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 $\overline{\mathrm{MS}}$
 
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 Tevatron Run II data on inclusive jet production, the lepton charge asymmetry from W decays and the Z rapidity distribution. Uncertainties are propagated from the experimental errors on the fitted data points using a new dynamic procedure for each eigenvector of the covariance matrix. We discuss the major changes compared to previous MRST fits, briefly compare to parton distributions obtained by other fitting groups, and give predictions for the W and Z total cross sections at the Tevatron and LHC.

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Parton distributions for the LHC

We provide an updated recommendation for the usage of sets of parton distribution functions (PDFs) and the assessment of PDF and PDF+$\alpha_s$ uncertainties suitable for applications at the LHC Run II. We review developments since the previous PDF4LHC recommendation, and discuss and compare the new generation of PDFs, which include substantial information from experimental data from the Run I of the LHC. We then propose a new prescription for the combination of a suitable subset of the available PDF sets, which is presented in terms of a single combined PDF set. We finally discuss tools which allow for the delivery of this combined set in terms of optimized sets of Hessian eigenvectors or Monte Carlo replicas, and their usage, and provide some examples of their application to LHC phenomenology.

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PDF4LHC recommendations for LHC Run II

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This Report summarizes the results of the first 10 months' activities of the LHC Higgs Cross Sections Working Group. The main goal of the working group was to present the status-of-art on Higgs Physics at the LHC integrating all new results that have appeared in the last few years. The Report is more than a mere collection of the proceedings of the general meetings. The subgroups have been working in different directions. An attempt has been made to present the first Report from these subgroups in a complete and homogeneous form. The subgroups' contributions correspondingly comprise the main parts of the Report. A significant amount of work has been performed in providing higher-order corrections to the Higgs-boson cross sections and pinning down the theoretical uncertainty of the Standard Model predictions. This Report comprises explicit numerical results on total cross sections, leaving the issues of event selection cuts and differential distributions to future publications. The subjects for further study are identified.

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Handbook of LHC Higgs Cross Sections: 1. Inclusive Observables

This note provides an interim summary of the current recommendations of the PDF4LHC working group for the use of parton distribution functions (PDFs) and of PDF uncertainties at the LHC, for cross section and cross section uncertainty calculations. It also contains a succinct user guide to the computation of PDFs, uncertainties and correlations using available PDF sets. A companion note (the PDF4LHC Working Group Interim Report) summarizes predictions for benchmark cross sections at the LHC at NLO using modern PDFs currently available from 6 PDF fitting groups.

/pdf/the-pdf4lhc-working-group-interim-recommendations-1qvc8xxa5r.pdf

The PDF4LHC Working Group Interim Recommendations

Utilizing recent DIS measurements (F2,L) and data on dilepton and high-ET jet production we determine the dynamical parton distributions of the nucleon generated radiatively from valence-like positive input distributions at optimally chosen low resolution scales. These are compared with ‘standard’ distributions generated from positive input distributions at some fixed and higher resolution scale. It is shown that up to the next-to-leading order NLO(
 $\overline{\text{MS}}$
 , DIS) of perturbative QCD considered in this paper, the uncertainties of the dynamical distributions are, as expected, smaller than those of their standard counterparts. This holds true in particular in the presently unexplored extremely small-x region relevant for evaluating ultrahigh energy cross sections in astrophysical applications. It is noted that our new dynamical distributions are compatible, within the presently determined uncertainties, with previously determined dynamical parton distributions.

Dynamical parton distributions of the nucleon and very small-x physics

Utilizing recent DIS measurements (F_{2,L}) and data on dilepton and high-E_{T} jet production we determine the dynamical parton distributions of the nucleon generated radiatively from valence-like positive input distributions at optimally chosen low resolution scales. These are compared with `standard' distributions generated from positive input distributions at some fixed and higher resolution scale. It is shown that up to the next to leading order NLO(\bar{MS}, DIS) of perturbative QCD considered in this paper, the uncertainties of the dynamical distributions are, as expected, smaller than those of their standard counterparts. This holds true in particular in the presently unexplored extremely small-x region relevant for evaluating ultrahigh energy cross sections in astrophysical applications. It is noted that our new dynamical distributions are compatible, within the presently determined uncertainties, with previously determined dynamical parton distributions.

Isospin violating valence and sea distributions are evaluated due to QED leading O(�) corrections to the standard QCD evolution equations. Unique perturbative predictions are obtained within the radiative parton model, and confirm earlier results. Nonperturbative contributions have been estimated and depend on a single free parameter chosen to be the current quark mass. The relevance of our predictions for extracting sin 2 �W from DIS �(¯�)N data (‘NuTeV anomaly’) is discussed as well.

P. Jimenez-Delgado

Papers

Dynamical parton distributions of the nucleon and very small-x physics

Dynamical parton distributions of the nucleon and very small-x physics

Radiatively Generated Isospin Violations in the Nucleon