Systematic Uncertainties for dσ/dy Measurement of Drell-Yan Dielectron Pairs with 2.1 fb -1

Authors: Jiyeon Han, Arie Bodek, Willis Sakumoto, Y.S.Chung
Last Updated: Mar, 26th, 2010

Systematic Study : Public Note

Abstract

We report on the systematic uncertainties for dσ/dy measurement. The dσ/dy measurement was done over the full kinematic range for e+e- pairs in the Z boson region mass range of 66 to 116 GeV/c2 from 2.1 fb-1 of proton anti-proton collisions at (s)^½ = 1.96 TeV taken by the CDF detector at Fermilab. The dσ/dy measurement is used in the global chi2 of PDFs group to extract the PDFs information. The global chi2 defined by PDFs group considers not only the statistical uncertainty (or uncorrelated errors) but also the correlated uncertainty. The systematic uncertainties in the measurement are stronly correlated in boson rapidity. We generate the root-based macro to produce the systematic correlations for the measurement. In the page, we describes how to use the macro to produce the systematic uncertainties.

Systematic Uncertainties

In the code, 11 independent parameters corresponding to the systematic sources are implemented.
An user can get the systematic uncertainty functions just running ''main()'' function in error_propagator_public.C code.
You can download the code from :

CERN ROOT Code for systematic errors : error_propagator_public.C

 CERN ROOT code generates a table and plots for the systematic errors of each sources.

C++ Code for systematic errors : error_propagator_g++.C

C++ code only generate a table for the systematic errors of each sources.

=>''main()'' function has two vectors, vector < double > onpar(11) and vector < double > sdev(11).




onpar[i] = 1 : turning on the i-th parameter in the systematic uncertainty calculation.
onpar[i] = 0 : turning off the i-th parameter in the systematic uncertainty calculation.

sdev[i] = 1 : calculate the systematic errors with +1 sigma change on i-th parameter
(If an user set sdev[i]=3, the macro produce the systematic uncertainty with +3 sigma change on i-th parameter.)
(the sign of sdev[i] is also considered, so the errors with sdev[i] = +1 has a different value from the errors with sdev[i] = -1. )


Procedure to run the macro(CERN ROOT Code) of the systematic uncertainties
: error_propagator_public.C

1) Determine the parameters to produce
onpar[i] = 1 (turn on ) or 0 (turn off)
(Defalt onpar[i] = 1 for all i)
2) Determine how much sigma deviates from the center
 sdev[i] = xxx
(Default sdev[i] = 1 for all i).
3) run root program root -l
4) load the macro .L error_propagator_public.C
5) run main() function main()

Procedure to run C++ code of the systematic uncertainties
: error_propagator_g++.C

1) Determine the parameters to produce
onpar[i] = 1 (turn on ) or 0 (turn off)
(Defalt onpar[i] = 1 for all i)
2) Determine how much sigma deviates from the center
 sdev[i] = xxx
(Default sdev[i] = 1 for all i).
3) Complie code g++ -o erro_propagator error_propagator_g++.C
4) Run the excutable file => produce the table ./erro_propagator

=> The terminal will print out the tables of systematic uncertainties from each components.
=> Three canvas will show up : systematic errors of each components, fractional systematic errors of each components, total systematic errors
=> Total systematic errors in the plot show the errors with ± 1 sigma change when onpar[i] and sdev[i] are the default value.

Result

σ = 256.6 ± 0.7(stat.) ± 2.0(sys. excluding luminosity factor) pb.
σ = 256.6 ± 0.7(stat.) ± 15.5(sys. including luminosity factor) pb.

Data To Theory Comparison

The ratio of data to theory prediction is used to compare the data to the predictions.



PDFs theoretical uncertainties



Data/Theory considering only data statistical uncertainties.

chi2 in CTEQ6.1M(NLO) = 30/27
chi2 in CTEQ6.6M(NLO) = 34/28
Data/Theory considering data statistical and data systematical uncertainties.
chi2 values are improved slightly including the data systematic uncertainties.

chi2 in CTEQ6.1M(NLO) = 29/28
chi2 in CTEQ6.6M(NLO) = 35/28

PDFs theoretical uncertainties(yellow band) are considered separately from the data systematic uncertainties.

 

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