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Using the HERAPDF fit formalism. HERAPDF uses

PDF fitting to ATLAS jet data- a first look A M Cooper-Sarkar, C Doglioni, E Feng, S Glazov, V Radescu, A Sapronov, P Starovoitov, S Whitehead ATLAS jet meeting 17/5/2011. Using the HERAPDF fit formalism. HERAPDF uses

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Using the HERAPDF fit formalism. HERAPDF uses

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  1. PDF fitting to ATLAS jet data- a first lookA M Cooper-Sarkar, C Doglioni, E Feng, S Glazov, V Radescu, A Sapronov, P Starovoitov, S WhiteheadATLAS jet meeting 17/5/2011 Using the HERAPDF fit formalism. HERAPDF uses • Comnined Inclusive cross-sections HERA-1 (1992-2000):arxiv:0911.0884, JHEP1001,209 • Comnined Inclusive cross-sections HERA-II (2003-2007)- (preliminary) • Has also been used to fit Tevatron data: W /Z data and jets • Has also been used to fit LHC W and Z data • Now let’s look at ATLAS jets

  2. A substantial part of the uncertainty on parton distributions comes from the need to use many different input data sets with large systematic errors and questionable levels of consistency • Combining H1 and ZEUS data provides a model independent tool to study consistency of the data and to reduce systematic uncertainties: •  Experiments cross calibrate each other. It’s effectively like combining the best features of each detector • The combination method includes accounting for full systematic error correlations. • The resulting combination is much more accurate than expected from the increased statistics of combining two experiments. • The post-averaging systematic errors are smaller than the statistical errors across a large part of the kinematic plane

  3. This page shows NC e+ combined data Results of the combination compared to the separate data sets

  4. These data are used for extracting parton distributions: HERAPDF • Some of the debates about the best way of estimating PDF uncertainties concern the use of many different data sets with varying levels of consistency. • The combination of the HERA data yields a very accurate and consistent data set for • 4 different processes: e+p and e-p Neutral and Charged Current reactions. • The cross-sections d2σ/dxdQ2 for these processes are measured across the x Q2 plane • Giving information on the low-x Sea(NCe+ data) • Giving information on the low-x Gluon via scaling violations(NCe+ data) • Giving information on high-x u (NCe+/e- and CCe-) and d ( CCe+ data) valence PDFs • Giving information on u and d-valence shapes down to x~3 10-2(from the difference between NCe+ and NCe-) • NOTE the use of a pure proton target means d-valence is extracted without need for heavy target/deuterium corrections or strong iso-spin assumptions these are the only PDFs for which this is true • The consistent data set gives us confidence to use Δχ2 =1 in error estimation rather than the inflated χ2 tolerances of e.g. MSTW, CTEQ

  5. HERA: H1 and ZEUS fitters– independent cross-checks A minimum Q2 cut Q2 > 3.5 GeV2 is applied to stay within the supposed region of validity of leading twist pQCD (no data are at low W2 ) The starting scale Q20 (= 1.9 GeV2) is below the charm mass2 (mc=1.4 GeV) and charm and beauty (mb=4.75) are generated dynamically A PDF fit usually assume a functional form of the PDFs at Q20 and then uses the DGLAP formalism to evolve these to any Q2 value where there is data. The PDFs are then convoluted with ME’s (coefficient functions) to calculate the relevant structure functions/cross-sections. The parameters of the functional form are determined by fitting data to these predictions. DGLAP formalism

  6. We chose to parametrize PDFs for: gluon, u-valence, d-valence and the Sea u and d-type flavours: Ubar and Dbar with the functional form The normalisations of the gluon and valence PDFs are fixed by the momentum and number sum-rules resp. Further constraints are: B(Dbar) = B(Ubar), low-x shape of Sea same for u-type+d-type A(Ubar) = A(Dbar) (1-fs), where sbar = fs Dbar, so that ubar → dbar as x→ 0 (fs=0.31) HERAPDF1.5f parametrisation with 14 free parameters HERAPDF1.5 with 10 free parameters, fixes these purple parameters extended gluon parametrisation Ag xBg (1-x)Cg (1+Dx+Ex2) – A’g xB’g (1-x) 25 The table summarises our usual parametrisation choices and the parametrisation variations that we consider in our uncertainty estimates (and we also vary the starting scale Q20).

  7. HERAPDF1.5 HERAPDF1.5f And somewhat more sensitivity to the low Q2 cut

  8. And how well does HERAPDF1.5f describe Tevatron W/Z data? Χ2= 27 /28 Χ2= 16 /28 Χ2= 25/11 Χ2= 21/13 Before fitting Tevatron W/Z data HERAPDF1.5 central PDF gives a good description of Tevatron W/Z data even before fitting. Fitting results in a PDF which is within the error bands. However PDF uncertainties on the d-valence quark are much reduced. After fitting Tevatron W/Z data 9

  9. And how well does HERAPDF1.5f describe LHC W/Z data? Χ2= 35/35→ 16/35 Χ2= 6.5 /12→ 4.5/12 Χ2= 30 /11→ 14/11 Χ2= 9/5→ 7.8/5 χ2 for the LHC W/Z data before fitting and after a fit which includes HERA data AND Tevatron W/Z data and each individual LHC data set The new fit PDFs do not move (much) outside HERAPDF1.5 error bands Only the CMS asymmetry data lead to any substantial further improvement in PDF uncertainties HERAPDF uncertainties after including Tevatron W/Z data HERAPDF uncertainties after including Tevatron W/Z data + CMS W-asymmetry 10

  10. How well are Tevatron jet data described by HERAPDF? Before fitting HERAPDF1.5 χ2/dp = 176/76 for CDF and 245/110 for D0 for the central PDF However this ignores the error band of the PDF fit If these data are included in a the fit we get χ2/dp = 113/76 and 157/110 resp. The resulting PDF is at the edge of HERAPDF1.5 (68%CL) error bands For HERAPDF1.5 NNLO the description is MUCH betterχ2/dp=72/76 for CDFeven for the central PDF

  11. And how well is LHC jet data described? Jet data will also soon be discriminating for PDFs The PDFs that fit the Tevatron jets best are not necessarily those that fit the LHC jets best. The mixture of q-q, q-g, g-g induced jets is different. HERAPDF1.5 looks to be doing a good job.. so let’s get quantitative 12

  12. The NLO jets calculations take too long to perform for every iteration of a PDF fit. Such problems have been circumvented by the use of NLO/LO k-factors- but these should also change as the PDF changes.FastNLO has been used for Tevatron jet fits. Now we will use APPLGrid for ATLAS jets APPLGrid and PDF fits QCD factorization separate (NLO) MEPDFs Store perturbative coefficients in a 'grid' Include and vary a posteriori: • normalization/factorization scales • strong coupling constant • PDF APPLgrid libraries: convolute Allows for PDF to evolve in fit until convergence reached

  13. Agreement between fitting packages H1 fitter: param error Buv 0.71733 0.20123E-01 Cuv 4.4795 0.11419 Euv 7.8197 1.1983 Cdv 4.7225 0.32435 Adbar 0.17500 0.60433E-02 BDbar -0.15706 0.47037E-02 CUbar 3.7759 0.40885 CDbar 2.4808 0.40599 Bg 0.21176 0.26145E-01 Cg 9.0350 0.54891 ZEUS fitter: param error Buv 0.711219854 0.020723584 Cuv 4.48758637 0.115328886 Euv 8.09226651 1.22168896 Cdv 4.62689822 0.381859445 Asea 0.566438355 0.0229963501 BDbar -0.162291912 0.00542332647 CUbar 3.48360526 0.459251629 Cdbar 2.70795625 0.603587245 Bg 0.206710524 0.0282354525 Cg 8.79500012 0.620813439 χ2 = 752.27 for 764 data points χ2=736.1 for 674 HERA data points χ2=16.2 for 90 ATLAS jet data points: anti-kt R=0.4 (χ2 even better for R=0.6 (7.8 for 90) Clearly this is far TOO GOOD. Systematic errors are large, if they are used as uncorrelated we seem to overestimate our errors- we need to account for correlated systematic errors

  14. Comparison of the shapes of PDFS with and without the jet data- very compatible More interesting to see any effect of reduction of PDF uncertainties Should consider experimental, model and parametrisation uncertainties However if the 14 parameter flexible parametrization is used then a large part of the effect comes from the experimental uncertainties alone, for this first preliminary study we have looked at just this component

  15. Concentrate just on high-x Observe a small reduction in high-x PDF uncertainty for both gluon and Sea quarks NOW an update on correlations..

  16. Assume 20% of the systematic error is uncorrelated and 80% is fully correlated for all points Then χ2 for anti-kt R=0.6 jets is 85 for 90 data points (R=0.4 107 for 90) And high-x PDF uncertainty is reduced more significantly PLUS the jet data change the shape of the high-x gluon.. making it a bit harder. Since the jet data clearly CAN have impact on the fit we really need to do the correlations properly to work out how much impact

  17. SUMMARY A very encouraging beginning to fitting ATLAS jet data These are well described by HERAPDF1.5 They can be included in the fit by the use of APPLGrid One can already see reduction of high-x PDF uncertainties and some impact on the shape of the PDFs at high-x BUT how much depends on the treatment of correlated systematic uncertainties We need a reliable estimate of the correlations to make it more meaningful

  18. extras

  19. Where does the information on parton distributions come from? CC e-p CC e+p d2(e-p) = GF2 M4W [x (u+c) + (1-y)2x (d+s)] d2(e+p) = GF2 M4W [x (u+c) + (1-y)2x (d+s)] dxdy 2x(Q2+M2W)2 dxdy 2x(Q2+M2W)2 • We can use the reduced cross-sections to learn about high-x valence PDFs For NC e+ and e- d2(e±N) = Y+ [ F2(x,Q2) - y2 FL(x,Q2) ± Y_xF3(x,Q2)], Y± = 1 ± (1-y)2 dxdy Y+ Y+ F2= F2γ –ve PZF2γZ + (ve2+ae2)PZ2F2Z xF3= - ae PZxF3γZ + 2veae PZ2 xF3Z Where PZ2 = Q2/(Q2 + M2Z) 1/sin2θW , and at LO [F2 ,,F2γZ, F2Z] = i [ei2,2eivi,vi2+ai2][xqi(x,Q2) + xqi(x,Q2)] [xF3γZ, xF3Z] = i [eiai,viai] [xqi(x,Q2) - xqi(x,Q2)] So that xF3γZ = 2x[euauuv + edaddv] = x/3(2uv+dv) Where xF3γZ is the dominant term in xF3 • The difference between NC e+ and e- cross-sections gives the valence structure function xF3 due to γ/Z interference and Z exchange • Note this is obtained on a pure proton target so • No heavy target corrections • No assumptions on strong isospin • (Unlike xF3 determined from neutrino scattering on heavy isocalar targets)

  20. RESULTS for HERAPDF1.0 –arxiv:0911.0884 And here is a summary plot of the HERAPDF results Experimental uncertainties on PDFs are extracted with Δχ2=1, and model and parametrization uncertainties are also evaluated.

  21. H1 and ZEUS have also combined preliminary high Q2 HERA-II data along with the HERA-I data and HERAPDF1.0 has recently been updated to HERAPDF1.5 by including these data The data on the left has been updated to the data on the right The HERAPDF1.0 fit on the left has been updated to the HERAPDF1.5 fit on the right Charged Current data are also updated.

  22. The data on the left has been updated to the data on the right The HERAPDF1.0 fit on the left has been updated to the HERAPDF1.5 fit on the right

  23. The data on the left has been updated to the data on the right The HERAPDF1.0 fit on the left has been updated to the HERAPDF1.5 fit on the right

  24. The PDF uncertainties have been reduced at high-x These plots show total uncertainties (model and parametrization included)

  25. Just HERA data HERA data +ATLAS jets

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