Combination and PDF Fit tools Used in ATLAS. A. Cooper-Sarkar, S. Glazov, V. Radescu, A. Sapronov, S. Whitehead. • Data Combination. • QCD Fit Programs. • Including LHC data in QCD Fits. CERN, April 2011 1
Combination of Data H1 and ZEUS 1.6 σ r,NC (x,Q 2 ) x=0.002 HERA I NC e + p x=0.0002 1.4 + ZEUS H1 1.2 x=0.008 1 0.8 x=0.032 0.6 x=0.08 0.4 x=0.25 0.2 0 2 3 4 1 10 10 10 10 Q 2 / GeV 2 Several combination tools on the market: BLUE, HERA combination package. HERA package is being used in ATLAS for e and µ channel data combination. HERA package takes into account correlated systematic errors, corrects for biases due to multiplicative nature of errors. 2
QCD Fit Packages and Settings • Evolution code: publicly available QCDNUM package, version 17.00 ( http://www.nikef.nl/h24/qcdnum/index.html) . Active exchange with M. Botje. • Two independent fitting packages, originated and actively developed within H1 and ZEUS collaborations. • Di ff erent approaches to experimental uncertainties: Hessian, o ff set, adding in quadrature. • Error propagation for PDFs: Hessian and MC method. • NLO and NNLO evolution. • FastNLO and APPLGRID interfaces. • Di ff erent codes for heavy flavor treatment: RT from R. Thorne, flavours of ACOT from F. Olness. • Fits to DIS, jet and DY data. HERA tools are more used in ATLAS, but some developers, e.g. orig- inal developer of the H1 fitter E. Perez, are in CMS. 3
Refernce: HERAPDF1.5 fit H1 and ZEUS σ r,NC (x,Q 2 ) x 2 i 10 7 August 2010 HERA I+II NC e + p (prel.) x = 0.00005, i=21 Fixed Target 10 6 x = 0.00008, i=20 x = 0.00013, i=19 HERAPDF1.5 x = 0.00020, i=18 x = 0.00032, i=17 10 5 x = 0.0005, i=16 + x = 0.0008, i=15 x = 0.0013, i=14 10 4 x = 0.0020, i=13 x = 0.0032, i=12 x = 0.005, i=11 10 3 x = 0.008, i=10 x = 0.013, i=9 x = 0.02, i=8 10 2 x = 0.032, i=7 x = 0.05, i=6 HERA Inclusive Working Group x = 0.08, i=5 10 x = 0.13, i=4 x = 0.18, i=3 1 x = 0.25, i=2 -1 x = 0.40, i=1 10 -2 x = 0.65, i=0 10 -3 10 2 3 4 5 1 10 10 10 10 10 Q 2 / GeV 2 • Fit to the combined preliminary inclusive HERA data, complete dataset. • Good agreement between data and NLO QCD. How HERA PDFs compare to pp observables and how they can be improved by them ? 4
HERAPDF1.5f fit H1 and ZEUS HERA I+II 10 parameter PDF Fit H1 and ZEUS HERA I+II 14 parameter PDF Fit 1 1 1 1 1 1 March 2011 March 2011 xf xf 2 2 2 2 Q = 10 GeV Q = 10 GeV HERAPDF1.5f (prel.) HERAPDF1.5 (prel.) 0.8 0.8 0.8 0.8 0.8 0.8 exp. uncert. exp. uncert. model uncert. model uncert. HERAPDF Structure Function Working Group HERAPDF Structure Function Working Group xu parametrization uncert. xu v v parametrization uncert. 0.6 0.6 0.6 0.6 0.6 0.6 HERAPDF1.5 (prel.) 0.4 0.4 0.4 0.4 0.4 0.4 xg ( × 0.05) xd xg ( × 0.05) xd v v 0.2 0.2 0.2 0.2 0.2 0.2 xS ( × 0.05) xS ( × 0.05) 0 0 0 0 0 0 -4 -3 -2 -1 -4 -3 -2 -1 10 10 10 10 1 10 10 10 10 1 x x • Fits parameterise x ¯ U , x ¯ D , xu v , xd v and x g using x f ( x ) = Ax B (1 − x ) C (1 + Dx + Ex 2 ) form. • Recently fits were extended from 10 to 14 parameters, by relaxing assumptions that B u v = B d v , using extra term for u v and flexible parameterisation for the gluon: x g ( x ) = Ax B (1 − x ) C − A ′ x B ′ (1 − x ) 25 . → similar overall errors, more flexible shapes (important for NNLO). 5
Tevatron y Z data 6
Fit including tevatron y Z data 7
Tevatron y Z data impact on PDF errors 8
Fit Including Tevatron W data 9
Tevatron W data impact on PDF errors 10
LHCb W data in the fit Fit including LHCb lepton asym- metry data gives χ 2 / dof = 7 . 9 / 5. Fit stays within HERAPDF error bands. HERAPDF1.5 (exp) HERAPDF1.5 + LHCb (exp) → some improvement for d v at low x . 11
CMS y Z data CMS data does not shift fit out- side HERAPDF1.5 error band, but does behave as Tevatron data. The reduction of PDF uncertainties is marginal. 12
ATLAS and CMS W Lepton Asymmetry 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 ATLAS muon asymmetry CMS lepton asymmetry 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 HERAPDF1.5(prel.) HERAPDF1.5(prel.) total uncert. 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 total uncert. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.5 0.5 0.5 0.5 0.5 0.5 1 1 1 1 1 1 1.5 1.5 1.5 1.5 1.5 1.5 2 2 2 2 2 2 2.5 2.5 2.5 2.5 2.5 2.5 0 0 0 0 0 0 0.5 0.5 0.5 0.5 0.5 0.5 1 1 1 1 1 1 1.5 1.5 1.5 1.5 1.5 1.5 2 2 2 2 2 2 2.5 2.5 2.5 2.5 2.5 2.5 P t , e > 25 GeV P t , e > 20 GeV, P t , miss > 25 GeV • LO fits with k -factors calculated using MCFM, taking into account di ff erent cuts. • HERAPDF1.5 provides good description of the CMS data with χ 2 / dof = 6 . 5 / 12 and not so good of ATLAS with χ 2 / dof = 30 / 11. 13
Fit to ATLAS W asymmetry data • 14 parameters fit, 6 free parameters for valence quarks, reasonable description of ATLAS asymmetry shape, partial χ 2 / dof = 16 / 11. • Uncertainty estimated using MC method. 14
Fits with LHC W asymmetry data CMS data keep the central line within HERAPDF1.5 error band, χ 2 / dof = 3 . 7 / 12 is extremely good. For ATLAS data fit is pulled somewhat outside the bands, the χ 2 / dof = 16 / 11 is Ok. ATLAS and CMS pull u v in opposite direction. 15
Fit to HERA + Tevatron + LHC data 16
Impact of LHC data on PDF errors 17
Including HERA Jets H1 and ZEUS HERA I+II PDF Fit H1 and ZEUS HERA I+II PDF Fit with Jets 1 1 1 1 1 1 March 2011 March 2011 xf xf Q 2 = 10 GeV 2 Q 2 = 10 GeV 2 HERAPDF1.5f (prel.) HERAPDF1.6 (prel.) 0.8 0.8 0.8 0.8 0.8 0.8 free α (M ) free α (M ) s s Z Z exp. uncert. exp. uncert. HERAPDF Structure Function Working Group HERAPDF Structure Function Working Group xu xu xu model uncert. model uncert. v v v parametrization uncert. parametrization uncert. 0.6 0.6 0.6 0.6 0.6 0.6 0.4 0.4 0.4 0.4 0.4 0.4 xd xg ( xg ( 0.05) 0.05) xd xd × × xg ( 0.05) × v v v 0.2 0.2 0.2 0.2 0.2 0.2 xS ( × 0.05) xS ( xS ( × × 0.05) 0.05) 0 0 0 0 0 0 -3 -3 10 -4 10 10 -2 10 -1 1 10 -4 10 10 -2 10 -1 1 x x Free α S , inclusive Free α S , + jets H1 and ZEUS (prel.) HERAPDF Structure Function Working Group March 2011 20 • Freeing α S in fits increases x g ( x ) uncertainty at min HERAPDF1.5f 2 χ - low x . 15 HERAPDF1.6 2 χ 10 • Inclusing jets allows to reduce uncertainty back. • α S ( M Z ) = 0 . 1202 ± 0 . 0013(exp) ± 0 . 0007(mod) ± 5 0 . 0012(had) + 0 . 0045 − 0 . 0036 (th). 0 0.114 0.116 0.118 0.12 0.122 0.124 0.126 α (M ) S Z 18
Tevatron jets • Tevatron jet data provides additional constraints on gluon at high x . • HERAPDF1.5 provides “reasonable” description of the data. • Putting the data in the fit gives χ 2 / dof = 113 / 76. 19
ATLAS jet data ATLAS ATLAS ∫ ∫ 1.5 Preliminary 1.5 Preliminary Ratio wrt CTEQ 6.6 Ratio wrt CTEQ 6.6 L -1 L -1 y y dt=37 pb dt=37 pb | | < 0.3 2.1 < | | < 2.8 s s =7 TeV =7 TeV 1 1 anti-k jets, R=0.4 anti-k jets, R=0.4 t t Data with Data with 0.5 statistical error 0.5 statistical error 1.5 1.5 Systematic y Systematic y 2.8 < | | < 3.6 0.3 < | | < 0.8 uncertainties uncertainties 1 1 × × NLO pQCD NLO pQCD Non-pert. corr. Non-pert. corr. 0.5 0.5 CTEQ 6.6 CTEQ 6.6 1.5 1.5 y 3.6 < | | < 4.4 y 0.8 < | | < 1.2 MSTW 2008 MSTW 2008 1 1 NNPDF 2.1 NNPDF 2.1 0.5 HERAPDF 1.5 HERAPDF 1.5 0.5 2 2 3 3 1.5 10 10 10 10 y p p 1.2 < | | < 2.1 [GeV] [GeV] T T 1 0.5 2 2 3 3 10 10 10 10 p p [GeV] [GeV] T T • New ATLAS measurement based on complete 2010 data set, extending to forward and lower p t regions, with improved JES uncertainty. • Data tend to be below CTEQ6.6 prediction, best agreement with HERAPDF1.5, however theory / experimental errors are sizable. 20
Summary • HERAPDF fits provide basis for QCD analysis with consistent, high accuracy input data having well understood systematic uncertainties and minimal theoretical assumptions. • The set of tools within the framework, from various methods of PDF error estimates to production of LHAPDF grid files are available for fast feedback to data analysers. • Extending dataset to p ¯ p data from Tevatron is important to improve accuracy for d -type quarks. W asymmetry data provide stronger constraints, however Z data are needed to separate light sea / valence quark e ff ects. • Early LHC data already have some impact on PDF uncertainties at small x . However, inclusion of ATLAS compared to CMS W lepton asymmetry data pulls PDFs in opposite direction. • ATLAS and CMS jet data should provide additional constraints for the gluon density at high x . 21
Extras 22
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