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 introducing higher twist terms which are fit to data. This results in much smaller effects on both PDFs and $α_S(M_Z^2)$, with changes generally smaller than uncertainties, except for quarks at very high $x$. I show that the fixed flavour scheme and variable flavour scheme structure functions differ significantly for $x \sim 0.01$ at high $Q^2$. I demonstrate that in the fixed flavour scheme there is a slow convergence of large logarithmic terms of the form $(α_S\ln(Q^2/m_c^2))^n$ in this regime. I conclude that some major differences in PDF sets are largely due to the choice of flavour scheme used.
We suggest the modified matching procedure for TMD PDF to the integrated PDF aimed to increase the amount of perturbative information in the TMD PDF expression. The procedure consists in the selection and usage of the non-minimal operator basis, which restricts the expansion to desired general behavior. The implication of OPE allows to systematic account of the higher order corrections. In the case of TMD PDF we assume the Gaussian behavior, which suggests Laguerre polynomial basis as the best for the convergence of OPE. We present the leading and next-to-leading expression of TMD PDF in this …
We consider the effect on LHC jet cross sections on partons distribution functions (PDFs), in particular the MSTW2008 set of PDFs. We first compare the published inclusive jet data to the predictions using MSTW2008, finding a very good description. We also use the parton distribution reweighting procedure to estimate the impact of these new data on the PDFs, finding that the combined ATLAS 2.76 TeV and 7 TeV data, and CMS 7 TeV data have some significant impact. We then also investigate the impact of ATLAS, CMS and D0 dijet data using the same techniques. In this case we investigate the effect…
The perturbative procedure of matching was proposed to connect parton quasi-distributions that are calculable in lattice QCD to the corresponding light-cone distributions which enter physical processes. Such a matching procedure has so far been limited to the twist-2 distributions. Recently, we addressed the matching for the twist-3 PDF $g_T(x)$. In this work, we extend our perturbative calculations to the remaining twist-3 PDFs, $e(x)$ and $h_{L}(x)$. In particular, we discuss the non-trivialities involved in the calculation of the singular zero-mode contributions for the quasi-PDFs.
We evaluate the uncertainties due to nuclear effects in global fits of proton parton distribution functions (PDFs) that utilise deep-inelastic scattering and Drell-Yan data on deuterium targets. To do this we use an iterative procedure to determine proton and deuteron PDFs simultaneously, each including the uncertainties in the other. We apply this procedure to determine the nuclear uncertainties in the SLAC, BCDMS, NMC and DYE866/NuSea fixed target deuteron data included in the NNPDF3.1 global fit. We show that the effect of the nuclear uncertainty on the proton PDFs is small, and that the in…
We present a new procedure to determine Parton Distribution Functions (PDFs), based on Markov Chain Monte Carlo (MCMC) methods. The aim of this paper is to show that we can replace the standard $χ^2$ minimization by procedures grounded on Statistical Methods, and on Bayesian inference in particular, thus offering additional insight into the rich field of PDFs determination. After a basic introduction to these technics, we introduce the algorithm we have chosen to implement -- namely Hybrid (or Hamiltonian) Monte Carlo. This algorithm, initially developed for Lattice QCD, turns out to be very i…
We quantify the impact of LHCb D-meson measurements at $\sqrt{s}=5 \, {\rm TeV}$ on the EPPS16 and nCTEQ15 nuclear PDFs. In our study, the theoretical description of D-meson production is based on the recently developed SACOT-$m_{\rm T}$ variant of the general-mass variable-flavour-number formalism, and the impact on PDFs is estimated via reweighting methods. We pay special attention on the theoretical uncertainties known to us, and are led to exclude the $p_{\rm T}<3 \, {\rm GeV}$ region from our main analysis. The LHCb data can be accommodated well within EPPS16 and nCTEQ15, and the data pro…
We show how theoretical uncertainties due to nuclear effects may be incorporated into global fits of proton parton distribution functions (PDFs) that include deep-inelastic scattering and Drell-Yan data on nuclear targets. We specifically consider the CHORUS, NuTeV and E605 data included in the NNPDF3.1 fit, which used Pb, Fe and Cu targets, respectively. We show that the additional uncertainty in the proton PDFs due to nuclear effects is small, as expected, and in particular that the effect on the $\bar{d}/\bar{u}$ ratio, the total strangeness $s+\bar{s}$, and the strange valence distribution…
The high statistics that will be collected during the LHC Run-II (and beyond) open the path to precision measurements at the TeV scale, where the PDFs will play a crucial role in BSM searches. In the di-lepton final state accurate measurements of the Forward-Backward Asymmetry (AFB) will be available, particularly in the invariant mass region around the Z peak. We show that this observable displays a statistical error which is competitive with that assigned to the existing PDF sets and which will rapidly become smaller than the latter as the integrated luminosity grows, thereby offering a mean…
We present the first global analysis of parton distribution functions (PDFs) at approximate N$^{3}$LO in the strong coupling constant $α_{s}$, 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 $α_{s}$ can provide consistent, justifiable and explainable approximate N$^{3}$LO (aN$^{3}$LO) PDFs. This includes estimat…
We complete the procedure of extracting parton distribution functions (PDFs) using large momentum effective theory (LaMET) at leading power accuracy in the hadron momentum. We derive a general factorization formula for the quasi PDFs in the presence of mixing, and give the corresponding hard matching kernel at $\mathcal O(α_s)$, both for the unpolarized and for the polarized quark and gluon quasi-PDFs. Our calculation is performed in a regularization-independent momentum subtraction scheme. The results allow us to match the nonperturbatively renormalized quasi-PDFs to normal PDFs in the presen…
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…
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…
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…
We motivate a measurement of various ratios of $W$ and $Z$ cross sections at the Large Hadron Collider (LHC) at large values of the boson transverse momentum ($p_T\gtrsim M_{W,Z}$). We study the dependence of predictions for these cross-section ratios on the multiplicity of associated jets, the boson $p_T$ and the LHC centre-of-mass energy. We present the flavour decomposition of the initial-state partons and an evaluation of the theoretical uncertainties. We show that the $W^+/W^-$ ratio is sensitive to the up-quark to down-quark ratio of parton distribution functions (PDFs), while other theo…
We summarize several projects carried out by the CTEQ global analysis of parton distribution functions (PDFs) of the proton during 2010. We discuss a recently released CT10 family of PDFs with a fixed and variable QCD coupling strength; implementation of combined HERA and Tevatron lepton asymmetry data sets; theoretical issues associated with the analysis of $W$ charge asymmetry in PDF fits; PDFs for leading-order shower programs; and constraints on new color-octet fermions from the hadronic data.
We extract new parton distribution functions (PDFs) of the proton by global analysis of hard scattering data in the general-mass framework of perturbative quantum chromodynamics. Our analysis includes new theoretical developments together with the most recent collider data from deep-inelastic scattering, vector boson production, and single-inclusive jet production. Due to the difficulty in fitting both the DO Run-II W lepton asymmetry data and some fixed-target DIS data, we present two families of PDFs, CT10 and CT10W, without and with these high-luminosity W lepton asymmetry data included in …
We discuss the recent progress in extracting partonic functions from the quasi-distribution approach, using twisted mass fermions. This concerns, among others, the investigation of several sources of systematic effects. Their careful analysis is a prerequisite to obtain precise determinations of PDFs from the lattice with realistic estimates of all uncertainties. In these proceedings, we shortly discuss systematic effects in the matching procedure. Moreover, we present preliminary results from our new simulations at the physical point. They involve, additionally, the dynamical strange and char…
Studying the possible breaking of various parton model symmetries by the parton distribution functions of the nucleon can provide important information for the non-perturbative structure of hadrons and the strong interaction. We review theoretical calculations for the breaking of flavor symmetry, quark-antiquark symmetry and charge symmetry in the unpolarized and polarized nucleons using the meson cloud model. We report an estimation for the total distribution of strange and antistrange quarks in the nucleon by combining theoretical calculations of SU(3) flavor symmetry breaking with light ant…
The parton distributions functions (PDFs) derived from the NNLO QCD analysis of existing light-targets deep-inelastic-scattering data are presented. The NLO and NNLO PDFs are compared in order to analyze perturbative stability of the analysis and estimate impact of the higher-order QCD corrections. The main theoretical uncertainties and experimental uncertainties in PDFs due to all sources of experimental errors in data are estimated and used to assess corresponding uncertainties in the cross sections of other hadronic processes.
We summarise recent developments in the path towards the "MMHT19" parton distribution functions. We concentrate on the extraction of the strange quark upon the improvement of theoretical calculations for NNLO charged current cross sections; the effect of an extension of our parameterisation; and the role of correlated uncertainties in some data sets which prove difficult to fit.
The HERAFitter project provides a framework for the determination of parton distribution functions (PDFs), and tools for assessing the impact of new data on PDFs. In this contribution, HERAFitter is used for a QCD analysis of the legacy measurements of the $W$-boson charge asymmetry and of the $Z$-boson production cross sections, performed at the Tevatron collider in Run II by the D0 and CDF collaborations. The Tevatron measurements are included in a PDF fit performed at next-to-leading order, and compared to the predictions obtained using other PDF sets from different groups. The measurements…
I consider variations in the definition of a General-Mass Variable Flavour Number Scheme (GM-VFNS) for heavy flavour structure functions, both at next-to-leading order (NLO) and at next-to-next-to leading order (NNLO). I also define a new "optimal" scheme choice improving the smoothness of the transition from one flavour number to the next. At both NLO and NNLO I investigate the variation of the structure function for a fixed set of parton distribution functions (PDFs) and also the change in the distributions when a new MSTW-type global fit to data is performed for each GM-VFNS. At NLO the par…
We examine the dependence of parton distribution functions (PDFs) on the value of the QCD coupling strength $α_{s}(M_{Z})$. We explain a simple method that is rigorously valid in the quadratic approximation normally applied in PDF fitting, and fully reproduces the correlated dependence of theoretical cross sections on $α_s$ and PDF parameters. This method is based on a statistical relation that allows one to add the uncertainty produced by $α_s$, computed with some special PDF sets, in quadrature with the PDF uncertainty obtained for the fixed $α_s$ value (such as the CTEQ6.6 PDF set). A serie…
We develop a unified algebraic model which satisfactorily describes the internal structure of pion and kaon as well as heavy quarkonia ($η_c$ and $η_b$). For each of these mesons, we compute their generalized parton distributions (GPDs), built through the overlap representation of their light-front wave function, tightly constrained by the modern and precise knowledge of their quark distribution amplitudes. From this three-dimensional knowledge of mesons, we deduce parton distribution functions (PDFs) as well as electromagnetic form factors and construct the impact parameter space GPDs. The PD…
We study several sources of theoretical uncertainty in the determination of parton distributions (PDFs) which may affect current PDF sets used for precision physics at the Large Hadron Collider, and explain discrepancies between them. We consider in particular the use of fixed-flavor versus variable-flavor number renormalization schemes, higher twist corrections, and nuclear corrections. We perform our study in the framework of the NNPDF2.3 global PDF determination, by quantifying in each case the impact of different theoretical assumptions on the output PDFs. We also study in each case the im…
Using recent and updated world data on polarized structure functions $g_1$ and $g_2$ we perform QCD analysis at the next-next-to-leading-order (NNLO) accuracy. We include also target mass correction and higher twist effect to get more precise results in our fitting procedure. To confirm the validity of our fitting results several sum rules are examined and we do a comparison for them with results from other models. In our analysis we employ Jacobi polynomials approach to obtain analytical solutions of the DGLAP evolution equations for parton distribution functions (PDFs). Using the extracted P…
We explore connections between two common methods for quantifying the uncertainty in parton distribution functions (PDFs), based on the Hessian error matrix and Monte-Carlo sampling. CT14 parton distributions in the Hessian representation are converted into Monte-Carlo replicas by a numerical method that reproduces important properties of CT14 Hessian PDFs: the asymmetry of CT14 uncertainties and positivity of individual parton distributions. The ensembles of CT14 Monte-Carlo replicas constructed this way at NNLO and NLO are suitable for various collider applications, such as cross section rew…
Studying the structure of nucleons is not only important to understanding the strong interactions of quarks and gluons, but also to improving the precision of new-physics searches. Since a broad class of experiments, including the LHC and dark-matter detection, require Standard-Model backgrounds with parton distribution functions (PDFs) as inputs for disentangling SM contributions from potential new physics. For a long time, lattice calculations of the PDFs (as well as many hadron structures) has been limited to the first few moments. In this talk, we present a first direct calculation of the …
We present the first unbiased determination of parton distribution functions (PDFs) with electroweak corrections. The aim of this thesis is to provide an exhaustive description of the theoretical framework and the technical implementation which leads to the determination of a set of PDFs which includes the photon PDF and quantum electrodynamics (QED) contributions to parton evolution. First, we introduce and motivate the need of including electroweak corrections to PDFs, providing phenomenological examples and presenting an overview of the current state of the art in PDF fits. The theoretical …
We investigate hysteresis effects in the perturbative solution of renormalisation group equations (RGEs). We present examples for the QCD running coupling and proton's parton distribution functions (PDFs), relevant to precision physics at the Large Hadron Collider (LHC) and future collider experiments. We propose the use of resummation scales to take into account the theoretical uncertainties from the solution of the RGEs. As a case study, we consider the $F_2$ structure function in a region relevant to the extraction of PDFs.
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…
Kashi University（喀什大学）；Michigan State University（密歇根州立大学）；Xinjiang University（新疆大学）；Kennesaw State University（肯尼索州立大学）；Argonne National Laboratory（阿贡国家实验室）；Shanghai Jiao Tong University（上海交通大学）
We present LO, NLO and NNLO sets of parton distribution functions (PDFs) of the proton determined from global analyses of the available hard scattering data. These MMHT2014 PDFs supersede the `MSTW2008' parton sets, but are obtained within the same basic framework. We include a variety of new data sets, from the LHC, updated Tevatron data and the HERA combined H1 and ZEUS data on the total and charm structure functions. We also improve the theoretical framework of the previous analysis. These new PDFs are compared to the `MSTW2008' parton sets. In most cases the PDFs, and the predictions, are …
The quantum statistical parton distributions approach proposed more than one decade ago is revisited by considering a larger set of recent and accurate Deep Inelastic Scattering experimental results. It enables us to improve the description of the data by means of a new determination of the parton distributions. This global next-to-leading order QCD analysis leads to a good description of several structure functions, involving unpolarized parton distributions and helicity distributions, in a broad range of $x$ and $Q^2$ and in terms of a rather small number of free parameters. There are severa…
We consider the impact that can be made on our understanding of parton distributions (PDFs) and QCD from early measurements at the LHCb experiment. The high rapidity values make the experiment uniquely suited to a detailed study of small-x parton distributions and hence will make a significant contribution towards the clarification of both experimental and theoretical uncertainties on PDFs and their applications.
We report on EPPS16 - the first analysis of NLO nuclear PDFs where LHC p-Pb data (Z, W, dijets) have been directly used as a constraint. In comparison to our previous fit EPS09, also data from neutrino-nucleus deeply-inelastic scattering and pion-nucleus Drell-Yan process are now included. Much of the theory framework has also been updated from EPS09, including a consistent treatment of heavy quarks in deeply-inelastic scattering. However, the most notable change is that we no longer assume flavour-blind nuclear modifications for valence and sea quarks. This significantly reduces the theoretic…
We investigate the influence of modified nuclear parton distribution functions (PDFs) on high-pT hadron production at RHIC and LHC energies using a pQCD-improved parton model. For application at RHIC, we focus on the possible contribution of the EMC modification of the nuclear PDFs in the x > 0.3 region to the observed suppression of pi0 production at pT > 10 GeV/c in dAu collisions. We study three different parameterizations of the nuclear PDF modifications and find that they give consistent results for R_dAu(pT) for neutral pions in the region 10 GeV/c < pT < 20 GeV/c. We find that the EMC s…
In global fits of parton distribution functions (PDFs) a large fraction of data points, mostly from the HERA collider, lies in a region of $x$ and $Q^2$ that is sensitive to small-$x$ logarithmic enhancements. Thus, the proper theoretical description of these data requires the inclusion of small-$x$ resummation. In this work we provide all the necessary ingredients to perform a PDF fit to deep-inelastic scattering (DIS) data which includes small-$x$ resummation in the evolution of PDFs and in the computation of DIS structure functions. To this purpose, not only we include the resummation of DI…
Within the theory of Quantum Chromodynamics (QCD), the rich structure of hadrons can be quantitatively characterized, among others, using a basis of universal non-perturbative functions: parton distribution functions (PDFs), generalized parton distributions (GPDs), transverse-momentum dependent distributions (TMDs) and distribution amplitudes (DAs). For more than half a century, there has been a joint experimental and theoretical effort to obtain these partonic functions. However, the complexity of the strong interactions has placed severe limitations, and first-principle results on the distri…
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 approa…
We consider some trends, achievements and a series of remaining problems in the precision determination of parton distribution functions. For the description of the scaling violations of the deep-inelastic scattering data, forming the key ingredients to all PDF fits, a solid theoretical framework is of importance. It is provided by the fixed flavor number scheme in describing the heavy-quark contributions which is found in good agreement with the present experimental data in a very wide range of momentum transfers. In this framework also a consistent determination of the heavy-quark masses is …
We present the leading-twist quark transverse momentum-dependent parton distribution functions (TMDs) for the spin-1 target, such as the $ρ$-meson, in the light-front framework. Specifically, we predict the TMDs in the light-front holographic model and compare with the light-front quark model predictions. We obtain the TMDs using the overlap of the light-front wave functions. We evaluate the ${\bf k}_\perp$ moments upto second order and compare with the available theoretical predictions. Further, we analyze the leading-twist parton distribution functions (PDFs) of the $ρ$-meson in the light-fr…
We assess the current phenomenological status of transverse momentum dependent (TMD) parton distribution functions (PDFs) and fragmentation functions (FFs) and study the effect of consistently including perturbative QCD (pQCD) evolution. Our goal is to initiate the process of establishing reliable, QCD-evolved parametrizations for the TMD PDFs and TMD FFs that can be used both to test TMD-factorization and to search for evidence of the breakdown of TMD-factorization that is expected for certain processes. In this article, we focus on spin-independent processes because they provide the simplest…
We perform the analysis of existing light-targets deep-inelastic-scattering (DIS) data in the leading-order (LO), next-to-leading-order (NLO), and next-to-next-to-leading-order (NNLO) QCD approximations and extract PDFs simultaneously with the value of the strong coupling constant $α_s$ and the high-twist contribution to the structure functions. The main theoretical uncertainties and experimental uncertainties due to all sources of experimental errors in data are estimated, the latter generally dominate for the obtained PDFs. The uncertainty in Higgs boson production cross section due to error…
In these proceedings we perform a brief review of machine learning (ML) applications in theoretical High Energy Physics (HEP-TH). We start the discussion by defining and then classifying machine learning tasks in theoretical HEP. We then discuss some of the most popular and recent published approaches with focus on a relevant case study topic: the determination of parton distribution functions (PDFs) and related tools. Finally, we provide an outlook about future applications and developments due to the synergy between ML and HEP-TH.
We present the new CTEQ-TEA global analysis of quantum chromodynamics (QCD). In this analysis, parton distribution functions (PDFs) of the nucleon are determined within the Hessian method at the next-to-next-to leading order (NNLO) in perturbative QCD, based on the most recent measurements from the Large Hadron Collider (LHC) and a variety of world collider data. Because of difficulties in fitting both the ATLAS 7 and 8 TeV $W$ and $Z$ vector boson production cross section data, we present two families of PDFs, named CT18 and CT18$Z$ PDFs, respectively, without and with the ATLAS 7 TeV $W$ and…
We review recent theoretical developments concerning the definition and the renormalization of equal-time correlators that can be computed on the lattice and related to Parton Distribution Functions (PDFs) through a factorization formula. We show how these objects can be studied and analyzed within the framework of a nongauge theory, gaining insight through a one-loop computation. We use scalar field theory as a playground to revise, analyze and present the main features of these ideas, to explore their potential, and to understand their limitations for extracting PDFs. We then propose a frame…
