Skip to main content
. 2013 Aug 3;73(8):2509. doi: 10.1140/epjc/s10052-013-2509-4

Table 3.

Agreement of the PDF fit with different datasets in terms of the χ 2 values, using various combinations of input datasets for the fit. HERA is used as baseline and in combination with ATLAS jet data from the single-jet double-differential cross-section measurements at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sqrt{s} = 2.76~\mbox{TeV}$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sqrt {s} = 7~\mbox{TeV}$\end{document} for anti-k t jets with two radius parameters, R=0.4 and R=0.6. When both ATLAS jet datasets at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sqrt{s} = 2.76~\mbox{TeV}$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sqrt{s} = 7~\mbox{TeV}$\end{document} are used, all correlations between the measurements are taken into account. The χ 2 value of the fit with respect to the individual datasets tested is given separately for the uncorrelated and the correlated components as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\chi^{2}_{\mathrm{uncor}}$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\chi^{2}_{\mathrm{cor}}$\end{document}, where the shifts of the systematic uncertainties are summed in quadrature for each category. In general, a very good fit quality is found. Comparison of χ 2 values of the fit using HERA data only with fits including both HERA and ATLAS jet data shows the pull of ATLAS jet data for both jet radius parameters, while the description of the HERA  data is almost unaffected. For example, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\chi^{2}_{\mathrm{uncor}}$\end{document} of the HERA dataset worsens only slightly by 8 units from 556 to 564 when the ATLAS jet data for R=0.6 is included in the fit, while \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\chi^{2}_{\mathrm{uncor}}$\end{document} improved from 33 (50) to 29 (40) for the 2.76 TeV (7 TeV) jet data. There is also an improvement from 22 to 12 in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\chi^{2}_{\mathrm{cor}}$\end{document} for jets

Input datasets Test dataset \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\chi^{2}_{\mathrm{uncor}}$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\chi ^{2}_{\mathrm{cor}}$\end{document} N points
HERA HERA 556 3.0 592
ATLAS jets 2.76 TeV, R=0.4 29 21 40
ATLAS jets 7 TeV, R=0.4 44 76
ATLAS jets 2.76 TeV, R=0.6 33 22 40
ATLAS jets 7 TeV, R=0.6 50 76

HERA

ATLAS jets 2.76 TeV, R=0.4

ATLAS jets 7 TeV, R=0.4

HERA 562 3.6 592
ATLAS jets 2.76 TeV, R=0.4 27 19 40
ATLAS jets 7 TeV, R=0.4 33 76
ATLAS jets 2.76 TeV, R=0.6 29 13 40
ATLAS jets 7 TeV, R=0.6 41 76

HERA

ATLAS jets 2.76 TeV, R=0.4

HERA 557 3.1 592
ATLAS jets 2.76 TeV, R=0.4 20 7.4 40

HERA

ATLAS jets 7 TeV, R=0.4

HERA 559 3.4 592
ATLAS jets 7 TeV, R=0.4 28 14 76

HERA

ATLAS jets 2.76 TeV, R=0.6

ATLAS jets 7 TeV, R=0.6

HERA 564 4.0 592
ATLAS jets 2.76 TeV, R=0.6 jets 29 12 40
ATLAS jets 7 TeV, R=0.6 40 76
ATLAS jets 2.76 TeV, R=0.4 26 18 40
ATLAS jets 7 TeV, R=0.4 32 76

HERA

ATLAS jets 2.76 TeV, R=0.6

HERA 558 3.2 592
ATLAS jets 2.76 TeV, R=0.6 21 4.9 40

HERA

ATLAS jets 7 TeV, R=0.6

HERA 560 3.6 592
ATLAS jets 7 TeV, R=0.6 34 9.4 76