A first unbiased global NLO determination of parton distributions and their uncertainties
Richard D. Ball, Luigi Del Debbio, Stefano Forte, Alberto Guffanti, Jose I. Latorre, Juan Rojo, Maria Ubiali
备注：
86 pages, 41 figures. PDF sets available from http://sophia.ecm.ub.es/nnpdf/nnpdf_pdfsets.htm and from LHAPDF. Final version to be published in Nucl. Phys. B. Various typos corrected and small clarifications added, fig. 4 added, extended discussion of data consistency especially in sect 5.1 and 5.4
We present a determination of the parton distributions of the nucleon from a global set of hard scattering data using the NNPDF methodology: NNPDF2.0. Experimental data include deep-inelastic scattering with the combined HERA-I dataset, fixed target Drell-Yan production, collider weak boson production and inclusive jet production. Next-to-leading order QCD is used throughout without resorting to K-factors. We present and utilize an improved fast algorithm for the solution of evolution equations and the computation of general hadronic processes. We introduce improved techniques for the training of the neural networks which are used as parton parametrization, and we use a novel approach for the proper treatment of normalization uncertainties. We assess quantitatively the impact of individual datasets on PDFs. We find very good consistency of all datasets with each other and with NLO QCD, with no evidence of tension between datasets. Some PDF combinations relevant for LHC observables turn out to be determined rather more accurately than in any other parton fit.
An NLO photon parton parametrization is presented based on the existing $F_2^γ$ measurements from $e^+e^-$ data and the low-$x$ proton structure function from $ep$ interactions. Also included in the extraction of the NLO parton distribution functions are the dijets data coming from $γp \to j_1 + j_2 +X$. The new parametrization is compared to other NLO parametrizations.
We present the matching of NLO QCD and NLO EW corrections to parton showers for vector-boson pair production at the LHC. We consider leptonic final states, including resonant and non-resonant diagrams, spin correlations and off-shell effects. Our results are obtained interfacing the Recola2-Collier one-loop provider with the POWHEG-BOX-RES framework. We discuss our implementation, we validate it at fixed order, and we show our final results matched to parton shower. A by-product of our work is also a general interface between Recola2-Collier and POWHEG-BOX-RES. This is the first time that EW a…
In this paper, we present the next-to-leading order predictions for diphoton production in the ADD model, matched to the HERWIG parton shower using the MC@NLO formalism. A selection of the results is presented for d=2-6 extra dimensions, using generic cuts as well as analysis cuts mimicking the search strategies as pursued by the ATLAS and CMS experiments.
Extending previous work on the predictions for the production of supersymmetric (SUSY) particles at the LHC, we present the fully differential calculation of the next-to-leading order (NLO) SUSY-QCD corrections to the production of squark and squark-antisquark pairs of the first two generations. The NLO cross sections are combined with the subsequent decay of the final state (anti)squarks into the lightest neutralino and (anti)quark at NLO SUSY-QCD. No assumptions on the squark masses are made, and the various subchannels are taken into account independently. In order to obtain realistic predi…
We present a set of NLO SUSY-QCD calculations for the pair production of neutralinos and charginos at the LHC, and their matching to parton-shower programs in the framework of the POWHEG-BOX program package. The code we have developed provides a SUSY Les Houches Accord interface for setting supersymmetric input parameters. Decays of the neutralinos and charginos and parton-shower effects can be simulated with PYTHIA. To illustrate the capabilities of our program, we present phenomenological results for a representative SUSY parameter point. We find that NLO-QCD corrections increase the product…
A new method of including the complete NLO QCD corrections to hard processes in the LO parton-shower Monte Carlo (PSMC) is presented. This method, called KrkNLO, requires the use of parton distribution functions in a dedicated Monte Carlo factorization scheme, which is also discussed in this paper. In the future, it may simplify introduction of the NNLO corrections to hard processes and the NLO corrections to PSMC. Details of the method and numerical examples of its practical implementation, as well as comparisons with other calculations, such as MCFM, MC@NLO, POWHEG, for single $Z/γ^*$-boson …
We discuss the impact of the treatment of NMC structure function data on parton distributions in the context of the NNPDF2.1 global PDF determination at NLO and NNLO. We show that the way these data are treated, and even their complete removal, has no effect on parton distributions at NLO, and at NNLO has an effect which is below one sigma. In particular, the Higgs production cross-section in the gluon fusion channel is very stable.
A dedicated test of the perturbative QCD NLO parton evolution in the very small-$x$ region is performed. We find a good agreement with recent precision HERA-data for $F_2^p(x,Q^2)$, as well as with the present determination of the curvature of $F_2^p$. Characteristically, perturbative QCD evolutions result in a positive curvature which increases as $x$ decreases. Future precision measurements in the very small $x$-region, $x<10^{-4}$, could provide a sensitive test of the range of validity of perturbative QCD
The PowHel framework allows to make predictions of total and differential cross-sections of multiparticle hadroproduction processes at both NLO QCD accuracy and NLO QCD matched to Parton Shower, on the basis of the interface between the POWHEG-BOX and HELAC-NLO codes. It has already been applied to study several processes involving a top-antitop pair in association with a third particle or hadronic jet. Our most recent predictions concern top-antitop-V hadroproduction (with V = W or Z), at both parton and hadron level, by considering different decay channels (hadronic and leptonic) of the heav…
In this study we tried to emphasize the role parton shower plays in event generation, and in the physics of high energy event generation. We achieved this task by comparing the next-to-leading order and next-to-next-to-leading order results from EERAD3 with the next-to-leading order plus parton shower results from Vincia, and comparing both with real data.
The pair production of squarks is one of the main search channels for supersymmetry at the LHC. We present a fully differential calculation of the next-to-leading order (NLO) SUSY-QCD corrections to the on-shell production of a pair of squarks in the Minimal Supersymmetric Standard Model (MSSM), supplemented by the leading-order decay of the squarks to the lightest neutralino and a quark. In addition, we use the Powheg method to match our NLO calculation with parton showers. To this end, the process was implemented in the Powheg-Box framework and interfaced with Pythia6 and Herwig++. We study …
We present predictions for the production cross section of a Standard Model Higgs boson in association with a top-antitop pair at next-to-leading order accuracy using matrix elements obtained from the HELAC-Oneloop package. The NLO prediction was interfaced to the PYTHIA and HERWIG shower Monte Carlo programs with the help of POWHEG-Box, allowing for decays of massive particles, showering and hadronization, thus leading to final results at the hadron level.
We present the implementation of electroweak Zjj and Wjj production via vector boson fusion with fully leptonic decays at NLO QCD in the POWHEG framework. These processes represent an important background to Higgs searches in vector boson fusion, but they also can be seen as signal processes to study anomalous triple vector boson couplings as well as the impact of a central jet veto. Observables related to the third jet are sensitive to the parton shower which is used, a fact which is demonstrated by a comparison between PYTHIA, the standard angular-ordered HERWIG++ shower and the new p_T-orde…
We present a calculation of the next-to-leading order QCD corrections to slepton pair production in association with a jet at the LHC together with their implementation in the POWHEG BOX. For the simulation of parton-shower effects and the decays of the sleptons we employ the multi-purpose Monte-Carlo program PYTHIA. We discuss the impact of next-to-leading order QCD corrections on experimentally accessible distributions and illustrate how the parton shower can modify observables that are sensitive to QCD radiation effects. Having full control on the hard jet in the process, we provide precise…
We give a prescription for attaching parton showers to next-to-leading order (NLO) partonic jet cross sections in electron-positron annihilation. Our method effectively extends to NLO the scheme of Catani, Krauss, Kuhn, and Webber for matching between m hard jets and (m+1) hard jets. The matching between parton splitting as part of a shower and parton splitting as part of NLO matrix elements is based on the Catani-Seymour dipole subtraction method that is commonly used for removing the singularities from the NLO matrix elements.}
We present a study of Higgs hadroproduction through vector-boson fusion at the NLO in QCD matched with parton showers. We discuss the matching systematics affecting this process through a comparison of the aMC@NLO predictions with the POWHEG and the pure-NLO ones.
We present the scalar leptoquark pair production process at the LHC computed at the next-to-leading order in QCD, matched to the PYTHIA parton shower using the MC@NLO formalism. We consider the leading order decay of a leptoquark to a lepton ($e,μ,τ$ or $ν_e,ν_μ,ν_τ$) and a jet and observe the effects of parton shower on the final states. For demonstration, we display the kinametical distributions of a selection of observables along with their scale uncertainties for the 13 TeV LHC. We also present pair production cross sections and $K$-factors using massless five-quark flavor scheme for diffe…
The main ideas of the NLO calculations in Parton Reggeization Approach are illustrated on the example of the simplest NLO subprocess, which contributes to DIS: $γ^\star+R\to q + \bar{q}$. The double counting with the LO contribution $γ^\star + Q \to q$ is resolved. The problem of matching of the NLO results for single-scale observables in the Parton Reggeization Approach on the corresponding NLO results in the Collinear Parton Model is considered. In the developed framework, the usual NLO PDFs in the $\overline{MS}$-scheme can be consistently used as the collinear input for the NLO calculation…
An NLO photon parton parametrization is presented based on the existing $F_2^γ$ measurements from $e^+e^-$ data and the low-$x$ proton structure function from $ep$ interactions. Also included in the extraction of the NLO parton distribution functions are the dijets data coming from $γp \to j_1 + j_2 +X$. The new parametrization is compared to other available NLO parametrizations.
We present predictions for the hadroproduction of $t\bar{t}b\bar{b}$ final states at the LHC with collision energies $\sqrt{s}$ = 8TeV and 14TeV at NLO accuracy matched with parton shower, as obtained with PowHel+ PYTHIA. We quantify the effects of parton shower and hadronization. We find these are in general moderate except the effect of the decay of heavy particles, which can modify significantly some distributions, like that of the invariant mass of the two leading b-jets. We also show kinematic distributions obtained with cuts inspired to those recently employed by the CMS collaboration. F…
We present a calculation of the next-to-leading order (NLO) QCD corrections to the hadroproduction process $gg\to ZZ \to e^+e^- μ^+ μ^-$, matched to the parton shower in the POWHEG framework. We take advantage of the POWHEG BOX tool for the implementation and rely on PYTHIA 8 for the showering and hadronization stages. We fully include $γ^*/Z$ interference effects, while also covering the single-resonant region. For this phenomenological study we focus on four lepton production as a signal process, neglecting all quark mass effects as well as the Higgs-mediated contributions, which are known t…
We present updated predictions for the cross-sections for pair production of squarks and gluinos at the LHC Run II. First of all, we update the calculations based on NLO+NLL partonic cross-sections by using the NNPDF3.0NLO global analysis. This study includes a full characterization of theoretical uncertainties from higher orders, PDFs and the strong coupling. Then, we explore the implications for this calculation of the recent NNPDF3.0 PDFs with NLO+NLL threshold resummation. We find that the shift in the results induced by the threshold-improved PDFs is within the total theory uncertainty ba…
The QCD coupling alpha_s is determined from a combined analysis of experimental e+e- and e-p jet data confronted to theoretical predictions of the energy evolution of the parton-to-hadron fragmentation functions (FFs) moments --multiplicity, peak, width, skewness-- at low fractional hadron momentum z. The impact of approximate next-to-leading order (NLO*) corrections plus next-to-next-to-leading log (NNLL) resummations, compared to previous LO+NLL calculations, is discussed. A global fit of the full set of existing data, amounting to 360 FF moments at collision energies sqrt(s)~1--200 GeV, res…
We present a calculation of the next-to-leading order (NLO) QCD corrections to gluon-induced electroweak gauge boson pair production, $gg \to ZZ$ and $gg \to W^+W^-$, matched to the PYTHIA8 parton shower in the POWHEG approach. The calculation consistently incorporates the continuum background, the Higgs-mediated $gg\to H^* \to VV$ process, and their interference. We consider leptonic decay modes of the massive vector bosons and retain offshell and non-resonant contributions. The processes considered are loop-induced at leading order and thus contain two-loop virtual contributions as well as l…
The decade-old technique of combining NLO-corrected hard process with LO-level parton shower Monte Carlo is now mature and used in practice of the QCD calculations in the LHC data analysis. The next step, its extension to an NNLO-corrected hard process combined with the NLO-level parton shower Monte Carlo, will require development of the latter component. It does not exist yet in a complete form. In this note we describe recent progress in developing the NLO parton shower for the initial-state hadron beams. The technique of adding NLO corrections in the fully exclusive form (defined in recent …
We show how parton distributions unintegrated over the parton transverse momentum, k_t, may be generated, at NLO accuracy, from the known integrated (DGLAP-evolved) parton densities determined from global data analyses. A few numerical examples are given, which demonstrate that sufficient accuracy is obtained by keeping only the LO splitting functions together with the NLO integrated parton densities. However, it is important to keep the precise kinematics of the process, by taking the scale to be the virtuality rather than the transverse momentum, in order to be consistent with the calculatio…
We discuss the Standard Model Effective Field Theory (SM-EFT) contributions to neutral- and charge-current Drell-Yan production, associated production of the Higgs and a vector boson, and Higgs boson production via vector boson fusion. We consider all the dimension-six SM-EFT operators that contribute to these processes at leading order, include next-to-leading order QCD corrections, and interface them with parton showering and hadronization in Pythia8 according to the POWHEG method. We discuss existing constraints on the coefficients of dimension-six operators and identify differential and an…
We describe the \POWHEGBOX{} package, a general computer code framework for implementing NLO calculations in Shower Monte Carlo programs according to the \POWHEG{} method.
In this review a new method is presented for attaching parton shower algorithms to NLO partonic jet cross sections in electron-positron annihilation. Our method is based on the Catani-Seymour dipole subtraction method and also uses an adaptation of the matching scheme of Catani, Krauss, Kuhn, and Webber.
Motivated by asking how to combine parton showers with nonleading QCD matrix elements, we discuss a subtractive technique based on gauge-invariant Wilson-line operators and how this can be used to treat the soft region.
We compare a NLO W gamma matrix element generator with the leading order calculation in Pythia . A matching scheme between a next-to-leading order W gamma matrix element generator by Baur et. al. and the Pythia parton shower is presented. The NLO package produces W gamma+0 jet and W gamma+1jet final states in the hard scattering and the objective is to consistently match these to the initial state radiation from Pythia parton shower. The proposed methodology preserves both the rate of the hard scattering process as well as various kinematic distributions of experimental interest.
We perform a detailed study of NLO parton shower matching uncertainties in Higgs boson pair production through gluon fusion at the LHC based on a generic and process independent implementation of NLO subtraction and parton shower matching schemes for loop-induced processes in the Sherpa event generator. We take into account the full top-quark mass dependence in the two-loop virtual corrections and compare the results to an effective theory approximation. In the full calculation, our findings suggest large parton shower matching uncertainties that are absent in the effective theory approximatio…
We present the interplay between the new IR-improved DGLAP-CS theory and the precision of NLO parton shower/ME matched MC`s as it is realized by the new MC Herwiri1.031 in interface to MC@NLO. We discuss phenomenological implications using comparisons with recent LHC data on single heavy gauge boson production.
The project of constructing a complete NLO-level Parton Shower Monte Carlo for the QCD processes developed in IFJ PAN in Krakow is reviewed. Four issues are discussed: (1) the extension of the standard inclusive collinear factorization into a new, fully exclusive scheme; (2) reconstruction of the LO Parton Shower in the new scheme; (3) inclusion of the exclusive NLO corrections into the hard process and (4) inclusion of the exclusive NLO corrections into the evolution (ladder) part.
We briefly summarize the Nagy-Soper parton shower and the MC@NLO-like matching scheme. Results obtained using HELAC-NLO framework in conjunction with DEDUCTOR for top quark pair production in association with one hard jet at the LHC are presented. A comparison of our results with other matching schemes and other parton showers is also discussed for various observables.
We present an implementation of electroweak W+W-jj production at hadron colliders in the POWHEG framework, a method that allows the interfacing of a next-to-leading order QCD calculation with parton shower Monte Carlo programs. We provide results for both, fully and semi-leptonic decay modes of the weak bosons, taking resonant and non-resonant contributions and spin correlations of the final-state particles into account. To illustrate the versatility of our implementation, we provide phenomenological results for two representative scenarios with a light and with a heavy Higgs boson, respective…
A new NLO DGLAP QCD fit to recent inclusive diffractive DIS data from the H1 collaboration is presented. Diffractive parton distributions are extracted, including their experimental and theoretical uncertainties. The parton distributions are used for comparisons with recent diffractive final state data from HERA and the TEVATRON.
We extend the lowest-order matching of tree-level matrix elements with parton showers to give a complete description at the next higher perturbative accuracy in alpha_s at both small and large jet resolutions, which has not been achieved so far. This requires the combination of the higher-order resummation of large Sudakov logarithms at small values of the jet resolution variable with the full next-to-leading order (NLO) matrix-element corrections at large values. As a by-product this combination naturally leads to a smooth connection of the NLO calculations for different jet multiplicities. I…
The MC@NLO method as implemented in the Sherpa MC generator is presented using the production of W-bosons in conjunction with up to three jets as an example. Corresponding results computed at next-to leading order in QCD and including parton shower corrections are compared to recent experimental data from the Large Hadron Collider.
We present results for the QCD production of Z/γ + 2 jets matched with parton showers using the POWHEG method. Some technicalities relevant for the merging of NLO corrections for this process with parton showers are discussed, and results for typical distributions are shown, in presence of different sets of cuts. A comparison with ATLAS data is also presented, and good agreement is found.
We discuss the positivity of the hadron density matrix in QCD. This basic property is shown to be preserved by QCD evolution, provided the relation $|ΔP_{ij}(z)| \leq P_{ij}$ is valid for all kernels for $z < 1$, and the usual "+" prescription is used. We comment on the positivity restrictions for the choice of the NLO factorization scheme for the evolution of the spin-dependent parton distributions.
An MC@NLO-like matching of NLO QCD calculations with the Nagy-Soper parton shower is briefly summarised. Uncertainties and ambiguities of the matching scheme are shortly discussed. A few results for the pp -> ttj + X production process at the LHC with sqrt(s) = 8 TeV are also shown. All results have been obtained using the Nagy-Soper parton shower implementation in the DEDUCTOR program together with the HELAC-NLO framework.
The aim of this work is to describe in detail the POWHEG method, first suggested by one of the authors, for interfacing parton-shower generators with NLO QCD computations. We describe the method in its full generality, and then specify its features in two subtraction frameworks for NLO calculations: the Catani-Seymour and the Frixione-Kunszt-Signer approach. Two examples are discussed in detail in both approaches: the production of hadrons in e+e- collisions, and the Drell-Yan vector-boson production in hadronic collisions.
The new methodology of adding QCD NLO corrections in the initial state Monte Carlo parton shower (hard process part) is presented using process of the heavy boson production at the LHC as an example. Despite the simplified model of the process, presented numerical results prove that the basic concept of the new methodology works correctly in the numerical environment of the Monte Carlo parton shower event generator. The presented method is an alternative to the well established methods, MC@NLO and POWHEG. Refinements of the new method with better computer CPU time efficiency are also discussed…
We quantify uncertainties in the Monte-Carlo simulation of inclusive and dijet final states, which arise from using the MC@NLO technique for matching next-to-leading order parton level calculations and parton showers. We analyse a large variety of data from early measurements at the LHC. In regions of phase space where Sudakov logarithms dominate over high-energy effects, we observe that the main uncertainty can be ascribed to the free parameters of the parton shower. In complementary regions, the main uncertainty stems from the considerable freedom in the simulation of underlying events.
Next steps in development of the KrkNLO method of implementing NLO QCD corrections to hard processes in parton shower Monte Carlo programs are presented. This new method is a simpler alternative to other well-known approaches, such as MC@NLO and POWHEG. The KrkNLO method owns its simplicity to the use of parton distribution functions (PDFs) in a new, so-called Monte Carlo (MC), factorization scheme which was recently fully defined for the first time. Preliminary numerical results for the Higgs-boson production process are also presented.
A new method to construct event-generators based on next-to-leading order QCD matrix-elements and leading-logarithmic parton showers is proposed. Matrix elements of loop diagrams as well as those of a tree level can be generated using an automatic system. A soft/collinear singularity is treated using a leading-log subtraction method. Higher order re-summation of the soft/collinear correction by the parton shower method is combined with the NLO matrix-element without any double-counting in this method.
In this paper, we present the next-to-leading order predictions for three photon production in the Standard Model, matched to the parton shower using the MC@NLO formalism. We have studied the role of parton shower on various observables and shown a selection of results for the 14 TeV LHC.
We review the methods developed for combining the parton shower approximation to QCD with fixed-order perturbation theory, in such a way as to achieve next-to-leading-order (NLO) accuracy for inclusive observables. This has made it possible to generate fully-simulated hadronic final states with the precision and stability of NLO calculations. We explain the underlying theory of the existing methods, MC@NLO and POWHEG, together with their similarities, differences, achievements and limitations. For illustration we mainly compare results on Higgs boson production at the LHC, with particular emph…
The associated production of charged Higgs bosons and top quarks at hadron colliders is an important discovery channel to establish the existence of a non-minimal Higgs sector. Here, we present details of a next-to-leading order (NLO) calculation of this process using the Catani-Seymour dipole formalism and describe its implementation in POWHEG, which allows to match NLO calculations to parton showers. Numerical predictions are presented using the PYTHIA parton shower and are compared to those obtained previously at fixed order, to a leading order calculation matched to the PYTHIA parton showe…
We present a selection of results from our recent study of $pp\to t\bar{t}W^\pm$ production matched to partons showers at NLO QCD at the LHC. Theoretical predictions are obtained at perturbative orders $\mathcal{O}(α_s^3α)$ and $\mathcal{O}(α_sα^3)$, where the different contributions are studied first separately at the inclusive level before being combined within a realistic two same-sign lepton signature. We investigate in detail uncertainties originating from missing higher-order corrections and from the parton-shower matching scheme employed.
We present new NLO sets of parton distributions in real photons based on a scheme invariant definition of the non-perturbative input. We compare the theoretical predictions with LEP data and a best fit allows us to constrain the parameters of the distributions. The shape of the gluon distribution is poorly constrained and we consider the possibility to measure it in photoproduction experiments. Three parametrizations which aim to take into account the scattering of LEP data are proposed. They are compared to other NLO parametrizations.
We propose a new approach for combining next-to-leading order (NLO) and parton shower (PS) calculations so as to obtain three core features: (a) applicability to general showers, as with the MCatNLO and POWHEG methods; (b) positive-weight events, as with the KrkNLO and POWHEG methods; and (c) all showering attributed to the parton shower code, as with the MCatNLO and KrkNLO methods. This is achieved by using multiplicative matching in phase space regions where the shower overestimates the matrix element and accumulative (additive) matching in regions where the shower underestimates the matrix …
We present a next-to-leading order (NLO) calculation of $t\bar{t}$ production in hadronic collisions interfaced to shower generators according to the POWHEG method. We start from an NLO result from previous work, obtained in the zero width limit, where radiative corrections to both production and decays are included. The POWHEG interface required an extension of the POWHEG BOX framework, in order to deal with radiation from the decay of resonances. This extension is fully general (i.e. it can be applied in principle to any process considered in the zero width limit), and is here applied for th…
