1

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

Outline•Introduction•Combination method•Results•Checks

H1-ZEUS 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

E. Tassi - Zeus Monday mtg August,6 2007

http://www-zeus.desy.de/~tassi/ZEUS_ONLY/combineLP07/main.html

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Electroweak Neutral currents at HERAH1prelim-06-142/ZEUS-prel-06-022

Interference structure function xF3(γZ):

order) (Leading )2(3

)2(2~~

3

32

3

vvZ

Zee

Ze

dux

xF

xFkavkxFaY

Y

- First combined H1-ZEUS SF result

- Improved xF3(γZ) determination

- Simple weighted average using the

total uncertainties (w/o correlations)

3

Parity violating cross section

asymmetries:

x) (large /4

/1

)()(

)()(2

2

2

vv

vv

Z

eLR

LR

LR

ud

udkA

F

Fka

PP

PP

PPA

Electroweak Neutral currents at HERAH1prelim-06-142/ZEUS-prel-06-022

- again simple data averaging method…

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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)

- Cross Check → also as a result of the studies in this WG, the 96-97 H1 low-Q2 data had to be scaled up by 3.4% (official)

Analysis focus on the combination method and the treatment of thesystematic 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 good (but see previous slide)

- 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

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Cross section averaging procedure and definition(s)

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exp2

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Data model (assume first only additive systematics):

Likelihood:

With:

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)1,0(~,

expby bin in unc. syst. correlated

expby bin iny uncertaint lstatistica

bin in section cross true

expby bin in section cross measured

Nrs

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eim

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Averaging procedure based on the Least Squares method

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Minimization

From the minimization one gets for the averaged (true) cross sections:

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Remember that ri ~ Norm(0,1)

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Multiplicative vs additive syst. uncert.Imagine that in addition to the additive syst. β we have a multiplicative systematic(e.g. lumi norm. unc.) α=1±ε…

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In order not to spoil the linearity of the approach an iterative procedureis adopted where initially the mult. syst. is treated as the other ones butin each iteration the (β=α) and σ are rescaled by μi(n)/mi .

Few iterations are sufficient for the fit to converge. The programremains extremely fast while avoiding possible biases.

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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):

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),(),(

),(),( 2820

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Qx

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ep

epep

for CC, additive for NC(see draft)

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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

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Results

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Fit results: and pulls

2599/510/2 ndf

CC e+p

NC e-p

CC e-p

NC e+p

μ=-0.05σ=1.7

μ=0.1σ=0.8

μ=0.01σ=0.7

μ=-0.09σ=1.4

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Fit Results : Syst. shifts 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 0.364510 h10_GP_BG_Spacal -0.5141 0.817911 h11_GP_BG_LAr 0.9073 0.851012 h12_BG_CC_94-97 0.3389 0.787113 h13_BG_CC_98-00 -0.7856 0.884614 h14_ChargeAsym 0.0262 0.999315 hllumi1_SPACAL_bulk 1.5543 0.558816 hllumi2_SPACAL_MB 0.8375 0.598417 h1lumi3_LAr_94-97_e+p -1.0706 0.621118 h1lumi4_LAr_e-p -0.0708 0.777819 h1lumi5_LAr_2000 -0.7462 0.5982

20 zd1_e_eff 0.4572 0.748621 zd2_e_theta_a 0.1576 0.679722 zd3_e_theta_b -0.3849 0.774623 zd4_e_escale 0.8342 0.507924 zd5_had1 0.3157 0.590625 zd6_had2 0.0581 0.649626 zd7_had3 -0.7649 0.741327 zd8_had_flow 0.6947 0.661928 zd9_bg -0.2358 0.417529 zd10_had_flow_b 0.0730 0.237530 zd11 -0.4055 0.617431 z1nce-_e_scale 0.1777 0.938332 z2nce-_bg -0.4073 0.917833 z3nce-_eff1 -0.1819 0.912034 z4nce-_eff2 0.5536 0.554435 z5nce-_vtx -0.5180 0.926236 z6nce- 0.1218 0.413837 z1cce- 0.0296 0.835038 z2cce- -0.0152 0.868039 zlumi2_zccem 0.0708 0.777840 zd5nc00 0.1386 0.984341 zd7nc00 0.1566 0.209342 zd8nc00 0.5163 0.928043 zluminc00 -0.4854 0.3837

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CC e-p

Preliminary request

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CC e-p

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CC e+p

Preliminary request

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CC e+p

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NC e-p

Preliminary request

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NC e+p

Preliminary request

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NC e+p

Preliminary request

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NC e+p: two low-Q2 bins

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NC e+p: two high-Q2 bins

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NC e+p

Preliminary request

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NC e+p

Preliminary request

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Systematic Checks

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CME corrections: FL =0

To test model (FL) dependenceat high-y we have repeated thecombination (with FL=0)

Almost negligible (but up to 4-5% at high-y)

(Default/NoFL -1)x1000

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Correlation between Experiments

To quantify them is a highly non trivial problem

Tried to evaluate them by identifyinga 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)

(Uncorrelated/Largest change -1)x1000

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Multiplicative vs Additive

Comparison of the averaged crosssections obtained assuming allsyst unc. as multiplicative in naturew.r.t. to a combination were only normalizations were treated ad multiplicative

Mostly negligible (but strangelylarge in a few high-x high-Q2 points)

(Uncorrelated/Largest change -1)x1000

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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

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Backup Slides

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Minimization

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Fitted cross sects and r parameters

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X = 0.02

35

36

Lumi unc.

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)…)

All Add.

Norms Mult.

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15 hllumi1_SPACAL_bulk 0.4054 0.570016 hllumi2_SPACAL_MB -0.0838 0.603517 h1lumi3_LAr_94-97_e+p -2.3520 0.613918 h1lumi4_LAr_e-p -0.6815 0.773819 h1lumi5_LAr_2000 -2.1614 0.59151 zlumi1_zncepl -0.9276 0.590139 zlumi2_zccem -0.7298 0.774043 zluminc00 -1.5020 0.379830 zd11 -0.1974 0.6159

15 hllumi1_SPACAL_bulk 1.5377 0.562816 hllumi2_SPACAL_MB 0.8464 0.600117 h1lumi3_LAr_94-97_e+p -1.0869 0.622718 h1lumi4_LAr_e-p -0.0808 0.778019 h1lumi5_LAr_2000 -0.7334 0.60021 zlumi1_zncepl 0.0277 0.591939 zlumi2_zccem 0.0809 0.777943 zluminc00 -0.5196 0.385930 zd11 -0.3856 0.6204