. Due to the non-conservation of the axial current, we elect to isolate the helicity PDFs normalized by the nucleon axial charge at the same scale μ2. The leading-twist helicity PDFs as well as several sources of systematic error, including higher-twist effects, discretization errors, and the aforementioned z2 contaminating amplitude are jointly determined by characterizing the computed pseudo-distribution in a basis of Jacobi polynomials. The Akaike Information Criterion is exploited to effectively average over distinct model parameterizations and cuts on the pseudo-distribution. Encouraging agreement is observed with recent global analyses of each non-singlet quark helicity PDF, notably a rather small non-singlet anti-quark helicity PDF for all quark momentum fractions.

Approximate N^{3}LO parton distribution functions with theoretical uncertainties: MSHT20aN^3LO PDFs

We present the first global analysis of parton distribution functions (PDFs) at approximate N^{3}LO in the strong coupling constant alpha _{s}, extending beyond the current highest NNLO achieved in PDF fits. To achieve this, we present a general formalism for the inclusion of theoretical uncertainties associated with the perturbative expansion in the strong coupling. We demonstrate how using the currently available knowledge surrounding the next highest order (N^{3}LO) in alpha _{s} can provide consistent, justifiable and explainable approximate N^{3}LO (aN^{3}LO) PDFs. This includes estimates for uncertainties due the currently unknown N^{3}LO ingredients, but also implicitly some missing higher order uncertainties (MHOUs) beyond these. Specifically, we approximate the splitting functions, transition matrix elements, coefficient functions and K-factors for multiple processes to N^{3}LO. Crucially, these are constrained to be consistent with the wide range of already available information about N^{3}LO to match the complete result at this order as accurately as possible. Using this approach we perform a fully consistent approximate N^{3}LO global fit within the MSHT framework. This relies on an expansion of the Hessian procedure used in previous MSHT fits to allow for sources of theoretical uncertainties. These are included as nuisance parameters in a global fit, controlled by knowledge and intuition based prior distributions. We analyse the differences between our aN^{3}LO PDFs and the standard NNLO PDF set, and study the impact of using aN^{3}LO PDFs on the LHC production of a Higgs boson at this order. Finally, we provide guidelines on how these PDFs should be used in phenomenological investigations.

Parton distribution functions and QCD coupling constant from LHC and non-LHC data

We present a new QCD analysis of parton distribution functions (PDFs) at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO). In the present paper, the role of special types of experimental measurements for extracting PDFs is investigated, and simultaneously the values of the strong coupling constant are determined. Essential elements of this QCD analysis are the HERA combined data as a base, heavy-quark cross-section measurement together with Tevatron data on jet production and H1 and ZEUS jet cross sections as ``non-LHC'' data, and especially the ``LHC'' dataset for top-quark and jet cross sections. These different datasets have allowed detailed information at low $x$, providing worthwhile information on the nucleon's flavor, and have played an important role for some PDFs at large-$x$ and strong coupling constant. Since the large-$x$ gluon PDF benefits from an accurate determination of quark PDFs, we have enough motivation to focus on the top-quark production and jet cross-section measurements from LHC to find the impact of these data on the gluon PDF and strong coupling constant. These experimental data have an impact on the relative uncertainties of PDF. The gluon PDF at large $x$ and the values of ${\ensuremath{\alpha}}_{s}({M}_{Z}^{2})$ are affected significantly. Although the main motivation of this paper is to focus on the gluon PDF and its uncertainty at large-$x$, giving notice to heavy PDF behavior in this region is also very important. We study the intrinsic charm (IC) using the BHPS model together with our extracted extrinsic charm PDF at large $x$, which can be very worthwhile for future experiments at the LHC.

Generalized parton distributions through universal moment parameterization: zero skewness case

We present a global analysis program for the generalized parton distributions (GPDs) based on conformal moment expansion. We apply the strategy of universal moment parameterization to fit both the collinear parton distribution functions (PDFs) from phenomenology and generalized form factors from lattice calculations, and show that the parameterization is flexible enough to accommodate these constraints. In addition, we can also fit direct lattice calculations of GPDs from large-momentum effective theory. In this work we focus on the analysis of t-dependent PDFs which correspond to GPDs in the ξ → 0 limit. The strategy also applies to the ξ ≠ 0 region with extra parameters, and therefore can be fitted to experimental observables in the future. With a demonstrative example of fitted GPDs, we exhibit the quark transverse angular momentum densities of the proton as well as the impact parameter space distributions of quarks in both unpolarized and transversely polarized protons.

Machine learning of log-likelihood functions in global analysis of parton distributions

Modern analysis on parton distribution functions (PDFs) requires calculations of the log-likelihood functions from thousands of experimental data points, and scans of multi-dimensional parameter space with tens of degrees of freedom. In conventional analysis the Hessian approximation has been widely used for the estimation of the PDF uncertainties. The Lagrange Multiplier (LM) scan while being a more faithful method is less used due to computational limitations, and is the main focus of this study. We propose to use Neural Networks (NNs) and machine learning techniques to model the profile of the log-likelihood functions or cross sections for multi-dimensional parameter space in order to overcome those limitations which work beyond the quadratic approximations and meanwhile ensures efficient scans of the full parameter space. We demonstrate the efficiency of the new approach in the framework of the CT18 global analysis of PDFs by constructing NNs for various target functions, and performing LM scans on PDFs and cross sections at hadron colliders. We further study the impact of the NOMAD dimuon data on constraining PDFs with the new approach, and find enhanced strange-quark distributions and reduced PDF uncertainties. Moreover, we show how the approach can be used to constrain new physics beyond the Standard Model (BSM) by a joint fit of both PDFs and Wilson coefficients of operators in the SM effective field theory.

Sea Asymmetry from Polarized W Boson Production

We present the results of a global QCD analysis of helicity parton distribution functions (PDFs) that includes the latest polarized W-lepton production data from the STAR collaboration at the Relativistic Heavy-Ion Collider (RHIC). This data allows the first extraction of a nonzero helicity light-quark sea asymmetry within a simultaneous global QCD analysis of unpolarized and helicity PDFs.

EPPS21: a global QCD analysis of nuclear PDFs

We present an updated global analysis of collinearly factorized nuclear parton distribution functions (PDFs) at next-to-leading order in perturbative QCD. In comparison to our previous fit, EPPS16, the present analysis includes more data from proton-lead collisions at the Large Hadron Collider: 5 TeV double-differential CMS dijet and LHCb D-meson data, as well as 8 TeV CMS W^pm data. These new data lead to significantly better-constrained gluon distributions at small and intermediate values of the momentum fraction x, confirming the presence of shadowing and antishadowing for gluons in large nuclei. In addition, we include Jefferson Lab measurements of deeply inelastic scattering which probe nuclear PDFs at large x and low virtualities. For the first time within the Hessian framework, we now also explore the uncertainties of nuclear PDFs due to the errors in the baseline proton PDFs. We release the results of our analysis as a new public parametrization of nuclear PDFs called EPPS21.

Snowmass 2021 Whitepaper: Proton Structure at the Precision Frontier

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).]

Isovector EMC Effect from Global QCD Analysis with MARATHON Data

We report the results of a MonteCarlo global QCD analysis of unpolarized parton distribution functions (PDFs), including for the first time constraints from ratios of ^{3}He to ^{3}H structure functions recently obtained by the MARATHON experiment at Jefferson Lab. Our simultaneous analysis of nucleon PDFs and nuclear effects in A=2 and A=3 nuclei reveals the first indication for an isovector nuclear EMC effect in light nuclei. We find that while the MARATHON data yield relatively weak constraints on the F_{2}^{n}/F_{2}^{p} neutron to proton structure function ratio and on the d/u PDF ratio, they suggest an enhanced nuclear effect on the d-quark PDF in the bound proton, questioning the assumptions commonly made in nuclear PDF analyses.

An analysis of parton distribution functions of the pion and the kaon with the maximum entropy input

We present pion and kaon parton distribution functions from a global QCD analysis of the experimental data within the framework of dynamical parton model. We use the DGLAP equations with parton–parton recombination corrections and the valence input of uniform distribution which maximizes the information entropy. At our input scale Q_0^2, there are no sea quark and gluon distributions. All the sea quarks and gluons of the pion and the kaon are completely generated from the parton splitting processes. The mass-dependent parton splitting kernel is applied for the strange quark distribution in the kaon. The obtained valence quark and sea quark distributions at high Q^{2} (Q^2>5 GeV^2) are compatible with the existed experimental measurements. Furthermore, the asymptotic behaviours of parton distribution functions at small and large x have been studied for both the pion and the kaon. Lastly, the first three moments of parton distributions at high Q^{2} scale are calculated, which are consistent with other theoretical predictions.

Improved Determination of Strange Distribution Function from the Global Analysis Using BHPS Model

We study the impact of intrinsic strange (IS) component of nucleon sea on the global analysis of parton distribution functions (PDFs) considering a wide range of experimental data. To this aim, we consider two scenarios on the basis of BHPS model results for the IS distribution. In the first scenario, we apply the results presented through the BHPS model and in the second scenario we use its evolved distributions. For each scenarios, we present the limit of the IS probability $$ \mathcal{P}_5^{s\bar{s}} $$ for the standard tolerance criteria $$ \Delta \chi ^2=1 $$ and 18.112 at $$ 1\sigma $$ and $$ 4\sigma $$ levels. Our results show that the experimental data can tolerate an IS component with a greater probability $$ \mathcal{P}_5^{s\bar{s}} $$ if one employs the second scenario. We obtain $$ \mathcal{P}_5^{s\bar{s}}\approx 0.01 $$ and $$ \mathcal{P}_5^{s\bar{s}}\approx 0.025 $$ for $$ \Delta \chi ^2=1 $$ and 18.112, respectively, at the $$ 4\sigma $$ level. We also calculate the ratio of strange-to-light sea-quark densities $$r_s$$ in the proton both including and excluding the IS component. Our results show that one can obtain a higher value for the ratio $$r_s$$ if the IS component is included.

Neural-network analysis of Parton Distribution Functions from Ioffe-time pseudodistributions

We extract two nonsinglet nucleon Parton Distribution Functions from lattice QCD data for reduced Ioffe-time pseudodistributions. We perform such analysis within the NNPDF framework, considering data coming from different lattice ensembles and dis- cussing in detail the treatment of the different source of systematics involved in the fit. We introduce a recipe for taking care of systematics and use it to perform our extraction of light-cone PDFs.

Parton distribution functions of the charged pion within the xFitter framework

We present the first open-source analysis of parton distribution functions (PDFs) of charged pions using xFitter, an open-source QCD fit framework to facilitate PDF extraction and analyses. Our calculations are implemented at next-to-leading order (NLO) using APPLgrids generated by MCFM generator. Using currently available Drell-Yan and photon production data, we find the valence distribution is well constrained; however, the considered data are not sensitive enough to unambiguously determine sea and gluon distributions. Fractions of momentum carried by the valence, sea and gluon components are discussed, and we compare with the results of JAM collaboration and the GRV group.

Implementation of target mass corrections and higher-twist effects in the xFitter framework

Knowledge of parton distribution functions (PDFs) at large momentum fraction $ x $ is not only important to study the flavor and spin dynamics of quarks in the nucleon, but also to search for signals of new physics at collider experiments. It is well known now that the nonperturbative QCD effects generally play a more significant role at such kinematic regions. In this work, we present an open-source QCD analysis of PDFs considering target mass corrections (TMCs) and higher-twist (HT) effects which are necessary when the analysis includes also data points from deep inelastic scattering (DIS) with larger values of $ x $ and smaller values of photon virtuality $ Q^2 $. To this aim, we use the xFitter package, as a comprehensive and powerful tool for studying PDFs. We report and discuss our recent activities on the implementation of TMCs and HT effects in the xFitter framework in a user-friendly way, so that the user can switch on or off them, and also choose between different options. We check the validity of the modifications by performing sample analyses of PDFs considering TMCs and HT effects and using a wide range of DIS data.

Towards ultimate parton distributions at the high-luminosity LHC

Since its start of data taking, the LHC has provided an impressive wealth of information on the quark and gluon structure of the proton. Indeed, modern global analyses of parton distribution functions (PDFs) include a wide range of LHC measurements of processes such as the production of jets, electroweak gauge bosons, and top quark pairs. In this work, we assess the ultimate constraining power of LHC data on the PDFs that can be expected from the complete dataset, in particular after the High-Luminosity (HL) phase, starting in around 2025. The huge statistics of the HL-LHC, delivering {mathcal {L}}=3hbox { ab}^{-1} to ATLAS and CMS and {mathcal {L}}=0.3hbox { ab}^{-1} to LHCb, will lead to an extension of the kinematic coverage of PDF-sensitive measurements as well as to an improvement in their statistical and systematic uncertainties. Here we generate HL-LHC pseudo-data for different projections of the experimental uncertainties, and then quantify the resulting constraints on the PDF4LHC15 set by means of the Hessian profiling method. We find that HL-LHC measurements can reduce PDF uncertainties by up to a factor of 2 to 4 in comparison to state-of-the-art fits, leading to few-percent uncertainties for important observables such as the Higgs boson transverse momentum distribution via gluon-fusion. Our results illustrate the significant improvement in the precision of PDF fits achievable from hadron collider data alone, and motivate the continuation of the ongoing successful program of PDF-sensitive measurements by the LHC collaborations.

First MonteCarlo Global QCD Analysis of Pion Parton Distributions.

We perform the first global QCD analysis of parton distribution functions (PDFs) in the pion, combining πA Drell-Yan data with leading neutron electroproduction from HERA within a MonteCarlo approach based on nested sampling. Inclusion of the HERA data allows the pion PDFs to be determined down to much lower values of x, with relatively weak model dependence from uncertainties in the chiral splitting function. The combined analysis reveals that gluons carry a significantly higher pion momentum fraction, ∼30%, than that inferred from Drell-Yan data alone, with sea quarks carrying a somewhat smaller fraction, ∼15%, at the input scale. Within the same effective theory framework, the chiral splitting function and pion PDFs can be used to describe the d[over ¯]-u[over ¯] asymmetry in the proton.

The impact of intrinsic charm on the parton distribution functions

In this work, we present a new investigation about the impact of intrinsic charm (IC) on the physical observables, in particular, on the heavy structure function $F_2^c$. Since IC distribution is dominant at large Bjorken variable $x$, normally, it is expected that it can be explored only at large $x$. But, by studying the correlation of the charm density in the proton with $F_2^c$, we are going to show that the IC component can also be effective at low $x$. To investigate further, we perform three QCD global analyses of parton distribution functions (PDFs), by including the EMC $F_2^c$ data that are recognized as clear evidence for existence of the intrinsic charm in the proton, and also by considering the IC component. Although the fit of the EMC data is extremely poor due to the data points with lower $x$ values, i.e. $x< $0.05, but these analyses can give us new information about the impact of EMC data and IC contribution on the behaviour of PDFs.

Role of the intrinsic charm content of the nucleon from various light-cone models on γ+c-jet production

Having a precise knowledge of the charm quark component can lead to a better understanding of the fundamental structure of the nucleon. Furthermore, the charm quark distribution function plays an important role in the study of many processes which are sensitive to the charm quark content of the nucleon. In the standard global analysis of parton distribution functions (PDFs), the charm quark distribution arises perturbatively through the splitting of the gluon into charm-anticharm pairs in the DGLAP evolution equations. Nevertheless, the existence of nonperturbative intrinsic charm quarks in the proton has also been predicted by QCD. In this paper, we study some phenomenological models within the light-cone framework to predict the nonperturbative intrinsic charm quark content of the nucleon. We investigate the impact of these models on the prediction of γ+c-jet production in pp collisions at the LHC and compare our results on pp̄→γ+c-jet with the experimental data of D0.