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Some statistical studies on H  

Some statistical studies on H  . Presented by: Nansi ANDARI Undergraduate student - LAL Orsay- Directed by: F.Polci, L.Fayard. Discussions : M.Escalier, M.Kado, Y.Fang, L.Roos. February 2009. Preliminary study of systematics on mass resolution

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Some statistical studies on H  

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  1. Somestatisticalstudies on H   Presented by: Nansi ANDARI Undergraduate student - LAL Orsay- Directed by: F.Polci, L.Fayard Discussions : M.Escalier, M.Kado, Y.Fang, L.Roos Nansi Andari 27-2-2009 February 2009

  2. Preliminary study of systematics on mass resolution • Study of discovery, Comparison with CSC note (Y.Fang, CSC meeting HG1 20-12-2007) http://indico.cern.ch/getFile.py/access?contribId=3&resId=1&materialId=slides&confId=25784 • Exclusion of Signal hypothesis • Systematics on the Cross Section of the Higgs Boson This study uses the program Hfitter (N.Berger, A.Hoecker,…) , the official simulation for the CSC note H   (N.Berger, Y.Fang, …) and techniques described in stat CSC note G.Aad & al.arXiv:0901.0512 Nansi Andari 27-2-2009

  3. I- Techniques for evaluating the systematic on the mass resolution in discovery Generate simulated experiments with only background (B toys) and signal+background (S+B toys), parametrizing m(gg) with: - A crystalball for the signal (Ns=355), with mass resolution  ; - An exponential for the background (Nb=50688) . Fit each toyMC fixing different resolutions: , +15%, -15% S+B toys B toys Methods to evaluate the significance: 1- evaluation of the p-value using the median of 2 ΔNLL of S+B toys assuming for the B toys distribution 2- evaluation of the p-value integrating above the median of S+B the B toys distribution 3- (approximative) 4- Ns/ error(Ns) 2 ΔNLL Nansi Andari 27-2-2009

  4. Checking the 2 approximation < 2 ΔNLL> = 0.4975 Standard 10fb-1 2 ΔNLL Good < 2 ΔNLL> = 0.4989 < 2 ΔNLL> = 0.4959 Up Down 10fb-1 10fb-1 2 ΔNLL 2 ΔNLL Nansi Andari 27-2-2009

  5. Method 3: We are fitting the same datasets => the significances are correlated => the error on the difference of the significance is even smaller! Δ= -(1.7 +/- 0.1)*10-2 Δ/significance= -0.57% Δ= -(1.0 +/- 0.1)*10-2 Δ/significance= -0.34% (-) – () (+) – () Nansi Andari 27-2-2009

  6. The difference of the significance obtained by the 4 methods Results for all methods are well coherent. Nansi Andari 27-2-2009

  7. Comparison with CSC Numbers -(9.7  1) % Y.Fang -4.2% <>= - 0.01527  0.003 1000 toys Similar to what was shown on previous page Small difference: Much higher in the CSC note! - 0.6%+/- 0.3% This is different from what namely expected ( -[1.3739/1.58] = - 6.75%) for a gaussian. Is this due to the use of crystalball? Difference of significances as result of fitting Toys (1.58) with 1.58 and 1.36 Nansi Andari 27-2-2009

  8. Parenthesis: Comparison CrystalBall vs Gaussian Black: Gaussian with  Red: Crystalball with - Green: Crystalball with  Blue: Crystalball with + Nansi Andari 27-2-2009

  9. Gaussian Function with  = 1.58 CrystalBall Function with  = 1.58 and - =1.36 Integral Integral Integral (mH #) /Total Integral vs the number of  #  # , - taking away the standard  /- effect Significance Significance Very small difference reduced significance vs the number of  Larger for Gaussian than for crystal ball #  # , - The max of significance corresponds to 1.5  and to 1.5 - The max of significance corresponds to 1.4  Nansi Andari 27-2-2009

  10. Ratio between the significance corresponding to the resolution 1.36 and that to 1.58 Ratio Effect < 1% (in the good direction) #  Nansi Andari 27-2-2009

  11. III- Systematics on exclusion due to the knowledge of mass resolution  Fit each toyMC fixing different resolutions: , +15%, -15% If S  Sfix If S > Sfix S+B toys B toys Equivalent to q1 (CSC Book p 1485) 2 ΔNLL’ Nansi Andari 27-2-2009

  12. Results At 10fb-1 Standard Good 2 ΔNLL’ Up Smaller than Down Larger than 2 ΔNLL’ 2 ΔNLL’ Toys with S>Sfix are more than in the Standard case: - the pic at zero is bigger; - the distribution of toys with S<Sfix is smaller than 1/22 & ViceVersa… Nansi Andari 27-2-2009

  13. Results At 0.5fb-1 Standard 2 ΔNLL’ The 2 gives a very similar result Up Down 2 ΔNLL’ 2 ΔNLL’ Nansi Andari 27-2-2009

  14. RESULT AT 0.5fb-1, NO LOWER LIMIT ON Ns If we don’t set a positive limit on the number of signal events fitted, we obtain a 2even at 0.5fb-1 Standard 2 ΔNLL’ Down Up 2 ΔNLL’ 2 ΔNLL’ Nansi Andari 27-2-2009

  15. CL(%) vs Luminosity(fb-1) Standard Up Down Nansi Andari 27-2-2009 No difference

  16. IV- Systematics on the signal Cross Section for the exclusion What happens if the cross section is different by 20%? Generate and fit toy MC assuming a theoretical uncertainty of 20% on the number of signal events. Background=50688 Nansi Andari 27-2-2009

  17. Standard Good 2 ΔNLL’ Up Down 2 ΔNLL’ 2 ΔNLL’ Nansi Andari 27-2-2009

  18. What happens if the cross section is different by 20% but we always make the same hypothesis? Generate and fit toy MC assuming a theoretical uncertainty of 20% on the signal cross section in the generation and fitting always with the SM hypothesis: Study of the exclusion Background=50688 Nansi Andari 27-2-2009

  19. Fit with S Standard 2 ΔNLL’ Up Down Not a 2 2 ΔNLL’ 2 ΔNLL’ Nansi Andari 27-2-2009

  20. V- Conclusion • Preliminary study of the systematic error due to the fixed mass resolution has been performed both for observation and exclusion of a signal. • For the observation different methods and significance estimators have been compared: results are coherent. • A variation of 15% on the mass resolution implies a systematic error of (9.7+/- 1)% (coherent with CSC note value 8.4%). The systematic error due to a fixed value different by 15% from the truth is (0.6+/-0.3)% , not coherent with the CSC value (4.2%) • We evaluated the exclusion (CL) as a function of the integrated luminosity: to exclude the Standard Model at 95%CL we need 3fb-1. • A first look at the impact of the Standard Model cross section uncertainty on the exclusion (CL) has been given: no big effects observed. (To be complete…) Nansi Andari 27-2-2009

  21. BACKUP Nansi Andari 27-2-2009

  22. Mediane=8.65482 P-Value=0.00163099 CL=99.83% En comptant: Pvalue=0.0017 CL=99.83% Mediane=8.5907 P-Value=0.00168942 CL=99.83% En comptant: Pvalue=0.008 CL=99.82% Mediane=8.54115 P-Value=0.00173603 CL=99.82% En Comptant: Pvalue=0.0021 CL=99.79% Nansi Andari 27-2-2009

  23. Up-Standard Difference of the total events number Down-Standard Nansi Andari 27-2-2009

  24. At Different Luminosities Nansi Andari 27-2-2009

  25. Fitted number of events Number of Signal events Number of Background events Nb Ns Nansi Andari 27-2-2009

  26. Distribution of the total events number <>=51043 Standard No difference in the mean value of the total events number <>=51043 <>=51043 Up Down Nansi Andari 27-2-2009

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