1. 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 1.Comnined Inclusive cross-sections HERA-1 (1992-2000):arxiv:0911.0884, JHEP1001,209 2.Comnined Inclusive cross-sections HERA-II (2003-2007)- (preliminary) 3.Has also been used to fit Tevatron data: W /Z data and jets 4.Has also been used to fit LHC W and Z data 5.Now let’s look at ATLAS jets

2.  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 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

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

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 d 2 σ/dxdQ 2 for these processes are measured across the x Q 2 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. DGLAP formalism HERA: H1 and ZEUS fitters– independent cross-checks A minimum Q 2 cut Q 2 > 3.5 GeV 2 is applied to stay within the supposed region of validity of leading twist pQCD (no data are at low W 2 ) The starting scale Q 2 0 (= 1.9 GeV 2 ) is below the charm mass 2 (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 Q 2 0 and then uses the DGLAP formalism to evolve these to any Q 2 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.

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) 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 Q 2 0 ). ABCDE uvSum rulefree dvSum rulefree var UBar=(1-fs)ADbar=BDbarfreevar DBarfree var glueSum rulefree var extended gluon parametrisation Ag x Bg (1-x) Cg (1+Dx+Ex 2 ) – A’g x B’g (1-x) 25 A’gB’g free HERAPDF1.5f parametrisation with 14 free parameters HERAPDF1.5 with 10 free parameters, fixes these purple parameters

8. And somewhat more sensitivity to the low Q 2 cut HERAPDF1.5HERAPDF1.5f

9. 9 Χ 2 = 27 /28Χ 2 = 16 /28 Χ 2 = 21/13 Χ 2 = 25/11 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 Before fitting Tevatron W/Z data And how well does HERAPDF1.5f describe Tevatron W/Z data?

10. 10 Χ 2 = 6.5 /12→ 4.5/12Χ 2 = 30 /11→ 14/11Χ 2 = 9/5→ 7.8/5 Χ 2 = 35/35→ 16/35 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 And how well does HERAPDF1.5f describe LHC W/Z data? HERAPDF uncertainties after including Tevatron W/Z data HERAPDF uncertainties after including Tevatron W/Z data + CMS W-asymmetry

11. 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 better χ2/dp=72/76 for CDF even for the central PDF

12. 12 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

13. APPLGrid and PDF fits QCD factorization separate (NLO) ME PDFs 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 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

14. 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 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 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

15. 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

16. 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..

17. 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

18. 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

19. extras

20. d 2  (e - p) = G F 2 M 4 W [x (u+c) + (1-y) 2 x (d+s)] d 2  (e + p) = G F 2 M 4 W [x (u+c) + (1-y) 2 x (d+s)] dxdy 2  x(Q 2 +M 2 W ) 2 CC e-pCC e+p We can use the reduced cross-sections to learn about high-x valence PDFs For NC e+ and e- d 2  (e±N) = Y+ [ F 2 (x,Q 2 ) - y 2 F L (x,Q 2 ) ± Y_xF 3 (x,Q 2 )], Y± = 1 ± (1-y) 2 dxdy Y+ F 2 = F 2 γ –v e P Z F 2 γZ + (v e 2 +a e 2 )P Z 2 F 2 Z xF 3 = - a e P Z xF 3 γZ + 2v e a e P Z 2 xF 3 Z Where P Z 2 = Q 2 /(Q 2 + M 2 Z ) 1/sin 2 θ W, and at LO [F 2,, F 2 γZ, F 2 Z ] =  i [e i 2,2e i v i,v i 2 +a i 2 ][xq i (x,Q 2 ) + xq i (x,Q 2 )] [xF 3 γZ, xF 3 Z ] =  i [e i a i,v i a i ] [xq i (x,Q 2 ) - xq i (x,Q 2 )] So that xF 3 γZ = 2x[e u a u u v + e d a d d v ] = x/3 (2u v +d v ) Where xF 3 γZ is the dominant term in xF 3 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 ) Where does the information on parton distributions come from?

21. 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.

22. H1 and ZEUS have also combined preliminary high Q 2 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.

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 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

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

26. Just HERA data HERA data +ATLAS jets