R. S. Thorne, A. D. Martin, W. J. Stirling, G. Watt
We outline the historical development of MRST/MSTW parton distribution functions (PDFs), and clarify how they should be regarded when compared to the most up-to-date 2008 MSTW sets, noting which sets are now obsolete and the reasons why.
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I present results on updates on PDFs which are obtained within the general framework which led to the MSTW2008 PDF sets. There are some theory and procedural improvements and a variety of new data sets, including many relevant up-to-date LHC data. A new set of PDFs is very close to being finalised, with no significant changes expected to the preliminary PDFs shown here.
We briefly summarise the "MSTW 2008" determination of parton distribution functions (PDFs), and subsequent follow-up studies, before reviewing some topical issues concerning the PDF dependence of cross sections at the Tevatron and LHC. We update a recently published study of benchmark Standard Model total cross sections (W, Z, gg->H and t-tbar production) at the 7 TeV LHC, where we account for all publicly available PDF sets and we compare to LHC data for W, Z, and t-tbar production. We show the sensitivity of the Higgs cross sections to the gluon distribution, then we demonstrate the ability …
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…
We investigate the Monte Carlo approach to propagation of experimental uncertainties within the context of the established "MSTW 2008" global analysis of parton distribution functions (PDFs) of the proton at next-to-leading order in the strong coupling. We show that the Monte Carlo approach using replicas of the original data gives PDF uncertainties in good agreement with the usual Hessian approach using the standard Delta(chi^2) = 1 criterion, then we explore potential parameterisation bias by increasing the number of free parameters, concluding that any parameterisation bias is likely to be …
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 …
A selection of the latest and most frequently used PDFs is incorporated in PYTHIA8, including the MC-adapted PDFs from the MSTW and CTEQ collaborations. This thesis examines the differences in PDFs as well as the effect they have on results of simulations. The results are also compared to data collected by the CDF experiment.
We previously investigated the compatibility of the $Kimber$-$Martin$-$Ryskin$ ($KMR$) $unintegrated$ parton distribution functions ($UPDF$) with the experimental data on the proton (longitudinal) structure functions ($PSF$ ($PLSF$)). Recently $Golec-Biernat$ and $Stasto$ ($GBS$) demonstrated that the differential version of $KMR$ prescription and the implementations of angular (strong) ordering ($AOC$ ($SOC$)) constraints, cause the negative-discontinuous $UPDF$ with the ordinary parton distribution functions ($PDF$) as the input, which leads to a sizable effect on the calculation of $PSF$. I…
We study the sensitivity of our recent MSTW 2008 NLO and NNLO PDF analyses to the values of the charm- and bottom-quark masses, and we provide additional public PDF sets for a wide range of these heavy-quark masses. We quantify the impact of varying m_c and m_b on the cross sections for W, Z and Higgs production at the Tevatron and the LHC. We generate 3- and 4-flavour versions of the (5-flavour) MSTW 2008 PDFs by evolving the input PDFs and alpha_S determined from fits in the 5-flavour scheme, including the eigenvector PDF sets necessary for calculation of PDF uncertainties. As an example of …
We present updated leading-order, next-to-leading order and next-to-next-to-leading order parton distribution functions ("MSTW 2008") determined from global analysis of hard-scattering data within the standard framework of leading-twist fixed-order collinear factorisation in the MSbar scheme. These parton distributions supersede the previously available "MRST" sets and should be used for the first LHC data-taking and for the associated theoretical calculations. New data sets fitted include CCFR/NuTeV dimuon cross sections, which constrain the strange quark and antiquark distributions, and Teva…
We present a new calculation of the cross sections for charged current (CC) and neutral current (NC) $νN$ and $\barν N$ interactions in the neutrino energy range $10^{4}<E_ν<10^{12}$ GeV using the most recent MSTW parton distribution functions (PDFs), MSTW 2008. We also present the associated uncertainties propagated from the PDFs, as well as parametrizations of the cross section central values, their uncertainty bounds, and the inelasticity distributions for ease of use in Monte Carlo simulations. For the latter we only provide parametrizations for energies above $10^7$ GeV. Finally, we asses…
The longitudinal proton structure function, $F_L(x,Q^2)$, from the $k_t$ factorization formalism by using the unintegrated parton distribution functions (UPDF) which are generated through the KMR and MRW procedures. The LO UPDF of the KMR prescription is extracted, by taking into account the PDF of Martin et al, i.e. MSTW2008-LO and MRST99-NLO and next, the NLO UPDF of the MRW scheme is generated through the set of MSTW2008-NLO PDF as the inputs. The different aspects of $F_L(x,Q^2)$ in the two approaches, as well as its perturbative and non-perturbative parts are calculated. Then the comparis…
We discuss selected topics in the forthcoming MSTW 2008 determination of parton distributions by global analysis. The tolerance parameter controlling the uncertainties on the parton distributions is now determined by a new dynamic procedure for each eigenvector of the covariance matrix. New data sets fitted include Tevatron Run II data on inclusive jet production, the lepton charge asymmetry from W decays and the Z rapidity distribution. Predictions are given for the total W and Z cross sections at the Tevatron and LHC.
A "meta-analysis" is a method for comparison and combination of nonperturbative parton distribution functions (PDFs) in a nucleon obtained with heterogeneous procedures and assumptions. Each input parton distribution set is converted into a "meta-parametrization" based on a common functional form. By analyzing parameters of the meta-parametrizations from all input PDF ensembles, a combined PDF ensemble can be produced that has a smaller total number of PDF member sets than the original ensembles. The meta-parametrizations simplify the computation of the PDF uncertainty in theoretical predictio…
We present sets of parton distribution functions (PDFs), based on the NNPDF3.0 family, which include the photon PDF from the NNPDF2.3QED sets, and leading-order QED contributions to the DGLAP evolution as implemented in the public code APFEL. The aim is to combine our state-of-the-art determination of quark and gluon PDFs with the so far only direct determination of the photon PDF from LHC data. In addition, the use of APFEL allowed us to employ a solution of the DGLAP equation that, differently from that used for the NNPDF2.3QED sets, includes QED corrections in a more accurate way. We briefl…
We present a set of parton distribution functions (PDFs), based on the NNPDF2.3 set, which includes a photon PDF, and QED contributions to parton evolution. We describe the implementation of the combined QCD+QED evolution in the NNPDF framework. We then provide a first determination of the full set of PDFs based on deep-inelastic scattering data and LHC data for W and Z/gamma* Drell-Yan production, using leading-order QED and NLO or NNLO QCD. We compare the ensuing NNPDF2.3QED PDF set to the older MRST2004QED set. We perform a preliminary investigation of the phenomenological implications of N…
The level of precision achieved by the experimental measurements at the LHC requires the inclusion of higher order electroweak effects to the processes of $ pp $ scattering. In particular the photon-induced process $ γγ\to \ell^+\ell^- $ make a significant contribution ($ \sim 10 \%$) to the dilepton invariant mass distribution. To evaluate the cross-section of this process one need to know the parton distribution function (PDF) of the photon in the proton $ γ(x,μ^2) $. The aim of the current study is to investigate the impact of QED corrections on PDFs and describe the implementation of QED-m…
In the extra dimension models of ADD and RS we study the dependence of the various parton distribution functions on observable of Drell-Yan process to NLO in QCD at LHC and Tevatron energies. Uncertainties at LHC due to factorisation scales in going from leading to next-to-leading order in QCD for the various distributions get reduced by about 2.75 times for a $μ_F$ range $0.5 ~Q < μ_F < 1.5 ~Q$. Further uncertainties arising from the error on experimental data are estimated using the MRST parton distribution functions.
We present a systematic study of uncertainties due to parton distributions and the strong coupling on the gluon-fusion production cross section of the Standard Model Higgs at the Tevatron and LHC colliders. We compare procedures and results when three recent sets of PDFs are used, CTEQ6.6, MSTW08 and NNPDF1.2, and we discuss specifically the way PDF and strong coupling uncertainties are combined. We find that results obtained from different PDF sets are in reasonable agreement if a common value of the strong coupling is adopted. We show that the addition in quadrature of PDF and alphas uncerta…
We study the charged current Drell-Yan process and we evaluate the proton parton densities uncertainties on the lepton transverse momentum distribution and their impact on the determination of the W-boson mass. We consider the global PDF sets CT10, MSTW2008CPdeut, NNPDF2.3, NNPDF3.0, MMHT2014, and apply the PDF4LHC recipe to combine the individual results, obtaining an uncertainty on MW that ranges between +-18 and +-24 MeV, depending on the final state, collider energy and kind. We discuss the dependence of the uncertainty on the acceptance cuts and the role of the individual parton densities…
We compute the next-to-leading order QCD predictions for the vertical flux of atmospheric muons and neutrinos from decays of charmed particles, for different PDF's (MRS-R1, MRS-R2, CTEQ-4M and MRST) and different extrapolations of these at small partonic momentum fraction x. We find that the predicted fluxes vary up to almost two orders of magnitude at the largest energies studied, depending on the chosen extrapolation of the PDF's. We show that the spectral index of the atmospheric leptonic fluxes depends linearly on the slope of the gluon distribution function at very small x. This suggests …
I consider variations in the definitions, at next-to-leading order (NLO) and at next-to-next-to leading order (NNLO), of a General-Mass Variable Flavour Number Scheme (GM-VFNS) for heavy flavour structure functions. I also define a new "optimal" scheme choice improving the smoothness of the transition from one flavour number to the next. I investigate the variation of the structure function for a fixed set of parton distribution functions (PDFs) and also the change in the PDFs when a new MSTW2008-type global fit to data is performed for each GM-VFNS. At NLO the parton distributions, and predic…
We study at a quantitative level the impact of the uncertainties on the value of the W boson mass measured at hadron colliders due to: the proton parton distribution functions (PDFs), the value of the strong coupling constant alpha_S and the value of the charm mass used in the PDF determination. The value of the W boson mass is extracted, by means of a template fit technique, from the lepton-pair transverse mass distribution measured in the charged current Drell-Yan process. We study the determination of M_W at the Tevatron and at the LHC with 7 and 14 TeV of center-of-mass energy in a realist…
We present a detailed comparison of the most recent sets of NNLO PDFs from the ABM, CT, HERAPDF, MSTW and NNPDF collaborations. We compare parton distributions at low and high scales and parton luminosities relevant for LHC phenomenology. We study the PDF dependence of LHC benchmark inclusive cross sections and differential distributions for electroweak boson and jet production in the cases in which the experimental covariance matrix is available. We quantify the agreement between data and theory by computing the chi2 for each data set with all the various PDFs. PDF comparisons are performed c…
We present a comparative study of the invariant mass and rapidity distributions in Drell-Yan lepton pair production, with particular emphasis on the role played by the QCD evolution. We focus our study around the Z resonance ($50 <Q < 200$ GeV) and perform a general analysis of the factorization/renormalization scale dependence of the cross sections, with the two scales included both in the evolution and in the hard scatterings. We also present the variations of the cross sections due to the errors on the parton distributions (pdf's) and an analysis of the corresponding $K$-factors. Prediction…
In a series of papers, we have investigated the compatibility of the $Kimber$-$Martin$-$Ryskin$ ($KMR$) and $Martin$-$Ryskin$-$Watt$ ($MRW$) $unintegrated$ parton distribution functions ($UPDF$) as well as the description of the experimental data on the proton structure functions. The present work is a sequel to that survey, via calculation of the transverse momentum distribution of the electro-weak gauge vector bosons in the $k_t$-factorization scheme, by the means of the $KMR$, the $LO\;MRW$ and the $NLO\;MRW$ $UPDF$, in the next-to leading order ($NLO$). To this end, we have calculated and …
In this work, we discuss: (i) The ratios of different parton distribution functions (PDFs), i.e., MMHT2014, CJ15, CTEQ6l1, HERAPDF15, MSTW2008, HERAPDF20 and MSHT20, and the corresponding Kimber-Martin-Ryskin (KMR) unintegrated parton distribution functions (UPDFs) sets versus the hard scale $Q^2$, to find out the sensibility of the KMR UPDFs with respect to the input PDFs sets. It is shown that there is not much difference between the different input-PDFs or corresponding UPDFs sets ratios. (ii) Then, the dependence of proton $k_t$-factorization structure functions on the different UPDFs sets…
Standard methods for higher-order calculations of QCD cross sections in hadron-induced collisions are time-consuming. The fastNLO project uses multi-dimensional interpolation techniques to convert the convolutions of perturbative coefficients with parton distribution functions and the strong coupling into simple products. By integrating the perturbative coefficients for a given observable with interpolation kernels, fastNLO can store the results of the time-consuming folding integrals in tables, which subsequently are used for very fast rederivations of the same observable for arbitrary parton…
We provide an assessment of the impact of parton distributions on the determination of LHC processes, and of the accuracy with which parton distributions (PDFs) can be extracted from data, in particular from current and forthcoming HERA experiments. We give an overview of reference LHC processes and their associated PDF uncertainties, and study in detail W and Z production at the LHC. We discuss the precision which may be obtained from the analysis of existing HERA data, tests of consistency of HERA data from different experiments, and the combination of these data. We determine further improv…
It is anticipated that hard double parton scatterings will occur frequently in the collisions of the LHC, producing interesting signals and significant backgrounds to certain single scattering processes. For double scattering processes in which the same hard scale t = ln(Q^2) is involved in both collisions, we require the double parton distributions (dPDFs) D_h^{j_1j_2}(x_1,x_2;t) in order to make theoretical predictions of their rates and properties. We describe the development of a new set of leading order dPDFs that represents an improvement on approaches used previously. First, we derive m…
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