S. Alekhin, M. V. Garzelli, S. -O. Moch, O. Zenaiev
备注：
33 pages, 22 figures, 4 tables, interpolation tables for top-antitop production available at https://ploughshare.web.cern.ch v2: minor revision accounting for the comments of the Referee, to be published in EPJC
We study the impact of state-of-the-art top-quark data collected at the Large Hadron Collider on parton distribution functions (PDFs). Following the ABMP methodology, the fit extracts simultaneously proton PDFs, the strong coupling $α_s(M_Z)$ and heavy-quark masses at next-to-next-to-leading order (NNLO) accuracy in QCD. It includes recent high-statistics data on absolute total inclusive cross sections for $t\bar{t}+X$, the sum of $(t + X)$ and $(\bar{t} + X)$ hadroproduction, and normalized inclusive data double-differential in the invariant mass and rapidity of the $t\bar{t}$ pair at $\sqrt{S}=13$ TeV. The gluon PDF at large $x$ and the top-quark mass value derived from these data are well compatible with the previous ABMP16 results, but with significantly smaller uncertainties, reduced by up to a factor of two. At NNLO in QCD we obtain for the strong coupling the value $α_s^{(n_f=5)}(M_Z)= 0.1150 \pm 0.0009$ and for the top-quark mass in the ${\overline{\mbox{MS}}}$-scheme $m_t(m_t) = 160.6 \pm 0.6$ GeV, corresponding to $m_t^{\rm pole} = 170.2 \pm 0.7$ GeV in the on-shell scheme. The new fit, dubbed ABMPtt, is publicly released in grids in LHAPDF format.
We report on an update of the next-to-next-to-leading order (NNLO) ABKM09 parton distributions functions. They are obtained with the use of the combined HERA collider Run I inclusive deep-inelastic scattering (DIS) data and the partial NNLO corrections to the heavy quark electro-production taken into account. The value of the strong couplig constant $α^{\rm NNLO}_{\rm s}(M_{\rm Z})=0.1147(12)$ is obtained. The standard candle cross sections for the Tevatron collider and the LHC estimated with the updated PDFs are provided.
We review progress in the global QCD analysis by the CTEQ-TEA group since the publication of CT18 parton distribution functions (PDFs) in the proton. Specifically, we discuss comparisons of CT18 NNLO predictions with the LHC 13 TeV measurements as well as with the FNAL SeaQuest and BNL STAR data on lepton pair production. The specialized CT18X PDFs approximating saturation effects are compared with the CT18sx PDFs obtained using NLL/NLO small-$x$ resummation. Short summaries are presented for the special CT18 parton distributions with fitted charm and with lattice QCD inputs. A recent comparat…
A new QCD analysis for nuclear parton distribution functions (nPDFs) at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) is presented. The framework of the analysis, including the form of the parameterization as well as the included DIS data sets, are discussed. The results of this QCD analysis are compared to the existing nPDF sets and to the fitted data. The presented framework is based on an open-source tool, xFitter, which has been modified to be applicable also for a nuclear PDF analysis. The required modifications are covered as well. Finally, an outlook for the next …
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 report an updated version of the ABKM09 NNLO PDF fit, which includes the most recent HERA collider data on the inclusive cross sections and an improved treatment of the heavy-quark contribution to deep-inelastic scattering using advantages of the running-mass definition for the heavy quarks. The ABM11 PDFs obtained from the updated fit are in a good agreement with the recent LHC data on the W- and Z-production within the experimental and PDF uncertainties. We also perform a determination of the strong coupling constant α_s in a variant of the ABM11 fit insensitive to the influence of the hi…
We report the parton distribution functions (PDFs) determined from the NNLO QCD analysis of the world inclusive DIS data with account of the precise NNLO QCD corrections to the evolution equations kernel. The value of strong coupling constant α_s^{NNLO}(M_Z)=0.1141(14), in fair agreement with one obtained using the earlier approximate NNLO kernel by van Neerven-Vogt. The intermediate bosons rates calculated in the NNLO using obtained PDFs are in agreement to the latest Run II results.
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 four families of (N)NLO CTEQ-TEA PDFs, named CT18, A, X and Z PDFs, respectively. We study the impact of …
Nuclear parton distribution functions (nPDFs) can be determined in a global QCD analysis using a wide range of experimental data. In addition to older fixed-target deep inelastic scattering and Drell-Yan (DY) dilepton production data, several analyses from p+Pb collisions at the LHC provide further constraints and extend the kinematic reach of applicable data. Here we present an update of our previous TUJU19 analysis where we now include also electroweak-boson production data recently measured by ATLAS and CMS. For the first time, LHC data are included in a nPDF analysis performed at next-to-n…
This contribution describes the HOPPET Fortran~95 package for carrying out DGLAP evolution and other common manipulations of PDFs. The PDFs are represented on a grid in $x$-space so as to avoid limitations on the functional form of input distributions. Good speed and accuracy are obtained through the representation of splitting functions in terms of their convolution with a set of piecewise polynomial basis functions. We briefly describe the structure of the code and discuss its quantitative performance. Finally we comment of future directions for the program's development.
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 perform a global fit of parton distribution functions (PDFs) together with the strong coupling constant $α_s$ and the quark masses $m_c$, $m_b$ and $m_t$ at next-to-leading order (NLO) in QCD. The analysis applies the $\overline{\mathrm{MS}}\, $ renormalization scheme for $α_s$ and all quark masses. It is performed in the fixed-flavor number scheme for $n_f=3, 4, 5$ and uses the same data as the previous fit of the ABMP16 PDF at next-to-next-to-leading order (NNLO). The new NLO PDFs complement the set of ABMP16 PDFs and are to be used consistently with NLO QCD predictions for hard scatterin…
In this paper, we present {\tt SMKA18} analysis which is a first attempt to extract the set of next-to-next-leading-order (NNLO) spin-dependent parton distribution functions (spin-dependent PDFs) and their uncertainties determined through the Laplace transform technique and Jacobi polynomial approach. Using the Laplace transformations, we present an analytical solution for the spin-dependent Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at NNLO approximation. The results are extracted using a wide range of proton $g_1^{p}(x, Q^2)$, neutron $g_1^{n}(x, Q^2)$ and deuteron $g_1^{…
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…
The reweighting method presented in earlier publications is applied for incorporating the LHC W lepton asymmetry data published in 2010 into the NNPDF2.1 NNLO analysis. We confirm the result of the NLO analysis which indicated that these data reduce PDF uncertainties of light quarks in the medium and small-x region, providing the first solid constraints on PDFs from LHC data.
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 perform the analysis of the existing inclusive deep inelastic scattering (DIS) data within NNLO QCD approximation. The parton distributions functions (PDFs) and the value of strong coupling constant $α_{s}(M_Z)=0.1143\pm0.0013 (exp)$ are obtained. The sensitivity of the PDFs to the uncertainty in the value of the NNLO corrections to the splitting functions is analyzed. It is shown that the PDFs errors due to this uncertainty is generally less than the experimental uncertainty in PDFs through the region of $x$ spanned by the existing DIS data.
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…
The extension of interpolation-grid frameworks for perturbative QCD calculations at next-to-next-to-leading order (NNLO) is presented for deep inelastic scattering (DIS) processes. A fast and flexible evaluation of higher-order predictions for any a posteriori choice of parton distribution functions (PDFs) or value of the strong coupling constant is essential in iterative fitting procedures to extract PDFs and Standard Model parameters as well as for a detailed study of the scale dependence. The APPLfast project, described here, provides a generic interface between the parton-level Monte Carlo…
We check the impact of the factorization scheme employed in the calculation of the heavy-quark deep-inelastic scattering (DIS) electro-production on the PDFs determined in the NNLO QCD analysis of the world inclusive neutral-current DIS data combined with the ones on the neutrino-nucleon DIS di-muon production and the fixed-target Drell-Yan process. The charm-quark DIS contribution is calculated in the general-mass variable-flavor-number (GMVFN) scheme: At asymptotically large values of the momentum transfer $Q$ it is given by the zero-mass 4-flavor scheme and at the value of $Q$ equal to the …
The HERAPDF2.0 family, introduced in 2015, is completed with fits HERAPDF2.0Jets NNLO (prel.) based on inclusive HERA data and selected jet production data. The result of a fit with the strong coupling constant, $α_s(M^2_Z)$, free is $α_s(M^2_Z) = 0.1150 \pm 0.0008{\rm (exp)} ^{+0.0002}_{-0.0005}$ (model/parameterisation) $\pm 0.0006{\rm (hadronisation)} \pm 0.0027 {\rm (scale)}$. Sets of parton density functions, PDFs, from fits with fixed $α_s(M^2_Z) = 0.115$ and $α_s(M^2_Z) = 0.118$ are presented and compared.
We present the first calculation of a fully-unintegrated parton distribution (beam function) at next-to-next-to-leading order (NNLO). We obtain the fully-differential beam function for quark-initiated processes by matching it onto standard parton distribution functions (PDFs) at two loops. The fully-differential beam function is a universal ingredient in resummed predictions of observables probing both the virtuality as well as the transverse momentum of the incoming quark in addition to its usual longitudinal momentum fraction. For such double-differential observables our result provides the …
We present a next-to-next-to-leading order (NNLO) calculation of the quasi parton distribution functions (Quasi-PDFs) in the large momentum effective theory (LaMET). We focus on the flavor non-diagonal quark-quark channel and demonstrate the LaMET factorization at the NNLO accuracy in the modified minimal subtraction scheme. The matching coefficient between the quasi-PDF and the light-cone PDF is derived. This provides a first step towards a complete NNLO analysis of quasi-PDFs and to better understand the nucleon structures from the first principle of QCD.
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 Te…
We present the next-to-next-to-leading order (NNLO) calculation of quark quasi parton distribution functions (PDFs) in the large momentum effective theory. The nontrivial factorization at this order is established explicitly and the full analytic matching coefficients between the quasi distribution and the lightcone distribution are derived. We demonstrate that the NNLO numerical contributions can improve the behavior of the extracted PDFs sizably. With the unprecedented precision study of nucleon tomography at the planned electron-ion collider, high precision Lattice QCD simulations with our …
We present a systematic investigation of jet production at hadron colliders from a phenomenological point of view, with the dual aim of providing a validation of theoretical calculations and guidance to future determinations of parton distributions (PDFs). We account for all available inclusive jet and dijet production measurements from ATLAS and CMS at 7 and 8 TeV by including them in a global PDF determination, and comparing to theoretical predictions at NNLO QCD supplemented by electroweak (EW) corrections. We assess the compatibility of the PDFs, specifically the gluon, obtained before and…
I consider the effects of including a variety of new LHC data sets into the MMHT approach for PDF determination. I consider the impact of fitting new LHC and Tevatron data, which leads to clear improvements in some PDF uncertainties. There are specific issues with ATLAS 7 TeV jet data and I include a discussion of the treatment of correlated uncertainties and briefly the effects of NNLO corrections. I also present preliminary results with the inclusion of the high precison final ATLAS 7 TeV $W,Z$ rapidity-dependent data.
We present a determination of the nucleon parton distribution functions (PDFs) and of the strong coupling constant $α_s$ at next-to-next-to-leading order (NNLO) in QCD based on the world data for deep-inelastic scattering and the fixed-target data for the Drell-Yan process. The analysis is performed in the fixed-flavor number scheme for $n_f=3,4,5$ and uses the $\bar{MS}$ scheme for $α_s$ and the heavy quark masses. The fit results are compared with other PDFs and used to compute the benchmark cross sections at hadron colliders to the NNLO accuracy.
We present new sets of nuclear parton distribution functions (nPDFs) at next-to-leading order and next-to-next-to-leading order in perturbative QCD. Our analyses are based on deeply inelastic scattering data with charged-lepton and neutrino beams on nuclear targets, and experimental data from measurements of $W^{\pm},\,Z$ boson production in p+Pb collisions at the LHC. In addition, a set of proton baseline PDFs is fitted within the same framework and with the same theoretical assumptions. The results of our global QCD analysis are compared to existing nPDF sets and to the previous nPDF set TUJ…
We investigate the effect of including the HERA run I + II combined cross section data on the MMHT2014 PDFs. We present the fit quality within the context of the global fit and when only the HERA data are included. We examine the changes in both the central values and uncertainties in the PDFs. We find that the prediction for the data is good, and only relatively small improvements in $χ^2$ and changes in the PDFs are obtained with a refit at both NLO and NNLO. PDF uncertainties are slightly reduced. There is a small dependence of the fit quality on the value of $Q^2_{\min}$. This can be impro…
We determine the parton distribution functions (PDFs) in a next-to-next-to-leading order (NNLO) QCD-analysis of the inclusive neutral-current deep-inelastic-scattering (DIS) world data combined with the neutri{-}no-nucleon DIS di-muon data and the fixed-target Drell-Yan data. The PDF-evolution is performed in the $N_f = 3$ fixed-flavor scheme and supplementary sets of PDFs in the 4- and 5-flavor schemes are derived from the results in the 3-flavor scheme using matching conditions. The charm-quark DIS contribution is calculated in a general-mass variable-flavor-number (GMVFN) scheme interpolati…
This contribution attempts to determine the $b$-quark pole mass $M_b$ and \MSbar running mass $\overline{m}_b$ with two different approaches at the next-to-next-to-leading order (NNLO) corrections. At the first approach, we derive a relation between the $b$-quark pole mass $M_b$ and its \MSbar running mass $\overline{m}_b$ at the NNLO corrections based on the perturbative Quantum Chromo Dynamics (pQCD) predictions. At the second approach, we extract numerical values of the $b$-quark pole and \MSbar running masses based on the NNLO phenomenology of H1 and ZEUS Collaborations combined beauty ver…
We present new sets of nuclear parton distribution functions (nPDFs) at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO). Our analyses are based on deeply inelastic scattering data with charged-lepton and neutrino beams on nuclear targets. In addition, a set of proton baseline PDFs is fitted within the same framework with the same theoretical assumptions. The results of this global QCD analysis are compared to existing nPDF sets and to the fitted cross sections. Also, the uncertainties resulting from the limited constraining power of the included experimental data are prese…
To obtain more precise parton distribution functions (PDFs) it is important to include data on inclusive high transverse energy jet production in the global parton analyses. These data have high statistics and the NNLO terms in the perturbative QCD (pQCD) description are now available. Our aim is to reduce the uncertainty in the comparison of the jet data with pQCD. To ensure the best convergence of the pQCD series it is important to choose the appropriate factorization scales, $μ_F$. We show that it is possible to absorb and resum in the incoming PDFs and fragmentation function ($D$) an essen…
We perform the next-to-next-leading-order (NNLO) QCD global fit of PDFs using inclusive charged-lepton and neutrino DIS data down to Q = 1 GeV. We also consider the data on neutrino-nucleon dimuon production, that allows us to disentangle the strange sea distribution. The fit results in χ^2/NDP = 5150/4338 = 1.2 that demonstrates a good consistency of the data sets used in analysis. The resulting value of α_s(M_Z) = 0.1136+- 0.0007(exp.) is in a good agreement with the previous version of the fit with a more stringent cut on Q. This analysis allows us to improve the accuracy of PDFs. The HT te…
We discuss the influence of fixed target Drell-Yan data on the extraction of parton distribution functions at next-to-next-to-leading order (NNLO) in QCD. When used in a parton distribution fit, the Drell-Yan (DY) data constrain sea quark distributions at large values of Bjorken x. We find that not all available DY data are useful for improving the precision of parton distribution functions (PDFs) obtained from a fit to the deep inelastic scattering (DIS) data. In particular, some inconsistencies between DIS-based parton distribution functions and DY data for large values of dilepton rapidity …
We present a determination of the parton distributions of the nucleon from a global set of hard scattering data using the NNPDF methodology at LO and NNLO in perturbative QCD, thereby generalizing to these orders the NNPDF2.1 NLO parton set. Heavy quark masses are included using the so-called FONLL method, which is benchmarked here at NNLO. We demonstrate the stability of PDFs upon inclusion of NNLO corrections, and we investigate the convergence of the perturbative expansion by comparing LO, NLO and NNLO results. We show that the momentum sum rule can be tested with increasing accuracy at LO,…
We present next-to-next-to-leading order (NNLO) parton distribution functions (PDFs) from the CTEQ-TEA group. The CT10NNLO PDF fit is based on essentially the same global data sets used in the CT10 and CT10W NLO PDF analyses. After exploring the goodness of the fits to the HERA combined data and the Tevatron jet data, we present various predictions at NNLO accuracy for both existing and forthcoming precision measurements from the CERN Large Hadron Collider. The range of variations in the gluon distribution introduced by correlated systematic effects in inclusive jet production is also examined…
We investigate the effect of including the HERA run I + II combined cross section data on the MMHT2014 PDFs. We present the fit quality within the context of the global fit and when only the HERA data are included. We examine the changes in both the central values and uncertainties in the PDFs. We find that the prediction for the data is good, and only relatively small improvements in $χ^2$ and changes in the PDFs are obtained with a refit at both NLO and NNLO. PDF uncertainties are slightly reduced. There is a small dependence of the fit quality on the value of $Q^2_{\min}$.
We analyze the impact of the recent HERA run I+II combination of inclusive deep inelastic scattering cross-section data on the CT14 global analysis of PDFs. New PDFs at NLO and NNLO, called CT14$_{\textrm{HERA2}}$, are obtained by a refit of the CT14 data ensembles, in which the HERA run I combined measurements are replaced by the new HERA run I+II combination. The CT14 functional parametrization of PDFs is flexible enough to allow good descriptions of different flavor combinations, so we use the same parametrization for CT14$_{\textrm{HERA2}}$ but with an additional shape parameter for descri…
One of the most popular definition for the charm-quark mass is the charm-quark pole mass $m_c^{\rm pole}$. In this contribution, we extract the charm-quark pole mass through perturbative Quantum Chromo Dynamics (pQCD) analysis up to the next-to-next-to-leading order (NNLO) corrections from HERA Combined and LHCb charm production recent data sets. Then, we investigate for the first time the charm-quark pole mass $m_c^{\rm pole}$ pure impact, as an extra pQCD parameter on the proton Parton Distribution Functions (PDFs) at the NNLO corrections.
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…
The LHC has recently released precise measurements of the transverse momentum distribution of the Z-boson that provide a unique constraint on the structure of the proton. Theoretical developments now allow the prediction of these observables through next-to-next-to-leading order (NNLO) in perturbative QCD. In this work we study the impact of incorporating these latest advances into a determination of parton distribution functions (PDFs) through NNLO including the recent ATLAS and CMS 7 TeV and 8 TeV $p_T^Z$ data. We investigate the consistency of these measurements in a global fit to the avail…
We present results for top quark production at the Tevatron including next-to-next-to-leading order (NNLO) soft-gluon corrections. We show the stability of the cross section with respect to kinematics choice and scale when the NNLO corrections are taken into account.
I present recent NNLO-NNLL results for top quark hadroproduction at the Tevatron. The total cross section as well as transverse momentum and rapidity distributions are shown.
We determine the NNLO electroweak correction to the $e^+ e^-\to b\bar{b}W^+W^- X$ production cross section near the top-pair production threshold. The calculation includes non-resonant production of the final state as well as electroweak effects in resonant top anti-top pair production with non-relativistic resummation, and elevates the theoretical prediction to NNNLO QCD plus NNLO electroweak accuracy. We then study the impact of the new contributions on the top-pair threshold scan at a future lepton collider.
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…
We present partial results on NLO and NNLO QCD, and NLO electroweak corrections to polarized top quark decays. In parallel we derive positivity bounds for the polarized structure functions in polarized top quark decays and check them against the perturbative corrections to the structure functions.
We study the effect of the charm quark mass in the CTEQ global analysis of parton distribution functions (PDFs) of the proton. Constraints on the $\bar{\rm MS}$ mass of the charm quark are examined at the next-to-next-to-leading order (NNLO) accuracy in the S-ACOT-$χ$ heavy-quark factorization scheme. The value of the charm quark mass from the hadronic scattering data in the CT10 NNLO fit, including semiinclusive charm production in DIS at HERA collider, is found to agree with the world average value. Various approaches for constraining $m_{c}$ in the global analysis and impact on LHC cross se…
We present a fully-differential calculation of the NNLO QCD corrections to the t-channel mechanism for producing single top quarks at the LHC. We work in the structure function approximation, computing QCD corrections to the light- and heavy-quark lines separately and neglecting the dynamical cross-talk between the two. The neglected contribution, which appears at NNLO for the first time, is color-suppressed and is expected to be sub-dominant. Within this approximation, we find that, for the total cross section, NNLO QCD corrections are in the few percent range and, therefore, are comparable t…
We present a first QCD analysis of next-to-next-leading-order (NNLO) contributions of the spin-dependent parton distribution functions (PPDFs) in the nucleon and their uncertainties using the Jacobi polynomial approach. Having the NNLO contributions of the quark-quark and gluon-quark splitting functions in perturbative QCD (Nucl. Phys. B 889 (2014) 351-400), one can obtain the evolution of longitudinally polarized parton densities of hadrons up to NNLO accuracy of QCD. A very large sets of recent and up-to-date experimental data of spin structure functions of the proton $g_1^p$, neutron $g_1^n…
