AT HERA heavy quarks may contribute up to 30% of the structure function $F_2$. The introduction of heavy quarks requires an extension of the DGLAP formalism. The effect of using different heavy flavour number schemes, and different approaches to the running of $α_s$, are compared using the ZEUS PDF fit formalism. The potential of including charm data in the fit is explored, using $D^*$ double differential cross-sections rather than the inclusive quantity $F_2^{c\bar{c}}$.
We study the sensitivity of our recent MSTW 2008 NLO and NNLO PDF analyses to the values of the charm- and bottom-quark masses, and we provide additional public PDF sets for a wide range of these heavy-quark masses. We quantify the impact of varying m_c and m_b on the cross sections for W, Z and Higgs production at the Tevatron and the LHC. We generate 3- and 4-flavour versions of the (5-flavour) MSTW 2008 PDFs by evolving the input PDFs and alpha_S determined from fits in the 5-flavour scheme, including the eigenvector PDF sets necessary for calculation of PDF uncertainties. As an example of …
I consider the effect on MSTW partons distribution functions (PDFs) due to changes in the choices of theoretical procedure used in the fit. I first consider using the 3-flavour fixed flavour number scheme instead of the standard general mass variable flavour number scheme used in the MSTW analysis. This results in the light quarks increasing at all relatively small $x$ values, the gluon distribution becoming smaller at high values of $x$ and larger at small $x$, the preferred value of the coupling constant $α_S(M_Z^2)$ falling, particularly at NNLO, and the fit quality deteriorates. I also con…
I consider the effect on partons distribution functions (PDFs) of changes in the theoretical procedure used in a PDF fit. I consider using the 3-flavour fixed flavour number scheme instead of the standard general mass variable flavour number scheme used in the MSTW analysis. This results in the light quarks increasing at most $x$ values, the gluon distribution becoming softer at high values of $x$ and larger at small $x$, and the coupling constant $α_S(M_Z^2)$ falling, particularly at NNLO. The fit quality also deteriorates.I also consider lowering the kinematic cut on $W^2$ for DIS data and i…
Due to the large masses of the charm and bottom quarks, their production cross sections are calculable within the perturbative QCD. This makes the heavy-quark mesons important observables in high-energy collisions of protons and nuclei. However, the available calculations for heavy-flavored-meson hadroproduction have been somewhat problematic in reliably describing the cross sections across the full kinematic range from zero to very high $p_{\rm T}$. This has put some question marks on the robustness of LHC heavy-flavored-meson measurements in studying the partonic structure of the colliding h…
There have been recent updates to the three global PDF fits (CT, MSHT and NNPDF), all adding large amounts of data from the LHC, and this has resulted in significant changes to the global PDFs. Given the impact that the new PDFs will have on physics comparisons at the LHC, it is crucial to perform a benchmarking among the PDFs, similar in spirit to that which was carried out for PDF4LHC15, widely used for LHC physics. In this article we detail a benchmarking comparison of three global PDF sets - CT18, MSHT20 and NNPDF3.1 - and their similarities and differences that have been observed. The end…
We show how to account for correlations between theoretical uncertainties incorporated in parton distribution function (PDF) fits, and the theoretical uncertainties in the predictions made using these PDFs. We demonstrate by explicit calculations, both analytical and numerical, that these correlations can lead to corrections to the central values of the predictions, and reductions in both the PDF uncertainties and the theoretical uncertainties in the prediction. We illustrate our results with predictions for top production rapidity distributions and the Higgs total cross-section at the LHC, us…
We present a discussion on the methods for extracting a given parameter from measurements of hadronic data, with particular focus on determinations of the strong coupling constant. We show that when the PDF dependency on the determination is adequately taken into account, the dispersion between the results from different measurements is significantly reduced. We speculatively propose the concept of preferred value of a parameter from a particular dataset.
At HERA heavy quarks may contribute up to 30% of the structure function $F_2$. The potential of including heavy-quark data in the ZEUS PDF fits is explored, using $D^*$ double differential cross-sections as well as the inclusive quantities $F_2^{c\bar{c}}$, $F_2^{c\bar{c}}$. The introduction of heavy quarks requires an extension of the DGLAP formalism. The effect of using different heavy flavour number schemes, and different approaches to the running of $α_s$, are compared.
An important limitation in current fits of parton distribution functions (PDFs) is that PDF uncertainties do not include any source of theoretical uncertainty. Here we present a general method for incorporating theoretical uncertainties into PDF fits, focussing in particular on perturbative missing higher order uncertainties (MHOUs). We consider two methods for estimating the effect of MHOUs on PDFs, both based on scale variations. Firstly, we present PDF fits based on theoretical predictions with varied scales, and use these to estimate the associated MHOUs. Secondly, we discuss the construct…
The strong coupling constant $α_s$ and the heavy-quark masses, $m_c$, $m_b$, $m_t$ are extracted simultaneosly with the parton distribution functions (PDFs) in the updated ABM12 fit including recent data from CERN-SPS, HERA, Tevatron, and the LHC. The values of \begin{eqnarray} \nonumber α_s(M_Z)&=&0.1147\pm0.0008~({\rm exp.)},\\ \nonumber m_c(m_c)&=&1.252\pm 0.018~({\rm exp.})~{\rm GeV},\\ \nonumber m_b(m_b)&=&3.83\pm0.12~({\rm exp.})~{\rm GeV},\\ \nonumber m_t(m_t)&=&160.9\pm1.1~({\rm exp.})~{\rm GeV} \end{eqnarray} are obtained with the $\overline{MS}$ heavy-quark mass definition being empl…
We investigate the information that can be gained by including flavour data in fits of the Standard Model Effective Field Theory (SMEFT) with the assumption of Minimal Flavour Violation (MFV), allowing - as initial conditions at the high scale - leading terms in spurionic Yukawas only. Starting therefore from a theory with no tree level flavour changing neutral currents at the scale of new physics, we calculate effects in flavour changing processes at one loop, and the resulting constraints on linear combinations of SMEFT coefficients, consistently parameterising the electroweak parameters and…
The use of machine learning algorithms in theoretical and experimental high-energy physics has experienced an impressive progress in recent years, with applications from trigger selection to jet substructure classification and detector simulation among many others. In this contribution, we review the machine learning tools used in the NNPDF family of global QCD analyses. These include multi-layer feed-forward neural networks for the model-independent parametrisation of parton distributions and fragmentation functions, genetic and covariance matrix adaptation algorithms for training and optimis…
We present a method for very fast repeated computations of higher-order cross sections in hadron-induced processes for arbitrary parton density functions. A full implementation of the method for computations of jet cross sections in Deep-Inelastic Scattering and in Hadron-Hadron Collisions is offered by the "fastNLO" project. A web-interface for online calculations and user code can be found at http://hepforge.cedar.ac.uk/fastnlo/ .
We describe the impact on PDF extractions of the 'Physical Scheme', a heavy-quark mass scheme that accounts for the effects of intrinsic heavy-quarks and provides a way to smoothly transition over the heavy-quark thresholds. The modifications made to the conventional $\overline{\text{MS}}$ scheme splitting functions and $α_s$ running will be emphasised, collectively giving rise to a new Physical Scheme PDF evolution. We also present the analytic formulae for the DIS coefficient functions at NLO in the Physical Scheme and show results for the $F_2$ charm DIS structure function. Motivated by the…
We investigate the variation in the MMHT2014 PDFs when we allow the heavy quark masses $m_c$ and $m_b$ to vary away from their default values. We make PDF sets available in steps of $Δm_c =0.05~{\rm GeV}$ and $Δm_b =0.25~{\rm GeV}$, and present the variation in the PDFs and in the predictions. We examine the comparison to the HERA data on charm and beauty structure functions and note that in each case the heavy quark data, and the inclusive data, have a slight preference for lower masses than our default values. We provide PDF sets with 3 and 4 active quark flavours, as well as the standard va…
We present the interface between MadGraph5_aMC@NLO, a self-contained program that calculates cross sections up to next-to-leading order accuracy in an automated manner, and APPLgrid, a code that parametrises such cross sections in the form of look-up tables which can be used for the fast computations needed in the context of PDF fits. The main characteristic of this interface, which we dub aMCfast, is its being fully automated as well, which removes the need to extract manually the process-specific information for additional physics processes, as is the case with other matrix element calculato…
A precise knowledge of the quark and gluon structure of the proton, encoded by the parton distribution functions (PDFs), is of paramount importance for the interpretation of high-energy processes at present and future lepton-hadron and hadron-hadron colliders. Motivated by recent progress in the PDF determinations carried out by the CT, MSHT, and NNPDF groups, we present an updated combination of global PDF fits: PDF4LHC21. It is based on the Monte Carlo combination of the CT18, MSHT20, and NNPDF3.1 sets followed by either its Hessian reduction or its replica compression. Extensive benchmark s…
The production of $W$/$Z$-bosons in association with jets is an important test of perturbative QCD predictions and also yields information about the parton distribution functions of the proton. We present fits to determine PDFs using inclusive $W$/$Z$-boson and $W$/$Z$+jets measurements from the ATLAS experiment at the LHC. The ATLAS measurements are used in combination with deep-inelastic scattering data from HERA. An improved determination of the sea-quark densities at high Bjorken-$x$ is seen, while confirming a strange-quark density similar in size to the up- and down-sea-quark densities i…
We discuss c\bar{c} and b\bar{b} pair productions at ep collider for studying extremely small x(g) region. It has been shown that Large Hadron electron Collider (LHeC) has a reach of about x(g)>10^{-6}. The aim of this work is to show that the PDF uncertainties in the heavy flavour production. Maximum difference of cross section between PDFs 60% has been found in the process of ep\rightarrow eq\bar{q}X.
We present the results of a PDF fit to differential top quark production within the MMHT framework. We in particular consider ATLAS data in the lepton + jet and dilepton channels and CMS data in the lepton + jet channel, at 8 TeV. While the fit quality to the ATLAS dilepton data is good, for the CMS case we see some issues in achieving a good fit quality for certain distributions. However, we focus on the ATLAS lepton + jet data, for which correlations of the statistical and systematic errors are provided across the four relevant distributions for PDF determination, namely $p_T^t$, $M_{tt}$, $…
The HERAPDF1.0 PDF set, which was an NLO QCD analysis based on H1 and ZEUS combined inclusive cross section data from HERA-I, has been updated to HERAPDF1.5 by including preliminary inclusive cross section data from HERA-II running. Studies have also been made by adding various other HERA data sets: combined charm data, combined low energy run data and H1 and ZEUS jet data. These data give information on the treatment of charm and the charm quark mass and on the value of $α_s(M_Z)$. The PDF analysis has also been extended to NNLO. The PDFs give a good description of Tevatron and early LHC data…
Direct photon production in hadronic collisions provides a handle on the gluon PDF by means of the QCD Compton scattering process. In this work we revisit the impact of direct photon production on a global PDF analysis, motivated by the recent availability of the next-to-next-to-leading (NNLO) calculation for this process. We demonstrate that the inclusion of NNLO QCD and leading-logarithmic electroweak corrections leads to a good quantitative agreement with the ATLAS measurements at 8 TeV and 13 TeV, except for the most forward rapidity region in the former case. By including the ATLAS 8 TeV …
We investigate the impact of displaced heavy quark matching scales in a global fit. The heavy quark matching scale $μ_{m}$ determines at which energy scale $μ$ the QCD theory transitions from $N_{F}$ to $N_{F}+1$ in the Variable Flavor Number Scheme (VFNS) for the evolution of the Parton Distribution Functions (PDFs) and strong coupling $α_S(μ)$. We study the variation of the matching scales, and their impact on a global PDF fit of the combined HERA data. As the choice of the matching scale $μ_{m}$ effectively is a choice of scheme, this represents a theoretical uncertainty; ideally, we would …
Any NLO calculation of a QCD final-state observable involves Monte Carlo integration over a large number of events. For DIS and hadron colliders this must usually be repeated for each new PDF set, making it impractical to consider many `error' PDF sets, or carry out PDF fits. Here we discuss ``a posteriori'' inclusion of PDFs, whereby the Monte Carlo run calculates a grid (in x and Q) of cross section weights that can subsequently be combined with an arbitrary PDF. The procedure is numerically equivalent to using an interpolated form of the PDF. The main novelty relative to prior work is the u…
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 th…
We have updated predictions for high energy neutrino and antineutrino charged current cross-sections within the conventional DGLAP formalism of NLO QCD using a modern PDF fit to HERA data, which also accounts in a systematic way for PDF uncertainties deriving from both model uncertainties and from the experimental uncertainties of the input data sets. Furthermore the PDFs are determined using an improved treatment of heavy quark thresholds. A measurement of the neutrino cross-section much below these predictions would signal the need for extension of the conventional formalism as in BFKL resum…
Using Nf=2+1+1 lattice QCD, we determine the fermionic connected contributions to the second and third moment of the pion PDF. Based on gauge configurations from the European Twisted Mass Collaboration, chiral and continuum extrapolations are performed using pion masses in the range of 230 to 500 MeV and three values of the lattice spacing. Finite volume effects are investigated using different volumes. In order to avoid mixing under renormalisation for the third moment, we use an operator with two non-zero spatial components of momentum. Momenta are injected using twisted boundary conditions.…
The xFitter project (former HERAFitter project) is an open-source package that provides a framework for the determination of the parton distribution functions (PDFs) of the proton for many different kinds of analyses in Quantum Chromodynamics (QCD). xFitter version 2.0.0 has recently been released, and offers an expanded set of tools and options. It incorporates experimental data from a wide range of experiments including fixed-target, Tevatron, HERA, and LHC. xFitter can analyze this data up to next-to-next-to-leading-order (NNLO) in perturbation theory with a variety of theoretical calculati…
We discuss an NNLO realization of the general mass scheme S-ACOT-$χ$ for treatment of heavy-flavour production in neutral current deep-inelastic scattering. Practical implementation of the NNLO calculation is illustrated on the example of semi-inclusive structure functions $F_{2 c}(x,Q)$ and $F_{L c}(x,Q)$.
We demonstrate that theoretical predictions using current resummation techniques for the lepton pair production (LPP) rapidity and $x_F$ distributions can be inconsistent with data in high rapidity and $x_F$ kinematic regions by observing their effect in global fits of parton distribution functions (PDFs). We present an enhanced resummation technique for the LPP rapidity and $x_F$ distributions that agrees with LPP data. The enhanced resummation method is used in conjunction with threshold resummation in deep inelastic scattering (DIS) to perform two global fits of PDFs using the minimal and B…
We present a detailed study of nuclear corrections in the deuteron (D) from an analysis of data from charged-lepton deep-inelastic scattering (DIS) off proton and D, as well as from dimuon pair production in pp and pD collisions and $W^\pm$ and the $Z$ boson production at pp (p$\rm \bar p$) colliders. In particular, we discuss the determination of the off-shell function describing the modification of parton distributions (PDF) in bound nucleons in the context of global PDF fits. Our results are consistent with the ones obtained earlier from the study of the ratios of DIS structure functions $F…
We present the results of a global fit to the Aligned Two-Higgs Doublet Model, assuming that there are no new sources of CP violation beyond the quark mixing matrix. We use the most constraining flavour observables, electroweak precision measurements and the available data on Higgs signal strengths and collider searches for heavy scalars, together with the theoretical requirements of perturbativity and positivity of the scalar potential. The combination of all these constraints restricts the values of the scalar masses, the couplings of the scalar potential and the flavour-alignment parameters…
We present an investigation of the theoretical uncertainties in parton distribution functions (PDFs) due to missing higher-order corrections in the perturbative predictions used in the fit, and their relationship to the uncertainties in subsequent predictions made using the PDFs. We consider in particular the standard approach of factorization and renormalization scale variation, and derive general results for the consistent application of these at the PDF fit stage. To do this, we use the fact that a PDF fit may be recast in a physical basis, where the PDFs themselves are bypassed entirely, a…
New, radiatively generated, NLO quark (u,d,s,c,b) and gluon densities in a real, unpolarized photon are presented. We perform three global fits, based on the NLO DGLAP evolution equations for Q^2>1 GeV^2, to all the available structure function F_2^gamma(x,Q^2) data. As in our previous LO analysis we utilize two theoretical approaches. Two models, denoted as FFNS_{CJK}1 & 2 NLO, adopt the so-called Fixed Flavour-Number Scheme for calculation of the heavy-quark contributions to F_2^gamma(x,Q^2), the CJK NLO model applies the ACOT(chi) scheme. We examine the results of our fits by a comparison w…
A thorough understanding of PDFs and their uncertainties is important for the LHC and for future collider experiments. The recently released NNPDF3.0 set was presented alongside results from closure tests, where PDF fits were performed on pseudo-data generated from a chosen input PDF set. The results there demonstrate the validity of the NNPDF methodology and also provide some information about different contributions to the PDF uncertainties. Here I present a number of additional closure test results, specifically an investigation into the effect of using cross-validation in the fits, and an …
I present a formulation of a Variable Flavour Number Scheme for heavy quarks that is implemented up to NNLO in the strong coupling constant and may be used in NNLO global fits for parton distributions.
Resummation-scale uncertainties in PDF determinations
School of Physics, Institute for Research in Fundamental Sciences (IPM)（基础科学研究所）；Department of Physics, Malayer University（马拉耶尔大学物理系）；IRFU, CEA, Université Paris-Saclay（巴黎萨克雷大学CEA IRFU）；Dipartimento di Fisica, Universitá di Cagliari（卡利亚里大学物理系）；INFN, Sezione di Cagliari（意大利国家核物理研究院卡利亚里分部）；Universitá degli Studi Link（林克大学）；INFN Sezione di Roma Tor Vergata（意大利国家核物理研究院罗马托维加塔分部）；Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器）；Physik-Institut, Universität Zürich（苏黎世大学物理学院）；Theoretical Physics Department, University of Oxford（牛津大学理论物理系）；SMU Physics（南卫理公会大学物理系）；University of Sharjah（沙迦大学）；II. Institut für Theoretische Physik, Universität Hamburg（汉堡大学第二理论物理研究所）
Using parton density functions (PDFs) with threshold-resummation improvement, we consistently calculate higgsino/gaugino and slepton pair production at next-to-leading order and next-to-leading logarithmic accuracy at the LHC. The smaller PDF uncertainty of the global PDF sets is exploited with a factorisation method, which also avoids complications arising in the refitting of threshold-resummation improved PDF replicas in Mellin space. We explicitly take into account the reduction of the scale uncertainty due to the resummation. We show that the resummation contributions in the PDF fits parti…
The determination of theoretical error estimates and PDF/$α_S$-fits require fast evaluations of differential cross sections for varied QCD input parameters. These include PDFs, the strong coupling constant $α_S$ and the renormalisation and factorisation scales. Beyond leading order QCD, a full dedicated calculation for each set of parameters is often too time-consuming, certainly when performing PDF-fits. We report on two methods to overcome this issue for any QCD NLO calculation: The novel event-reweighting feature in Sherpa and the automated generation of interpolation grids using the recent…
Constraining new physics effective interactions via a global fit of electroweak, Drell-Yan, Higgs, top, and flavour observables
Universidad de Granada（格拉纳达大学）；Florida State University（佛罗里达州立大学）；Universitat d’Alacant（阿利坎特大学）；University of Manchester（曼彻斯特大学）；INFN, Sezione di Roma（罗马国家核物理研究所）
We review one-particle inclusive production of heavy-flavoured hadrons in a framework which resums the large collinear logarithms through the evolution of the FFs and PDFs and retains the full dependence on the heavy-quark mass without additional theoretical assumptions. We focus on presenting results for the inclusive cross section for the production of charmed mesons in p anti-p collisions and the comparison with CDF data from the Tevatron as well as on inclusive B-meson production and comparison with recent CDF data. The third topic is the production of D^* mesons in photoproduction and com…
We consider the role of the charm mass in PDF fits, and in particular the reliability of recent determinations of the MSbar running mass from fits to inclusive charm production data. We explain how the use of the pole mass, with a charm PDF determined empirically, can reduce PDF uncertainties from charm mass effects, and thereby lead to more reliable predictions for hard processes at the LHC.
This proceeding presents a new set of proton parton distribution functions, ATLASepWZVjet20, produced in an analysis at next-to-next-to-leading-order in QCD. The new datasets considered are the ATLAS measurements of $W^{\pm}$ and $Z$ boson production in association with jets in $pp$ collisions at $\sqrt{s}$ = 8 TeV at the LHC with integrated luminosities of 20.2 fb$^{-1}$ and 19.9 fb$^{-1}$ respectively. The analysis also considers the ATLAS measurements of differential $W^{\pm}$ and $Z$ boson production at $\sqrt{s}$ = 7 TeV with an integrated luminosity of 4.6 fb$^{-1}$ and deep-inelastic sc…
We investigate the MSHT20 global PDF sets, demonstrating the effects of varying the strong coupling $α_S(M_Z^2)$ and the masses of the charm and bottom quarks. We determine the preferred value, and accompanying uncertainties, when we allow $α_S(M_Z^2)$ to be a free parameter in the MSHT20 global analyses of deep-inelastic and related hard scattering data, at both NLO and NNLO in QCD perturbation theory. We also study the constraints on $α_S(M_Z^2)$ which come from the individual data sets in the global fit by repeating the NNLO and NLO global analyses at various fixed values of $α_S(M_Z^2)$, s…
In this work, the impact of recent measurements of heavy-flavour production in $pp$ collisions on parton distribution functions (PDFs) and their uncertainties is studied. In this regard, the absolute and normalised cross sections of beauty hadron production measured by LHCb at center-of-mass energy of 7 TeV and 13 TeV are separately included in the next-to-leading order (NLO) global QCD analysis together with the measurements of the inclusive and heavy-flavour production cross sections at HERA. It is illustrated that the heavy-flavour data of the LHCb experiment impose additional constraints o…
