Abstract
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 predictions and provide an alternative to the 2010 PDF4LHC convention for combination of PDF uncertainties. As a practical example, we construct a META ensemble for computation of QCD observables at the Large Hadron Collider using the next-to-next-to-leading order PDF sets from CTEQ, MSTW, and NNPDF groups as the input. The META ensemble includes a central set that reproduces the average of LHC predictions based on the three input PDF ensembles and Hessian eigenvector sets for computing the combined PDF+α s uncertainty at a common QCD coupling strength of 0.118.
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ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].
CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].
Higgs Working Group Report, Snowmass’2013 Community Planning study, http://www.snowmass2013.org/tiki-index.php?page=The+Higgs+Boson.
J. Gao et al., The CT10 NNLO Global Analysis of QCD, Phys. Rev. D 89 (2014) 033009 [arXiv:1302.6246] [INSPIRE].
A.D. Martin, W.J. Stirling, R.S. Thorne and G. Watt, Parton distributions for the LHC, Eur. Phys. J. C 63 (2009) 189 [arXiv:0901.0002] [INSPIRE].
R.D. Ball et al., Parton distributions with LHC data, Nucl. Phys. B 867 (2013) 244 [arXiv:1207.1303] [INSPIRE].
S. Alekhin, J. Blumlein and S. Moch, Parton Distribution Functions and Benchmark Cross Sections at NNLO, Phys. Rev. D 86 (2012) 054009 [arXiv:1202.2281] [INSPIRE].
S. Alekhin, J. Bluemlein and S. Moch, The ABM parton distributions tuned to LHC data, Phys. Rev. D 89 (2014) 054028 [arXiv:1310.3059] [INSPIRE].
P. Jimenez-Delgado and E. Reya, Dynamical NNLO parton distributions, Phys. Rev. D 79 (2009) 074023 [arXiv:0810.4274] [INSPIRE].
P. Jimenez-Delgado and E. Reya, Variable Flavor Number Parton Distributions and Weak Gauge and Higgs Boson Production at Hadron Colliders at NNLO of QCD, Phys. Rev. D 80 (2009) 114011 [arXiv:0909.1711] [INSPIRE].
ZEUS and H1 collaborations, A.M. Cooper-Sarkar, PDF Fits at HERA, PoS(EPS-HEP2011)320 [arXiv:1112.2107] [INSPIRE].
J. Pumplin et al., Uncertainties of predictions from parton distribution functions. 2. The Hessian method, Phys. Rev. D 65 (2001) 014013 [hep-ph/0101032] [INSPIRE].
J. Pumplin et al., New generation of parton distributions with uncertainties from global QCD analysis, JHEP 07 (2002) 012 [hep-ph/0201195] [INSPIRE].
W.T. Giele and S. Keller, Implications of hadron collider observables on parton distribution function uncertainties, Phys. Rev. D 58 (1998) 094023 [hep-ph/9803393] [INSPIRE].
NNPDF collaboration, L. Del Debbio, S. Forte, J.I. Latorre, A. Piccione and J. Rojo, Neural network determination of parton distributions: the nonsinglet case, JHEP 03 (2007) 039 [hep-ph/0701127] [INSPIRE].
R.D. Ball et al., Parton distribution benchmarking with LHC Data, JHEP 04 (2013) 125 [arXiv:1211.5142] [INSPIRE].
J.F. Owens, A. Accardi and W. Melnitchouk, Global parton distributions with nuclear and finite-Q 2 corrections, Phys. Rev. D 87 (2013) 094012 [arXiv:1212.1702] [INSPIRE].
J. Pumplin, H.L. Lai and W.K. Tung, The Charm Parton Content of the Nucleon, Phys. Rev. D 75 (2007) 054029 [hep-ph/0701220] [INSPIRE].
S. Dulat et al., Intrinsic Charm Parton Distribution Functions from CTEQ-TEA Global Analysis, Phys. Rev. D 89 (2014) 073004 [arXiv:1309.0025] [INSPIRE].
A.D. Martin, R.G. Roberts, W.J. Stirling and R.S. Thorne, Parton distributions incorporating QED contributions, Eur. Phys. J. C 39 (2005) 155 [hep-ph/0411040] [INSPIRE].
NNPDF collaboration, R.D. Ball et al., Parton distributions with QED corrections, Nucl. Phys. B 877 (2013) 290 [arXiv:1308.0598] [INSPIRE].
E.M. Askanazi, K.A. Holcomb and S. Liuti, Self-Organizing Maps Parametrization of Deep Inelastic Structure Functions with Error Determination, arXiv:1309.7085 [INSPIRE].
K. Kovarik et al., CTEQ nuclear parton distribution functions, PoS(DIS 2013)274 [arXiv:1307.3454] [INSPIRE].
M. Hirai, S. Kumano and T.-H. Nagai, Determination of nuclear parton distribution functions and their uncertainties in next-to-leading order, Phys. Rev. C 76 (2007) 065207 [arXiv:0709.3038] [INSPIRE].
K.J. Eskola, H. Paukkunen and C.A. Salgado, EPS09: A New Generation of NLO and LO Nuclear Parton Distribution Functions, JHEP 04 (2009) 065 [arXiv:0902.4154] [INSPIRE].
D. de Florian, R. Sassot, P. Zurita and M. Stratmann, Global Analysis of Nuclear Parton Distributions, Phys. Rev. D 85 (2012) 074028 [arXiv:1112.6324] [INSPIRE].
M. Botje et al., The PDF4LHC Working Group Interim Recommendations, arXiv:1101.0538 [INSPIRE].
S. Alekhin et al., The PDF4LHC Working Group Interim Report, arXiv:1101.0536 [INSPIRE].
S. Forte and G. Watt, Progress in the Determination of the Partonic Structure of the Proton, Ann. Rev. Nucl. Part. Sci. 63 (2013) 291 [arXiv:1301.6754] [INSPIRE].
S. Forte, Parton distributions at the dawn of the LHC, Acta Phys. Polon. B 41 (2010) 2859 [arXiv:1011.5247] [INSPIRE].
Particle Data Group collaboration, J. Beringer et al., Review of Particle Physics (RPP), Phys. Rev. D 86 (2012) 010001 [INSPIRE].
P.M. Nadolsky and Z. Sullivan, PDF uncertainties in WH production at Tevatron, eConf C 010630 (2001) P510 [hep-ph/0110378] [INSPIRE].
P.M. Nadolsky et al., Implications of CTEQ global analysis for collider observables, Phys. Rev. D 78 (2008) 013004 [arXiv:0802.0007] [INSPIRE].
J. Pumplin, Parametrization dependence and Δχ2 in parton distribution fitting, Phys. Rev. D 82 (2010) 114020 [arXiv:0909.5176] [INSPIRE].
A. Glazov, S. Moch and V. Radescu, Parton Distribution Uncertainties using Smoothness Prior, Phys. Lett. B 695 (2011) 238 [arXiv:1009.6170] [INSPIRE].
A.D. Martin et al., Extended Parameterisations for MSTW PDFs and their effect on Lepton Charge Asymmetry from W Decays, Eur. Phys. J. C 73 (2013) 2318 [arXiv:1211.1215] [INSPIRE].
S. Moch, J.A.M. Vermaseren and A. Vogt, The Three loop splitting functions in QCD: The Nonsinglet case, Nucl. Phys. B 688 (2004) 101 [hep-ph/0403192] [INSPIRE].
A. Vogt, S. Moch and J.A.M. Vermaseren, The Three-loop splitting functions in QCD: The Singlet case, Nucl. Phys. B 691 (2004) 129 [hep-ph/0404111] [INSPIRE].
G.P. Salam and J. Rojo, A Higher Order Perturbative Parton Evolution Toolkit (HOPPET), Comput. Phys. Commun. 180 (2009) 120 [arXiv:0804.3755] [INSPIRE].
C. Anastasiou, L.J. Dixon, K. Melnikov and F. Petriello, High precision QCD at hadron colliders: Electroweak gauge boson rapidity distributions at NNLO, Phys. Rev. D 69 (2004) 094008 [hep-ph/0312266] [INSPIRE].
C. Anastasiou, S. Buehler, F. Herzog and A. Lazopoulos, Total cross-section for Higgs boson hadroproduction with anomalous Standard Model interactions, JHEP 12 (2011) 058 [arXiv:1107.0683] [INSPIRE].
P. Bärnreuther, M. Czakon and A. Mitov, Percent Level Precision Physics at the Tevatron: First Genuine NNLO QCD Corrections to \( q\overline{q} \) → \( t\overline{t} \) + X, Phys. Rev. Lett. 109 (2012) 132001 [arXiv:1204.5201] [INSPIRE].
M. Czakon and A. Mitov, NNLO corrections to top-pair production at hadron colliders: the all-fermionic scattering channels, JHEP 12 (2012) 054 [arXiv:1207.0236] [INSPIRE].
M. Czakon and A. Mitov, NNLO corrections to top pair production at hadron colliders: the quark-gluon reaction, JHEP 01 (2013) 080 [arXiv:1210.6832] [INSPIRE].
M. Czakon and A. Mitov, Top++: A Program for the Calculation of the Top-Pair Cross-Section at Hadron Colliders, arXiv:1112.5675 [INSPIRE].
M. Beneke, P. Falgari and C. Schwinn, Soft radiation in heavy-particle pair production: all-order colour structure and two-loop anomalous dimension, Nucl. Phys. B 828 (2010) 69 [arXiv:0907.1443] [INSPIRE].
M. Czakon, A. Mitov and G.F. Sterman, Threshold Resummation for Top-Pair Hadroproduction to Next-to-Next-to-Leading Log, Phys. Rev. D 80 (2009) 074017 [arXiv:0907.1790] [INSPIRE].
M. Cacciari, M. Czakon, M. Mangano, A. Mitov and P. Nason, Top-pair production at hadron colliders with next-to-next-to-leading logarithmic soft-gluon resummation, Phys. Lett. B 710 (2012) 612 [arXiv:1111.5869] [INSPIRE].
fastNLO collaboration, M. Wobisch, D. Britzger, T. Kluge, K. Rabbertz and F. Stober, Theory-Data Comparisons for Jet Measurements in Hadron-Induced Processes, arXiv:1109.1310 [INSPIRE].
ATLAS collaboration, Measurement of inclusive jet and dijet production in pp collisions at \( \sqrt{s} \) = 7 TeV using the ATLAS detector, Phys. Rev. D 86 (2012) 014022 [arXiv:1112.6297] [INSPIRE].
G. Watt and R.S. Thorne, Study of Monte Carlo approach to experimental uncertainty propagation with MSTW 2008 PDFs, JHEP 08 (2012) 052 [arXiv:1205.4024] [INSPIRE].
J. Pumplin et al., Collider Inclusive Jet Data and the Gluon Distribution, Phys. Rev. D 80 (2009) 014019 [arXiv:0904.2424] [INSPIRE].
J. Gao, J. Huston and P.M. Nadolsky, in preparation.
H.-L. Lai et al., Uncertainty induced by QCD coupling in the CTEQ global analysis of parton distributions, Phys. Rev. D 82 (2010) 054021 [arXiv:1004.4624] [INSPIRE].
A.D. Martin, W.J. Stirling, R.S. Thorne and G. Watt, Uncertainties on α s in global PDF analyses and implications for predicted hadronic cross sections, Eur. Phys. J. C 64 (2009) 653 [arXiv:0905.3531] [INSPIRE].
R.D. Ball et al., Precision NNLO determination of α s (M Z ) using an unbiased global parton set, Phys. Lett. B 707 (2012) 66 [arXiv:1110.2483] [INSPIRE].
ATLAS collaboration, Measurement of the inclusive W ± and Z/γ* cross sections in the electron and muon decay channels in pp collisions at \( \sqrt{s} \) = 7 TeV with the ATLAS detector, Phys. Rev. D 85 (2012) 072004 [arXiv:1109.5141] [INSPIRE].
LHCb collaboration, Inclusive W and Z production in the forward region at \( \sqrt{s} \) = 7 TeV, JHEP 06 (2012) 058 [arXiv:1204.1620] [INSPIRE].
CMS collaboration, Measurement of the electron charge asymmetry in inclusive W production in pp collisions at \( \sqrt{s} \) = 7 TeV, Phys. Rev. Lett. 109 (2012) 111806 [arXiv:1206.2598] [INSPIRE].
J.M. Campbell, J.W. Huston and W.J. Stirling, Hard Interactions of Quarks and Gluons: A Primer for LHC Physics, Rept. Prog. Phys. 70 (2007) 89 [hep-ph/0611148] [INSPIRE].
M. Sutton et al., A posteriori inclusion of parton density functions in NLO QCD final-state calculations at hadron colliders: The APPLGRID Project, PoS(DIS 2010)051.
T. Kluge, K. Rabbertz and M. Wobisch, FastNLO: Fast pQCD calculations for PDF fits, hep-ph/0609285 [INSPIRE].
NNPDF collaboration, R.D. Ball et al., Reweighting NNPDFs: the W lepton asymmetry, Nucl. Phys. B 849 (2011) 112 [Erratum ibid. B 854 (2012) 926] [arXiv:1012.0836] [INSPIRE].
N. Sato, J.F. Owens and H. Prosper, Bayesian Reweighting for Global Fits, arXiv:1310.1089 [INSPIRE].
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Gao, J., Nadolsky, P. A meta-analysis of parton distribution functions. J. High Energ. Phys. 2014, 35 (2014). https://doi.org/10.1007/JHEP07(2014)035
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DOI: https://doi.org/10.1007/JHEP07(2014)035