Sets Of Parton Distribution Functions Research Articles

Enhancing the Large Hadron Collider sensitivity to charged and neutral broad resonances of new gauge sectors

In scenarios beyond the Standard Model (BSM) characterised by charged (W′) or neutral (Z′) massive gauge bosons with large width, resonant mass searches are not very effective, so that one has to exploit the tails of the mass distributions measured at the Large Hadron Collider (LHC). In this case, the LHC sensitivity to new physics signals is influenced significantly by systematic uncertainties associated with the Parton Distribution Functions (PDF), particularly in the valence quark sector relevant for the multi-TeV mass region. As a BSM framework featuring such conditions, we consider the 4-Dimensional Composite Higgs Model (4DCHM), in which multiple W′ and Z′ broad resonances are present, with strongly correlated properties. By using the QCD tool xFitter, we study the implications on W′ and Z′ searches in Drell-Yan (DY) lepton decay channels that follow from the reduction of PDF uncertainties obtained through combining high-statistics precision measurements of DY lepton-charge and forward-backward asymmetries. We find that the sensitivity to the BSM states is greatly increased with respect to the case of base PDF sets, thereby enabling one to set more stringent limits on (or indeed discover) such new particles, both independently and in correlated searches.

QED parton distribution functions in the MSHT20 fit

We present the MSHT20qed set of parton distribution functions (PDFs). These are obtained from the MSHT20 global analysis via a refit including QED corrections to the DGLAP evolution at {{{mathcal {O}}}}(alpha ),{{{mathcal {O}}}}(alpha alpha _S) and mathcal{O}(alpha ^2), and containing the photon PDF of the proton. As in the previous MMHT15qed study we use an input distribution for the photon that is derived from the LUXqed formulation, and find good consistency for the photon PDF with that of MMHT15qed, as well as with other recent sets. We also present a set of QED corrected neutron PDFs and accompanying photon distribution, and provide the photon PDF of the nucleons separated into elastic and inelastic contributions. We assess the general expectations for the impact of photon-initiated (PI) corrections to processes entering PDF fits, and review the effect of QED corrections on the other partons and on the fit quality, where electroweak corrections (including PI production) are appropriately added to the cross sections wherever possible. We explore the phenomenological implications of this set by comparing to a variety of benchmark cross sections, finding small but significant corrections due to the inclusion of QED effects in the PDFs.

Measurement of the W boson mass

The W boson mass is measured using proton-proton collision data at sqrt{s} = 13 TeV corresponding to an integrated luminosity of 1.7 fb−1 recorded during 2016 by the LHCb experiment. With a simultaneous fit of the muon q/pT distribution of a sample of W → μν decays and the ϕ* distribution of a sample of Z → μμ decays the W boson mass is determined to bemw=80354±23stat±10exp±17theory±9PDFMeV,\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$ {m}_w=80354\\pm {23}_{\\mathrm{stat}}\\pm {10}_{\\mathrm{exp}}\\pm {17}_{\\mathrm{theory}}\\pm {9}_{\\mathrm{PDF}}\\mathrm{MeV}, $$\\end{document}where uncertainties correspond to contributions from statistical, experimental systematic, theoretical and parton distribution function sources. This is an average of results based on three recent global parton distribution function sets. The measurement agrees well with the prediction of the global electroweak fit and with previous measurements.

A Novel Feature of Valence Quark Distributions in Hadrons

Examining the evolution of the maximum of valence quark distribution, qV, weighted by Bjorken x, h(x,t)≡xqV(x,t), it is observed that h(x,t) at the peak becomes a one-parameter function; h(xp,t)=Φ(xp(t)), where xp is the position of the peak, t=logQ2, and Q2 is the resolution scale. This observation is used to derive a new model-independent relation which connects the partial derivative of the valence parton distribution functions (PDFs) in xp to the quantum chromodynamics (QCD) evolution equation through the xp derivative of the logarithm of the function Φ(xp(t)). A numerical analysis of this relation using empirical PDFs results in an observation of the exponential form of the Φ(xp(t))=h(xp,t)=CeDxp(t) for leading to next-to-next leading order approximations of PDFs for the range of Q2, covering four orders in magnitude. The exponent, D, of the observed “height-position” correlation function converges with the increase in the order of approximation. This result holds for all the PDF sets considered. A similar relation is observed also for the pion valence quark distribution, indicating that the obtained relation may be universal for any non-singlet partonic distribution. The observed “height-position” correlation is used also to indicate that no finite number of exchanges can describe the analytic behavior of the valence quark distribution at the position of the peak at fixed Q2.

Neutrino-nucleon DIS from holographic QCD: PDFs of sea and valence quarks, form factors, and structure functions of the proton

We discuss unpolarized neutrino- and anti-neutrino-nucleon deep inelastic scattering using a chiral doublet of baryonic sources with explicit symmetry breaking, in a slice of ${\mathrm{AdS}}_{5}$ with both a hard and soft wall. We explicitly derive the direct and transition form factors for the vector and axial-vector currents for the holographic dual of a proton and neutron. We use them to derive the $s$-channel structure functions for neutrino and antineutrino scattering on a proton and neutron in bulk. The $t$-channel contributions stemming from the Pomeron and Reggeon exchanges are also evaluated explicitly. The pertinent even and odd structure functions in the limit of large and small parton momentum fraction $x$ are given. The results allow for the extraction of the nonperturbative parton distribution functions carried by the sea and valence quarks both at large-$x$ and small-$x$ regimes. Our holographic parton distribution function (PDF) sets compare well with the Les Houches accord PDF (LHAPDF) and the coordinated theoretical-experiment project on QCD (CTEQ) PDF sets in the large-$x$ and small-$x$ regimes in the intermediate range of ${Q}^{2}<10\text{ }\text{ }{\mathrm{GeV}}^{2}$.

Reweighted nuclear PDFs using heavy-flavor production data at the LHC

We present the reweighting of two sets of nuclear parton distribution functions (PDFs), nCTEQ15 and EPPS16, using a selection of experimental data on heavy-flavor meson [${D}^{0}$, $J/\ensuremath{\psi}$, $B\ensuremath{\rightarrow}J/\ensuremath{\psi}$ and $\mathrm{\ensuremath{\Upsilon}}(1S)$] production in proton-lead collisions at the LHC which were not used in the original determination of these nuclear PDFs. The reweighted PDFs exhibit significantly smaller uncertainties thanks to these new heavy-flavor constraints. We present a comparison with another selection of data from the LHC and relativistic heavy ion collider (RHIC) which were not included in our reweighting procedure. The comparison is overall very good and serves as a validation of these reweighted nuclear PDF sets, which we dub $\mathrm{nCTEQ}{15}_{\mathrm{rwHF}}$ and $\mathrm{EPPS}{16}_{\mathrm{rwHF}}$. This indicates that the LHC and forward RHIC heavy-flavor data can be described within the standard collinear factorization framework with the same (universal) small-$x$ gluon distribution. We discuss how we believe such reweighted PDFs should be used as well as the limitations of our procedure.

Impact of lepton p T threshold on charge asymmetry predictions for inclusive W boson production in pp collisions at 13 TeV

This paper presents the impact of the lepton transverse momentum threshold on the boson charge asymmetry predictions in perturbative QCD for the inclusive production in proton-proton ( ) collisions. The predictions are obtained at various low- thresholds 20, 25, 30, and 40 GeV in a fiducial region encompassing both the central and forward detector acceptances in terms of the lepton pseudorapidity . The predicted distributions for the lepton charge asymmetry, which is defined by ( ), at the next-to-next-to-leading order (NNLO) accuracy are compared with the CMS and LHCb data at 8 TeV center-of-mass collision energy. The 8 TeV predictions reproduce the data fairly well within the quoted uncertainties. The predictions from the CT14 parton distribution function (PDF) model are in a slightly better agreement with the data over the other PDF sets that are tested. The 13 TeV predictions using various thresholds are reported for and the charge asymmetries that are defined in terms of the differential cross sections in bins of the boson rapidity ( ) and transverse momentum ( ). The NNLO predictions for the , , and distributions are assessed to be in close correlation with the value. The and distributions are particularly shown to be more correlated at a higher threshold. The distributions are also reported from the merged predictions with improved accuracy by the inclusion of the next-to-next-to-next-to-leading logarithm (N3LL) corrections, i.e., at NNLO+N3LL. The predicted distributions from various thresholds represent a finer probe in terms of the capability to provide more constraints on the ratio of and quark distribution functions in the parton momentum fraction range .

NNLO QCD predictions of electron charge asymmetry for inclusive pp → W + X production in forward region at 13 and 14 TeV

This paper presents perturbative QCD predictions of the electron charge asymmetry for inclusive production in proton-proton (pp) collisions. Perturbative QCD calculations are performed at next-to-next-to-leading order (NNLO) accuracy using different parton distribution function (PDF) models at 8, 13, and 14 TeV center-of-mass energies of CERN LHC pp collisions. NNLO calculations are performed for electrons with transverse momenta above 20 GeV in the forward electron pseudorapidity region . NNLO predictions are first compared at 8 TeV with the measurements of the LHCb experiment at the LHC for the / cross section ratio and charge asymmetry distributions. The 8 TeV predictions using NNPDF3.1, CT14, and MMHT2014 PDF sets are reported to be in good agreement with the LHCb data for the entire region, justifying the extension of the calculations to 13 and 14 TeV energies. The charge asymmetry predictions at NNLO accuracy are reported in the forward bins at 13 and 14 TeV and compared among NNPDF3.1, CT14, and MMHT2014 PDF sets. Overall, the predicted differential cross-section and charge asymmetry distributions based on different PDF sets are found to be consistent with each other for the entire region. The charge asymmetry distributions are shown to be more sensitive to discriminate among different PDF models in terms of the 14 TeV predictions.

Higher-order corrections for tW production at high-energy hadron colliders

We discuss cross sections for tW production in proton-proton collisions at the LHC and at higher-energy colliders with energies of up to 100 TeV. We find that, remarkably, the soft-gluon corrections are numerically dominant even at very high collider energies. We present results with soft-gluon corrections at approximate NNLO and approximate N3LO matched to complete NLO results. These higher-order corrections are large and need to be included for better theoretical accuracy and smaller scale dependence. Total cross sections as well as top-quark and W-boson transverse-momentum and rapidity distributions are presented using various recent sets of parton distribution functions.

PDFFlow: Parton distribution functions on GPU

We present PDFFlow, a new software for fast evaluation of parton distribution functions (PDFs) designed for platforms with hardware accelerators. PDFs are essential for the calculation of particle physics observables through Monte Carlo simulation techniques. The evaluation of a generic set of PDFs for quarks and gluon at a given momentum fraction and energy scale requires the implementation of interpolation algorithms as introduced for the first time by the LHAPDF project. PDFFlow extends and implements these interpolation algorithms using Google's TensorFlow library providing the capabilities to perform PDF evaluations taking fully advantage of multi-threading CPU and GPU setups. We benchmark the performance of this library on multiple scenarios relevant for the particle physics community. Program summaryProgram Title:PDFFlowCPC Library link to program files:https://doi.org/10.17632/rtp8xr3hn9.1Developer's repository link:https://github.com/N3PDF/pdfflowLicensing provisions: GPLv3Programming language: Python, CNature of problem: The evaluation of a generic set of parton distribution functions requires the implementation of interpolation algorithms. Currently, there are no public available implementations with hardware acceleration support.Solution method: Implementation of interpolation algorithms for the evaluation of parton distribution functions and the strong coupling αs using the dataflow graph infrastructure provided by the TensorFlow framework, taking advantage of multi-threading CPU and GPU setups.

Parton distributions from LHC, HERA, Tevatron and fixed target data: MSHT20 PDFs

We present the new MSHT20 set of parton distribution functions (PDFs) of the proton, determined from global analyses of the available hard scattering data. The PDFs are made available at NNLO, NLO, and LO, and supersede the MMHT14 sets. They are obtained using the same basic framework, but the parameterisation is now adapted and extended, and there are 32 pairs of eigenvector PDFs. We also include a large number of new data sets: from the final HERA combined data on total and heavy flavour structure functions, to final Tevatron data, and in particular a significant number of new LHC 7 and 8 TeV data sets on vector boson production, inclusive jets and top quark distributions. We include up to NNLO QCD corrections for all data sets that play a major role in the fit, and NLO EW corrections where relevant. We find that these updates have an important impact on the PDFs, and for the first time the NNLO fit is strongly favoured over the NLO, reflecting the wider range and in particular increased precision of data included in the fit. There are some changes to central values and a significant reduction in the uncertainties of the PDFs in many, though not all, cases. Nonetheless, the PDFs and the resulting predictions are generally within one standard deviation of the MMHT14 results. The major changes are the u-d valence quark difference at small x, due to the improved parameterisation and new precise data, the {bar{d}}, {bar{u}} difference at small x, due to a much improved parameterisation, and the strange quark PDF due to the effect of LHC W, Z data and inclusion of new NNLO corrections for dimuon production in neutrino DIS. We discuss the phenomenological impact of our results, and in general find reduced uncertainties in predictions for processes such as Higgs, top quark pair and W, Z production at post LHC Run-II energies.

$${W}^{{\pm}}{/Z}$$ Cross Section Ratios Through (N)NLO Predictions in QCD

This paper presents $$W^{\pm}/Z$$ cross section ratio predictions for the $$W$$ and $$Z$$ boson productions in their subsequent electron decay channels with next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) calculations in perturbative QCD. The predicted ratios from the fiducial cross sections are primarily compared with the ATLAS measurement based on 13 TeV LHC proton–proton collisions. The predicted fiducial ratios for 14 TeV proton–proton collisions are also presented at (N)NLO accuracies. The 13 TeV and 14 TeV differential distributions for the ratios are provided as a function of the boson transverse momentum at NNLO using different parton distribution functions (PDFs). The 13 TeV and 14 TeV differential distributions for the ratios are also provided for the boson production in association with at least one jet as functions of the first leading jet transverse momentum and absolute pseudorapidity at NLO using various PDF sets. The focus is to predict the ratios more precisely in terms of the reduced theoretical scale uncertainties for the fiducial calculations and to assess sensitivity of the ratios to different PDF sets for the differential calculations. The 13 TeV ratio is predicted as 10.55 $$\pm$$ 0.35 at NLO and 10.57 $$\pm$$ 0.07 at NNLO and found to be in good agreement with the ATLAS data. The 14 TeV ratio is predicted consistently as 10.50 $$\pm$$ 0.36 at NLO and 10.37 $$\pm$$ 0.07 at NNLO. Estimated scale uncertainties are reduced to less than percent level at NNLO in the fiducial ratios. The differential ratios distributions are consistently predicted by using different PDF sets at both 13 TeV and 14 TeV. The differential ratios exhibit more sensitivity to choice of PDF sets in higher regions of the distributions.

New CTEQ global analysis of quantum chromodynamics with high-precision data from the LHC

We present the new parton distribution functions (PDFs) from the CTEQ-TEA collaboration, obtained using a wide variety of high-precision Large Hadron Collider (LHC) data, in addition to the combined HERA I+II deep-inelastic scattering data set, along with the data sets present in the CT14 global QCD analysis. New LHC measurements in single-inclusive jet production with the full rapidity coverage, as well as production of Drell-Yan pairs, top-quark pairs, and high-$p_T$ $Z$ bosons, are included to achieve the greatest sensitivity to the PDFs. The parton distributions are determined at NLO and NNLO, with each of these PDFs accompanied by error sets determined using the Hessian method. Fast PDF survey techniques, based on the Hessian representation and the Lagrange Multiplier method, are used to quantify the preference of each data set to quantities such as $\alpha_s(m_Z)$, and the gluon and strange quark distributions. We designate the main resulting PDF set as CT18. The ATLAS 7 TeV precision $W/Z$ data are not included in CT18, due to their tension with other data sets in the global fit. Alternate PDF sets are generated including the ATLAS precision 7 TeV $W/Z$ data (CT18A), a new scale choice for low-$x$ DIS data (CT18X), or all of the above with a slightly higher choice for the charm mass (CT18Z). Theoretical calculations of standard candle cross sections at the LHC (such as the $gg$ fusion Higgs boson cross section) are presented.

Preliminary Examination of Uncertainties due to Parton Distribution Functions in Far-Forward Neutrino Production at the Large Hadron Collider

A large flux of neutrinos is expected in the forward direction of the pp collisions [1, 3] at the Large Hadron Collider (LHC) at CERN. Several experiments have recently been proposed at CERN to detect these neutrinos and discussion has started on the possibility of building a Forward Physics Facility grouping many of them. Among the others, the FASER-nu [2] proposal consists of a lead + emulsion neutrino detector at a distance of 480 m from the ATLAS interaction region along the tangent to the LHC beamline. Old calculations of neutrinos rates in the forward direction were done to leading order in the QCD perturbative series. We have included next-to-leading order (NLO) terms in our calculation. We have also studied the effect of incorporating a non-perturbative Gaussian intrinsic kT. This kT effect mimics the contribution from missing higher-order terms in QCD calculations. We present the study of uncertainties due to scale variations and Parton Distribution Function (PDF) variations in the production rate of $D_s^ \pm$ and tau neutrinos in the far-forward Production at the Large Hadron Collider. We compare our predictions with the LHCb data with $D_s^ \pm$ production in the rapidity range of [2–4.5] at the LHC. In our studies, for which we consider various modern PDF sets, we also include the comparison of predictions obtained by different dynamical central scale assumptions.

Measurement of hbox {t}{bar{hbox {t}}} normalised multi-differential cross sections in {text {p}}{text {p}} collisions at sqrt{s}=13,{text {TeV}} , and simultaneous determination of the strong coupling strength, top quark pole mass, and parton distribution functions

Normalised multi-differential cross sections for top quark pair (hbox {t}{bar{hbox {t}}}) production are measured in proton-proton collisions at a centre-of-mass energy of 13,{text {TeV}} using events containing two oppositely charged leptons. The analysed data were recorded with the CMS detector in 2016 and correspond to an integrated luminosity of 35.9{,{text {fb}}^{-1}} . The double-differential hbox {t}{bar{hbox {t}}} cross section is measured as a function of the kinematic properties of the top quark and of the hbox {t}{bar{hbox {t}}} system at parton level in the full phase space. A triple-differential measurement is performed as a function of the invariant mass and rapidity of the hbox {t}{bar{hbox {t}}} system and the multiplicity of additional jets at particle level. The data are compared to predictions of Monte Carlo event generators that complement next-to-leading-order (NLO) quantum chromodynamics (QCD) calculations with parton showers. Together with a fixed-order NLO QCD calculation, the triple-differential measurement is used to extract values of the strong coupling strength alpha _{S} and the top quark pole mass (m_{{text {t}}}^{{text {pole}}}) using several sets of parton distribution functions (PDFs). The measurement of m_{{text {t}}}^{{text {pole}}} exploits the sensitivity of the hbox {t}{bar{hbox {t}}} invariant mass distribution to m_{{text {t}}}^{{text {pole}}} near the production threshold. Furthermore, a simultaneous fit of the PDFs, alpha _{S}, and m_{{text {t}}}^{{text {pole}}} is performed at NLO, demonstrating that the new data have significant impact on the gluon PDF, and at the same time allow an accurate determination of alpha _{S} and m_{{text {t}}}^{{text {pole}}}. The values alpha _{S}(m_{{text {Z}}}) = 0.1135{}^{+0.0021}_{-0.0017} and m_{{text {t}}}^{{text {pole}}} = 170.5 pm 0.8 ,{text {GeV}} are extracted, which account for experimental and theoretical uncertainties, the latter being estimated from NLO scale variations. Possible effects from Coulomb and soft-gluon resummation near the hbox {t}{bar{hbox {t}}} production threshold are neglected in these parameter extractions. A rough estimate of these effects indicates an expected correction of m_{{text {t}}}^{{text {pole}}} of the order of +1 ,{text {GeV}} , which can be regarded as additional theoretical uncertainty in the current m_{{text {t}}}^{{text {pole}}} extraction.

Study of proton parton distribution functions at high x using ZEUS data

At large values of x the parton distribution functions (PDFs) of the proton are poorly constrained and there are considerable variations between different global fits. Data at such high x have already been published by the ZEUS Collaboration, but not yet used in PDF extractions. A technique for comparing predictions based on different PDF sets to the observed number of events in the ZEUS data is presented. It is applied to compare predictions from the most commonly used PDFs to published ZEUS data at high Bjorken x. A wide variation is found in the ability of the PDFs to predict the observed results. A scheme for including the ZEUS high-x data in future PDF extractions is discussed.

Determination of the strong coupling constant \u03b1S(mZ) from measurements of inclusive W\xb1 and Z boson production cross sections in proton-proton collisions at sqrt{mathrm{s}} = 7 and 8 TeV

Twelve measurements of inclusive cross sections of W± and Z boson production, performed in proton-proton collisions at centre-of-mass energies of 7 and 8 TeV, are compared with perturbative quantum chromodynamics calculations at next-to-next- to-leading order (NNLO) accuracy obtained with the CT14, HERAPDF2.0, MMHT14, and NNPDF3.0 parton distribution functions (PDFs). Data and theory agree well for all PDF sets, taking into account the experimental and theoretical uncertainties. A novel procedure is employed to extract the strong coupling constant at the Z pole mass from a detailed comparison of all the experimental fiducial cross sections to the corresponding NNLO theoretical predictions, yielding {alpha}_{mathrm{S}}left({m}_{mathrm{Z}}right)={0.1163}_{-0.0031}^{+0.0024} (CT14), {0.1072}_{-0.0040}^{+0.0043} (HERAPDF2.0), 0.1186 ± 0.0025 (MMHT14), and 0.1147 ± 0.0023 (NNPDF3.0). Using the results obtained with the CT14 and MMHT14 PDFs, which yield the most robust and stable αS(mZ) extractions, a value {alpha}_{mathrm{S}}left({m}_{mathrm{Z}}right)={0.1175}_{-0.0028}^{+0.0025} is determined.

Measurement of differential cross sections and charge ratios for t-channel single top quark production in proton\u2013proton collisions at sqrt{s}=13,text {Te}text {V}

A measurement is presented of differential cross sections for t-channel single top quark and antiquark production in proton–proton collisions at a centre-of-mass energy of 13,text {Te}text {V} by the CMS experiment at the LHC. From a data set corresponding to an integrated luminosity of 35.9,text {fb}^{-1}, events containing one muon or electron and two or three jets are analysed. The cross section is measured as a function of the top quark transverse momentum (p_{mathrm{T}} ), rapidity, and polarisation angle, the charged lepton p_{mathrm{T}} and rapidity, and the p_{mathrm{T}} of the text {W}{}{} boson from the top quark decay. In addition, the charge ratio is measured differentially as a function of the top quark, charged lepton, and text {W}{}{} boson kinematic observables. The results are found to be in agreement with standard model predictions using various next-to-leading-order event generators and sets of parton distribution functions. Additionally, the spin asymmetry, sensitive to the top quark polarisation, is determined from the differential distribution of the polarisation angle at parton level to be 0.440 pm 0.070, in agreement with the standard model prediction.

Extraction and validation of a new set of CMS pythia8 tunes from underlying-event measurements

New sets of CMS underlying-event parameters (“tunes”) are presented for the pythia8 event generator. These tunes use the NNPDF3.1 parton distribution functions (PDFs) at leading (LO), next-to-leading (NLO), or next-to-next-to-leading (NNLO) orders in perturbative quantum chromodynamics, and the strong coupling evolution at LO or NLO. Measurements of charged-particle multiplicity and transverse momentum densities at various hadron collision energies are fit simultaneously to determine the parameters of the tunes. Comparisons of the predictions of the new tunes are provided for observables sensitive to the event shapes at LEP, global underlying event, soft multiparton interactions, and double-parton scattering contributions. In addition, comparisons are made for observables measured in various specific processes, such as multijet, Drell–Yan, and top quark-antiquark pair production including jet substructure observables. The simulation of the underlying event provided by the new tunes is interfaced to a higher-order matrix-element calculation. For the first time, predictions from pythia8 obtained with tunes based on NLO or NNLO PDFs are shown to reliably describe minimum-bias and underlying-event data with a similar level of agreement to predictions from tunes using LO PDF sets.

Updating and optimizing error parton distribution function sets in the Hessian approach. II.

In an earlier publication, we introduced the software package Error PDF Updating Method Package (epump) that can be used to update or optimize a set of parton distribution functions (PDFs), including the best-fit PDF set and Hessian eigenvector pairs of PDF sets (i.e., error PDFs), and to update any other set of observables, in the Hessian approach. Here, we validate the epump program with a detailed comparison against a full global analysis, and we demonstrate the potential of epump by presenting selected phenomenological applications relevant to the Large Hadron Collider. For example, we use the package to estimate the impact of the recent LHC data of the measurements of $W$ and $Z$ boson and top quark pair differential distributions on the CT14HERA2 PDFs.