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Proposal to change limits for exclusion

N.Andari, L. Fayard, M.Kado, F.Polci

LAL- Orsay

Y.Fang, Y.Pan, H.Wang, Sau Lan WuUniversity of Wisconsin-Madison

Atlas Statistics Forum

08/07/2009

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Related recent references in ATLAS

H.Wang, this afternoon, Higgs meeting

H.Wang, HSG1 meeting 25-06-2009http://indico.cern.ch/getFile.py/access?contribId=4&resId=0&materialId=slides&confId=51092

F.Pozuelos HSG1 meeting 20-05-2009http://indico.cern.ch/getFile.py/access?contribId=2&resId=0&materialId=slides&confId=51090

H.Wang HSG1 meeting 20-05-2009http://indico.cern.ch/getFile.py/access?contribId=3&resId=0&materialId=slides&confId=51090

H.Wang HSG1 meeting 20-03-2009(background estimation )http://indico.cern.ch/getFile.py/access?contribId=9&resId=0&materialId=slides&confId=51088

N.Andari HSG1 meeting 27-02-2009http://indico.cern.ch/getFile.py/access?contribId=3&resId=0&materialId=slides&confId=51087

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• Aim of the study : Evaluate expected exclusion limits with errors

• General TeVatron Higgs result: CDF,D0 arXiv:0903.4001v1 [hep-ex]• Higgs into gamma gamma result

• D0 collaboration: D0 Note 5858-CONF

http://www.d0.fnal.gov/Run2Physics/WWW/results/prelim/HIGGS/H66/H66.pdf

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To exclude a given hypothesis, we follow the method described in the CSC note.

Simulate events (MC) with only Background (B Toys) and with Signal+Background (S+B Toys) following the CSC parametrisation:

-A crystalball + tail gaussian for the signal;

-An exponential for the background.

Fit each toyMC fixing different hypothesis.

Evaluate the given by:

Generalities on exclusion

'2 NLL

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B toys

S+B toys

2 ΔNLL’Pvalue

median

The p-value (CLS+B) is the fraction of S+B toys having a value of higher than the median of B toys.

The Confidence Level (CL) is given by:

pvalueCL 1

The S+B toys (S>0) follow a distribution at high luminosities (10fb-1). So simply one can compute the p-value as the integral of this function above the median of B toys divided by the total integral.

What about low luminosities?

)(2

1 2f

)(2

1 2f

'2 NLL

Problem of notation

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)(2

1 2f and low luminosities

At low luminosities (i.e 0.5 fb-1) the S+B distribution (S>0) don’t follow the

distribution)(2

1 2f

0.5 fb-1

Therefore, we can’t use the method of

integration of to compute the

p-value

)(2

1 2f

How can we simplify the task of computing CL at low luminosities?

B toys

S+B toys

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• If we don’t set the positive limit on the number of signal events fitted,

we obtain a even at low luminosities. )(2

1 2f

So we can use the method of integration the mathematical function even at low luminosities with the condition of letting the signal events being as well positive as negative.

Let us return to our aim!

B toys

S+B toys

0.5 fb-1

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• We generate 10000 toys MC and fitting them using the following values

For a luminosity 0.2 fb-1 & a center of mass energy 10TeV

Nb=1006.78

120 GeV 130GeV 140GeV

Ns=4.41 Ns=3.92 Ns=3.51

mRes=1.45 mRes=1.53 mRes=1.65

(instead of 4.17 due to different values of

acceptances obtained recently by A.-C.Bourgaux , M.Escalier and Haichen Wang (see his talk this afternoon)

Evaluating error bands

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We fit the toys with different hypothesis: 1SM, 2SM….16SM…

To obtain the CL corresponding to each hypothesis, we check several methods (explained above)

Talk of F.Pozuelos 20/05/2009

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Taken from F.Pozuelos 20-5-2009

B toys,8SM

Median Median+1sigmaMedian-1sigmaMedian+2sigma

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Counting chi2

S>0 -<S< S>0 -<S<

Median 60.04 60.03 60.07 60.10

+1sigma 89.22 89.12 76.63 89.37

+2sigma 98.86 98.87 84.1459 98.86

Results for the Standard Model Hypothesis

Good Agreement

The simplest to use

Wrong when not median used by Francisco Pozuelos on 20-5-9

Suggestion 1 : use this

12Results for 120GeV

CL=95%Median+/- 1 sigma+/- 2sigma

97.75

84.15

Greater than 95% . Therefore we always put a + 2 sigma limit at least at 97.75% CL

CL = 1 – p = 1 – CLS+B [%]

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Repeating the same for 130 GeV and 140 GeV, we obtain:

D0 expected

D0 observed

95%

CL

Cro

ss s

ecti

on

/ S

M

mH (GeV)

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The Modified Frequentist CLS method ( LEP and TeVatron)

CLS = CLS+B/CLB

1- CLS goes to 0 while 1-CLS+B does not go to 0

T.Junk NIM A434(1999)435. A.Read CERN-2000-005 p 81

With this method (CLs) 0 times the SM will never be excluded at 95%CL

Suggestion 2 : use this

Another method solving the problem

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1 – CLS = 1 – CLS+B/CLB [%]

However the limit is worse ( 8.1 instead of 6.7)but probably more correct? ( and one can compare to TeVatron ! )

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95%

CL

Cro

ss s

ecti

on

/ S

M

mH (GeV)

Exclusion plot using CLS

D0 expected

D0 observed

This plot can correctly be compared with the Tevatron plot

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95%

CL

Cro

ss s

ecti

on

/ S

M

energy (TeV)

Limit (CLS) for various energies for MH=120 GeV and different luminosities

0.2 fb-1

0.05 fb-1

D0 expected

D0 observed

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Systematics : + 25 % background

95%

CL

Cro

ss s

ecti

on

/ S

M

mH (GeV)

standard backgroundbackground + 25 %

Systematics on signal not discussed , the NNLO gg cross section is 54 pb (instead of 37 as taken by us ) see for instance Anne-Claire Bourgauxhttp://indico.cern.ch/getFile.py/access?contribId=6&resId=1&materialId=slides&confId=61618

D0 expected

D0 observed

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Conclusions

1st suggestion : do not put the NS >0 limit

2nd suggestion (more important) : go to CLS=CLS+B/CLB instead of CLS+B