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 developments of the QCD analysis for nuclear PDFs is given.
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…
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 present analytic results that describe fully-differential NNLO QCD corrections to deep-inelastic scattering processes within the nested soft-collinear subtraction scheme. This is the last building block required for the application of this scheme to computations of NNLO QCD corrections to arbitrary processes at hadron colliders.
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…
We discuss how the UN2LOPS scheme for matching NNLO calculations to parton showers can be applied to processes with large higher-order perturbative QCD corrections. We focus on Higgs-boson production through gluon fusion as an example. We also present an NNLO fixed-order event generator for this reaction.
We compute the total cross-section for direct production of the pseudoscalar Higgs boson in hadron collisions at next-to-next-to-leading order (NNLO) in perturbative QCD. The O(alpha_s^2) QCD corrections increase the NLO production cross-section by approximately 20-30 per cent.
The significance of NNLO (3-loop) QCD contributions to the flavor non-singlet sector of F_2^ep and F_2^ed has been studied as compared to uncertainties (different factorization schemes, higher twist and QED contributions) of standard NLO (and LO) QCD analyses. The latter effects turn out to be comparable in size to the NNLO contributions. Therefore the minute NNLO effects are not observable with presently available data on non-singlet structure functions.
We consider Higgs boson production through gluon--gluon fusion in hadron collisions, when a veto is applied on the transverse momenta of the accompanying hard jets. We compute the QCD radiative corrections to this process at NLO and NNLO. The NLO calculation is complete. The NNLO calculation uses the recently evaluated NNLO soft and virtual QCD contributions to the inclusive cross section. We find that the jet veto reduces the impact of the NLO and NNLO contributions, the reduction being more sizeable at the LHC than at the Tevatron.
We give an overview of our calculation of the next-to-next-to-leading order (NNLO) QCD corrections to W + jet production in hadronic collisions. Phenomenological results for multiple differential distributions are compared to CMS data for 8 TeV proton-proton collisions. We further discuss the application of the calculation to the transverse momentum spectrum of inclusive W boson production, again accompanied by a comparison to 8 TeV CMS data. In both cases, the inclusion of NNLO QCD effects give an improved agreement between theory and data with considerably reduced scale uncertainties with re…
I present a master formula for the next-to-next-to-leading order (NNLO) soft and virtual QCD corrections for any process in hadron-hadron and lepton-hadron colliders. The formula is derived from a unified threshold resummation formalism. Applications to various QCD processes are discussed.
We present a new implementation of the NNLO QCD corrections to three-jet final states and related event-shape observables in electron--positron annihilation. Our implementation is based on the antenna subtraction method, and is performed in the NNLOJET framework. The calculation improves upon earlier results by taking into account the full kinematical information on the initial state momenta, thereby allowing the event orientation to be computed to NNLO accuracy. We find the event-orientation distributions at LEP and SLC to be very robust under higher order QCD corrections.
High precision analyses of experimental data for e+ e- annihillation, such as determination of jet rates or event shape observables, call for complete next-to-next-to-leading order (NNLO) perturbative QCD predictions. In this talk, we discuss the various ingredients entering the calculation of the NNLO corrections in e+ e- annihillation.
I describe MiNNLO$_{\rm PS}$, a novel method to match NNLO QCD computations with Parton Showers, and present a selection of results for color-singlet production at the LHC.
We discuss interplay between the high-twist (HT) terms in the operator-product expansion and the next-to-next-to-leading-order (NNLO) QCD corrections to the deep-inelastic-scattering structure functions in analysis of the high-precision data for charged leptons. Under account of the NNLO corrections the observed HT terms change within their experimental errors only and do not vanish in the NNLO.
We present a parton-shower matched NNLO QCD calculation for hadronic final state production in Deep Inelastic Scattering. The computation is based on the UNLOPS method and is implemented in the publicly available event generation framework SHERPA. Results are compared to measurements performed by the H1 collaboration.
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 simple approach to combine NNLO QCD calculations and parton showers, based on the UNLOPS technique. We apply the method to the computation of Drell-Yan lepton-pair production at the Large Hadron Collider. We comment on possible improvements and intrinsic uncertainties.
We present a subtraction scheme for computing jet cross sections in electron-positron annihilation at next-to-next-to-leading order accuracy in perturbative QCD. In this second part we deal with the regularization of the real-virtual contribution to the NNLO correction.
We review recent progress in next-to-next-to-leading order (NNLO) perturbative QCD calculations with special emphasis on results ready for phenomenological applications. Important examples are new results on structure functions and jet or Higgs boson production. In addition, we describe new calculational techniques based on twistors and their potential for efficient calculations of multiparticle amplitudes.
We present the next-to-next-to-leading order (NNLO) QCD corrections to dijet production in the purely gluonic channel retaining the full dependence on the number of colours. The sub-leading colour contribution in this channel first appears at NNLO and, as expected, increases the NNLO correction by around 10% and exhibits a pT dependence, rising from 8% at low pT to 15% at high pT . The present calculation demonstrates the utility of the antenna subtraction method for computing the full colour NNLO corrections to dijet production at the Large Hadron Collider.
We present a subtraction scheme for computing jet cross sections in electron-positron annihilation at next-to-next-to-leading order accuracy in perturbative QCD. In this first part we deal with the regularization of the doubly-real contribution to the NNLO correction.
The next-to-next-to-leading order (NNLO) QCD analysis of the experimental $xF_3$ structure function from CCFR data is performed. The theoretical uncertainties of the analysis are discussed.
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 compute the soft and virtual NNLO QCD corrections to Higgs production through gluon-gluon fusion at hadron colliders. We present numerical results obtained at the LHC and at the Tevatron Run II.
We present results from the first fully differential next-to-next-to leading order NNLO QCD computation of ZZ production, including off-shell effects, the leptonic decay and non-resonant contributions. We compare theoretical predictions to fiducial cross sections and distributions measured by ATLAS and CMS at 8 TeV and also perform a first comparison with early ATLAS measurements at 13 TeV.
We continue the systematic next-to-next-to-leading order (NNLO) QCD analysis of the CCFR data for $xF_3$ SF. The NNLO results forthe $Q^2$-dependence of the parameters, which describe the $x$-dependence of this SF, are presented.
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 …
We present a detailed phenomenological study of Z-boson production in association with a jet through next-to-next-to-leading order (NNLO) in perturbative QCD. Fiducial cross sections and differential distributions for both 8 TeV and 13 TeV LHC collisions are presented. We study the impact of different parton distribution functions (PDFs) on predictions for the Z+jet process. Upon inclusion of the NNLO corrections, the residual scale uncertainty is reduced such that both the total rate and the transverse momentum distributions can be used to discriminate between various PDF sets.
Precision studies of QCD at electron-positron colliders are based on measurements of event shapes and jet rates. To match the high experimental accuracy, theoretical predictions to next-to-next-to-leading order (NNLO) in QCD are needed for a reliable interpretation of the data. We report the first calculation of NNLO corrections O(alpha_s^3) to three-jet production and related event shapes, and discuss their phenomenological impact.
The production of Higgs bosons in weak boson fusion has the second largest cross section among Higgs-production processes at the LHC. As such, this process plays an important role in detailed studies of Higgs interactions with vector bosons. In this paper we extend the available description of Higgs boson production in weak boson fusion by considering anomalous $HVV$ interactions and NNLO QCD radiative corrections at the same time. We find that, while leading order QCD predictions are too uncertain to allow for detailed studies of the anomalous couplings, NLO QCD results are sufficiently preci…
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.
For precision studies with QCD observables at colliders, higher order perturbative corrections are often mandatory. For exclusive observables, like jet cross sections or differential distributions, these corrections were until recently only known to next-to-leading order (NLO) in perturbation theory. Owing to many new technical developments, first next-to-next-to-leading order (NNLO) QCD calculations are now becoming available. We review the recent progress in this field.
NNLOJET: a parton-level event generator for jet cross sections at NNLO QCD accuracy
CERN（欧洲核子研究组织）；Universität Zürich（苏黎世大学）；University of Durham（杜伦大学）；ETH（苏黎世联邦理工学院）；Shandong University（山东大学）；Max-Planck-Institut für Physik, Werner-Heisenberg-Institut（马克斯·普朗克物理研究所）；KIT（卡尔斯鲁厄理工学院）；TU Dresden（德累斯顿工业大学）；LIP（葡萄牙粒子与核物理研究所）；Universidade de Lisboa（里斯本大学）；University of Wuppertal（伍珀塔尔大学）；Georg-August-Universität Göttingen（哥廷根大学）
Recent developements in the calculation of the NNLO QCD corrections to the charm quark mass dependent matrix elements in B -> X_s gamma are reported. Special emphasis is put on the new results of the virtual O(alpha_s^2) fermionic contribution to these matrix elements [1].
We analyze, in the antenna subtraction framework, the real radiation antenna functions for processes involving the production of a pair of heavy quarks and two gluons by an uncolored initial state at NNLO QCD. We provide explicit expressions for these functions and discuss their infrared singular behaviour. Our main results are the corresponding integrated antenna functions which are computed analytically. They are expressed in terms of harmonic polylogarithms.
We present analytic formulas that describe fully-differential production of color-singlet final states in $q\bar q$ and $gg$ annihilation, including all the relevant partonic channels, through NNLO QCD. We work within the nested soft-collinear scheme which allows for fully local subtraction of infrared divergences. We demonstrate analytic cancellation of soft and collinear poles and present formulas for finite parts of all integrated subtraction terms. These results provide an important building block for calculating NNLO QCD corrections to arbitrary processes at hadron colliders within the ne…
The results of the more detailed NNLO QCD analysis of the CCFR data for $xF_3$ SF are presented. The factorization scale uncertainties are analysed. The NNLO results for $alpha_s(M_Z)$ and twist-4 contributions are obtained. Despite the fact that the amplitude of the $x$-shape of the twist-4 factor is consequently decreasing at the NLO and NNLO, our new QCD analysis seems to reveal the remaining twist-4 structure at the NNLO level. The definite N$^3$LO uncertainties are fixed using the [0/2] Padé resummation technique.
We finish the definition of a subtraction scheme for computing NNLO corrections to QCD jet cross sections. In particular, we perform the integration of the soft-type contributions to the doubly unresolved counterterms via the method of Mellin-Barnes representations. With these final ingredients in place, the definition of the scheme is complete and the computation of fully differential rates for electron-positron annihilation into two and three jets at NNLO accuracy becomes feasible.
We use the next-to-next-to-leading order (NNLO) contributions to anomalous dimension governing the evolution of non-singlet quark distributions. We use the xF3 data of the CCFR collaboration to obtain some unknown parameters which exist in the non-singlet quark distributions in the NNLO approximation. In the fitting procedure, Bernstein polynomial method is used. The results of valence quark distributions in the NNLO, are in good agreement with the available theoretical model.
We report on the first calculation of next-to-next-to-leading order (NNLO) QCD corrections to the inclusive production of ZZ pairs at hadron colliders. Numerical results are presented for pp collisions with centre-of-mass energy ($\sqrt{s}$) ranging from 7 to 14 TeV. The NNLO corrections increase the NLO result by an amount varying from $11\%$ to $17\%$ as $\sqrt{s}$ goes from 7 to 14 TeV. The loop-induced gluon fusion contribution provides about $60\%$ of the total NNLO effect. When going from NLO to NNLO the scale uncertainties do not decrease and remain at the $\pm 3\%$ level.
We compute the total cross-section for direct Higgs boson production in hadron collisions at NNLO in perturbative QCD. A new technique which allows us to perform an algorithmic evaluation of inclusive phase-space integrals is introduced, based on the Cutkosky rules, integration by parts and the differential equation method for computing master integrals. Finally, we discuss the numerical impact of the O(alpha_s^2) QCD corrections to the Higgs boson production cross-section at the LHC and the Tevatron.
