Combination of H1 and ZEUS DIS e ± p inclusive cross sections

1. E. Tassi - Zeus Monday mtg August,6 2007 Combination of H1 and ZEUS DIS e±p inclusive cross sections H1-ZEUS Structure Function working group A. Cooper-Sarkar, C.Gwenlan, K. Nagano, J. Ferrando, Y. Ri, S. U. Noor, A.F. Zarnecky, E.T,J. Feltesse, S. Glazov, M. Klein, V. Shekelian, Z. Zhang, E. Rizvi, U. Martyn Outline Introduction Combination method Results Checks http://www-zeus.desy.de/~tassi/ZEUS_ONLY/combineLP07/main.html

2. Electroweak Neutral currents at HERAH1prelim-06-142/ZEUS-prel-06-022 Interference structure function xF3(γZ): - First combined H1-ZEUS SF result - Improved xF3(γZ) determination - Simple weighted average using the total uncertainties (w/o correlations)

3. Electroweak Neutral currents at HERAH1prelim-06-142/ZEUS-prel-06-022 Parity violating cross section asymmetries: - again simple data averaging method…

4. Aim of the analysis Go a step forward: combine the HERA I NC and CC ep inclusive cross sections including full correlations. - Simplicity → provide a single set of “HERA” inclusive cross sections measurements blessed by the experiments - Cross Calibration → Reduction of syst. unc. as a result of averaging (S. Glazov - DIS05 and HERA-LHC WS) - Precise Pdfs and αs determination → longer term Analysis focus on the combination method and the treatment of the systematic uncert. in data combination (no tables will be provided). Would like to present these results to LP07 → Preliminary Status

5. Main technical issues addressed - consistency of input data → generally very good (H1 small Q2 sample scaled up by 3.4%) - Treatment of systematic errors additive or multiplicative - x-Q2 common grid → H1 x and ZEUS Q2 (basically) - assumptions on correlations between data sets and H1 and ZEUS (mostly uncorrelated but theory links – QED and γp) - treatment of 820 GeV and 920 GeV (see later) - some of the average assumptions cause extra uncertainties at the few % level (with few exceptions) – added to the averaged data points

6. Cross section averaging procedure and definition(s) Averaging procedure based on the Least Squares method Data model (assume first only additive systematics): Likelihood: With:

7. Minimization From the minimization one gets the following system: That can be re-written in matrix form

8. Minimization

9. Fitted cross sects and r parameters Basic Idea: We can now determine the parameters Once the are known we can easily determine the

10. Multiplicative vs additive syst. uncert. Imagine that in addition to the additive syst. βwe have a multiplicative systematic (e.g. lumi norm. unc.) α=1±ε… In order not to spoil the linearity of the approach an iterative procedure is adopted where initially the mult. syst. is treated as the other ones but in each iteration the (β=α) and σ are rescaled by μi(n)/mi . Few iterations are sufficient for the fit to converge. The program remains extremely fast while avoiding possible biases.

11. Data sets and treatment - All HERA I cross sections: NC and CC e±p - 1.5 < Q2 <30000 GeV2→ ~230 pb-1 - averages cross sections determined in a simultaneous fit of these data. - prior to combination the H1 and ZEUS measurements are transformed to a common grid of x-Q2 points - treatment of the 820 GeV and 920 GeV data sets In this analysis and just for illustration have decide to move all data points to 920 GeV – In the future may/will not correct points at high-y (y>0.35) in order to reduce model dependence (FL): for CC, additive for NC (see draft)

12. X-Q2 common grid The grid points are chosen such that - interpolation corrections are small - no two separate measurements interpolate to common grid point - 38x25 points → Q2 ~ ZEUS → x ~ H1 (4 points per decade) Detailed list in the analysis web page

13. Results

14. Fit results: and pulls NC e+p NC e-p μ=-0.09 σ=1.4 μ=0.01 σ=0.7 CC e+p CC e-p μ=0.1 σ=0.8 μ=-0.05 σ=1.7

15. Fit Results : Syst. shifts 20 zd1_e_eff 0.4572 0.7486 21 zd2_e_theta_a 0.1576 0.6797 22 zd3_e_theta_b -0.3849 0.7746 23 zd4_e_escale 0.8342 0.5079 24 zd5_had1 0.3157 0.5906 25 zd6_had2 0.0581 0.6496 26 zd7_had3 -0.7649 0.7413 27 zd8_had_flow 0.6947 0.6619 28 zd9_bg -0.2358 0.4175 29 zd10_had_flow_b 0.0730 0.2375 30 zd11 -0.4055 0.6174 31 z1nce-_e_scale 0.1777 0.9383 32 z2nce-_bg -0.4073 0.9178 33 z3nce-_eff1 -0.1819 0.9120 34 z4nce-_eff2 0.5536 0.5544 35 z5nce-_vtx -0.5180 0.9262 36 z6nce- 0.1218 0.4138 37 z1cce- 0.0296 0.8350 38 z2cce- -0.0152 0.8680 39 zlumi2_zccem 0.0708 0.7778 40 zd5nc00 0.1386 0.9843 41 zd7nc00 0.1566 0.2093 42 zd8nc00 0.5163 0.9280 43 zluminc00 -0.4854 0.3837 Name Syst Unc. 1 zlumi1_zncepl 0.0554 0.5887 2 h2_Ee_Spacal 0.6568 0.3314 3 h3_Ee_Lar_00 -0.3645 0.4448 4 h4_ThetaE_spacal -0.7437 0.6556 5 h5_ThetaE_94-97 -0.0655 0.7799 6 h6_ThetaE_00 -0.4051 0.5290 7 h7_H_Scale_Spacal 0.4592 0.4755 8 h8_H_Scale_Lar -0.9265 0.5351 9 h9_Noise_Hcal -0.5037 0.3645 10 h10_GP_BG_Spacal -0.5141 0.8179 11 h11_GP_BG_LAr 0.9073 0.8510 12 h12_BG_CC_94-97 0.3389 0.7871 13 h13_BG_CC_98-00 -0.7856 0.8846 14 h14_ChargeAsym 0.0262 0.9993 15 hllumi1_SPACAL_bulk 1.5543 0.5588 16 hllumi2_SPACAL_MB 0.8375 0.5984 17 h1lumi3_LAr_94-97_e+p -1.0706 0.6211 18 h1lumi4_LAr_e-p -0.0708 0.7778 19 h1lumi5_LAr_2000 -0.7462 0.5982

16. CC e-p Preliminary request

17. CC e-p

18. CC e+p Preliminary request

19. CC e+p

20. NC e-p Preliminary request

21. NC e+p Preliminary request

22. NC e+p Preliminary request

23. NC e+p: two low-Q2 bins

24. NC e+p: two high-Q2 bins

25. NC e+p Preliminary request

26. NC e+p Preliminary request

27. Systematic Checks

28. CME corrections: FL =0 (Default/NoFL -1)x1000 To test model (FL) dependence at high-y we have repeated the combination (with FL=0) Almost negligible (but up to 4-5% at high-y)

29. Correlation between Experiments (Uncorrelated/Largest change -1)x1000 To quantify them is a highly non trivial problem Tried to evaluate them by identifying a list of possible common sources (γp back, lumi,CAL E scales, θe, etc), assume 100% correlation, and compare the new averages with uncorrelated ones Mostly negligible (but up to 2-3% in particular regions of the phase space)

30. Multiplicative vs Additive (Uncorrelated/Largest change -1)x1000 Comparison of the averaged cross sections obtained assuming all syst unc. as multiplicative in nature w.r.t. to a combination were only normalizations were treated ad multiplicative Mostly negligible (but strangely large in a few high-x high-Q2 points)

31. Summary • Thinking the results are interesting we would like, if approved by collaborations, to present the results to LP07 → feedback wider circle… • Draft being completed… • E. Rizvi will present these results to H1 tomorrow For additional information visit analysis web page: http://www-zeus.desy.de/~tassi/ZEUS_ONLY/combineLP07/main.html

32. Backup Slides

33. X = 0.02

34. Lumi unc. Norms Mult. All Add. Use of the correct underlying model for each error contribution is important → Improper treatment may lead to strong biases (G. D’agostini (CELLO 87) – Peelle’s Pertinent Puzzle (R. Peelle 87)…)