1. 1 Studies on Exclusion Limits N.Andari, L. Fayard, M.Kado, F.Polci LAL- Orsay LAL meeting 23/07/2009

2. 2 Related recent references in ATLAS N.Andari Statistical forum 08-07-2009 http://indico.cern.ch/contributionDisplay.py?contribId=6&confId=62456 H.Wang, HSG1 meeting 08-07-2009 http://indico.cern.ch/contributionDisplay.py?contribId=6&confId=62507 H.Wang, HSG1 meeting 25-06-2009 http://indico.cern.ch/getFile.py/access?contribId=4&resId=0&materialId=slides&confId=51092 F.Pozuelos HSG1 meeting 20-05-2009 http://indico.cern.ch/getFile.py/access?contribId=2&resId=0&materialId=slides&confId=51090 H.Wang HSG1 meeting 20-05-2009 http://indico.cern.ch/getFile.py/access?contribId=3&resId=0&materialId=slides&confId=51090 H.Wang HSG1 meeting 20-03-2009 http://indico.cern.ch/getFile.py/access?contribId=9&resId=0&materialId=slides&confId=51088 N.Andari HSG1 meeting 27-02-2009 http://indico.cern.ch/getFile.py/access?contribId=3&resId=0&materialId=slides&confId=51087

3. 3 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

4. 4 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

5. 5 B toys S+B toys 2 ΔNLL’ Pvalue median The p-value (CL S+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: 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? Problem of notation

6. 6 and low luminosities At low luminosities (i.e 0.5 fb-1) the S+B distribution (S>0) don’t follow the distribution 0.5 fb-1 Therefore, we can’t use the method of integration of to compute the p-value How can we simplify the task of computing CL at low luminosities? B toys S+B toys

7. 7 If we don’t set the positive limit on the number of signal events fitted, we obtain a even at low luminosities. 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

8. 8 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 GeV130GeV140GeV Ns=4.41Ns=3.92Ns=3.51 mRes=1.45mRes=1.53mRes=1.65 (instead of 4.17 due to different values of acceptances obtained recently by A.-C.Bourgaux, M.Escalier and Haichen Wang Evaluating error bands 1SM

9. 9 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

10. 10 Taken from F.Pozuelos 20-5-2009 B toys,8SM Median Median+1sigma Median-1sigma Median+2sigma

11. 11 Countingchi2 S>0 -  <S<  S>0 -  <S<  Median60.0460.0360.0760.10 +1sigma89.2289.1276.6389.37 +2sigma98.8698.8784.145998.86 Results for the Standard Model Hypothesis Good Agreement The simplest to use Wrong when not median used by Francisco Pozuelos on 20-5-9

12. 12 Results 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 – CL S+B [%]

13. 13 Repeating the same for 130 GeV and 140 GeV, we obtain: D0 expected D0 observed 95% CL Cross section / SM mH (GeV) 0 SM excluded!

14. 14 In order to be able to compare to the D0 plot we use the Modified Frequentist CL S method ( LEP and TeVatron) CL S = CL S+B /CL B 1- CL S goes to 0 while 1-CL S+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 Another method solving the problem

15. 15 1 – CL S = 1 – CL S+B /CL B [%] However the limit is worse ( 8.1 instead of 6.7) But one can compare to TeVatron ! ) Using Q and the chi2 approximation

16. 16 95% CL Cross section / SM mH (GeV) Exclusion plot using CL S D0 expected D0 observed This plot can correctly be compared with the Tevatron plot

17. 17 95% CL Cross section / SM energy (TeV) Limit (CL S ) for various energies for MH=120 GeV and different luminosities 0.2 fb-1 0.05 fb-1 D0 expected D0 observed

18. 18 Systematics : + 25 % background 95% CL Cross section / SM mH (GeV) standard background background + 25 % For systematics on signal not discussed see for instance Anne-Claire Bourgaux http://indico.cern.ch/getFile.py/access?contribId=6&resId=1&materialId=slides&confId=61618 D0 expected D0 observed

19. 19 Conclusion Suggestion: Use the chi2 approximation Question: Use CLs instead of CLs+b ?