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Application of CLs Method to ATLAS

Application of CLs Method to ATLAS. Catherine Wright Samir Ferrag 03/12/07. Introduction. Our aim : To introduce the LEP Statistical methods to ATLAS and assess the usefulness of the method in the context of Higgs discovery at ATLAS. What we will show :

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Application of CLs Method to ATLAS

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  1. Application of CLs Method to ATLAS Catherine Wright Samir Ferrag 03/12/07

  2. Introduction Our aim: To introduce the LEP Statistical methods to ATLAS and assess the usefulness of the method in the context of Higgs discovery at ATLAS. • What we will show: • LEP Style results for the ttH and H-> channels. And now H too. • But first.. • Introduce Shape Analysis and CLs method of interpretation. • Results with CLS method using T.Junk’s mclimits.C code -CDF/DOC/STATISTICS/PUBLIC/8128 • https://plone4.fnal.gov:4430/P0/phystat/packages/0711001/1.0.0/view

  3. Discovery Process To quote Alex Read: ‘EXCLUSION  OBSERVATION  DISCOVERY  MEASURE’ LEP2 placed a 95% Confidence Level exclusion on the mass of the Higgs at lower than 114.4GeV. All we have so far, are exclusion limits. Tevatron are close to exclusion (or discovery) at 160GeV. Will ATLAS need to place limits? Or are we just going to jump in at the deep end and find the Higgs? If yes (to calculating limits), we should exploit the expertise of previous experiments and examine the usefulness of CLs at LHC.

  4. Log-Likelihood Ratio Analysis Bin-by-bin Log-Likelihood Ratio analysis on the signal and background distributions of the channel in question. The LLR is given by:- • Where:- • si and bi are the number of signal and background events in bin, i, respectively. • N is the total number of bins. • ni is the total number of events in the bin, i. • Basically, it is a sum of the weights, where the weight is given by:

  5. Getting the Probability Density Functions • There are two LLR distributions – representing the H1 and H0hypotheses. • H1 is thetest hypothesis, of signal plus background (One Test Hypothesis per mass point). • H0 is thenull hypothesis of background only. • How to make the LLR Distributions: • Make template for the null hypothesis, H0 (say t0) from reconstructed data. • Make template for the signal plus background hypothesis, H1 (say t1) from reconstructed data. • ‘Generate’ fake data in ROOT, which follows the reconstructed signal plus background template, t1 within Poisson statistical fluctuations. •  Calculate LLR for background (H0) and for signal plus background (H1). • Generate ‘Data’ 10,000 times (i.e. make 10,000 pseudo experiments) •  Get -2lnQ distributions for H1 and H0.

  6. 1 - CLb CLs+b Interpreting Results Equivalent to the CLS method from LEP Only no data yet so can’t quote a significance, only the potential for discovery/exclusion and Luminosity requirements for each. 1-CLs+b = Discovery potential. CLs+b = False Exclusion Rate CLb = Exclusion potential 1-CLb = False Discovery Rate  Significance Level So, to Exclude at 95% CL: CLb i.e. the False Exclusion Rate (CLs+b) cannot be any more than 5% of the Exclusion Potential (CLb). 1 – CLs+b LEP Exclusion Tool: To exclude at given modified Confidence Level (CL):

  7. Example Results @ 30fb-1 - H: mass=120GeV Significance*~3.5s H1 H0 - ttH (Hbb): mass=120GeV Significance*~1.5s

  8. Combining Channels Bin-by-bin Log-Likelihood Ratio analysis on the signal and background distributions of each of the channels in the analysis – as for Tevatron combination exercises. (See CDF Note 8384/ D0 5227.) The LLR is given by:- (as for one channel) • Where:- • si and bi are the number of signal and background events in bin, i, respectively over all analyses. • N is the total number of bins over all analyses. • ni is the total number of events in the bin, i, for the hypothesis being tested. i.e. the sum now runs over the total number of bins and/or analyses being considered.

  9. ttH, H-> Combination Results • Combined significance at 120 GeV using • plots in mass range 0-350 GeV is ~4.2 Feasibility of discovery/exclusion with 30fb-1 of data, increased by combining two low mass channel results.

  10. Where we are now… Preparing to present exclusion limits, discovery limits etc on the channels: (ttH(Hbb), H, H) e.g. Also like to include systematics that affect rate… running on H  at the moment. For ttH – hoping to get new distributions to work from soon. For H - have distributions, but are normalised to 1fb-1 so expected event in bin < 1… not feasible for use with mclimits code so working to attain unnormalised plots or scale factors and uncertainties. Can’t place a limit on the mass til we have more than one mass point… so PTO for all the data we will need..

  11. Relevant Mass Points & Channels Included.. To be included.. And then possibly CMS Channels… May not be used..

  12. A Foray into systematics…

  13. Effect of Systematics Some systematic uncertainties affect the expectedrate of the signal and background, whilst others affect the expectedshape of the distributions. The systematics shown here are preliminary and are estimated from Performance Group results, theoretical uncertainties and the systematic uncertainties from the Tevatron (ref: FERMILAB-PUB-03/320-E). • In mclimits these two systematics are treated separately. • A number is provided for the nuisance parameters that affect expected rate. • A histogram must be provided for those affecting expected shape.

  14. Systematic Uncertainties (Rate) These systematics all affect the expected rate of signal and background.

  15. Systematic Uncertainty (Shape) The expected shape of the signal and background distributions can be affected by JES, Lepton Energy Scale, b-tagging (ttH) etc. We approximate this as a 5% effect on the resolution of the distributions. Signal (H->) Background (,j,Z->ee) Distributions corresponds to a 1 shift in the shape of the signal and background distributions. Background (ttbb,ttjj) Signal (ttH)

  16. Results – Including Systematics Probabilities are reduced as a result of including the systematics though not hugely… Discovery/Exclusion limits with 30fb-1 remains feasible in this channel. With 30fb-1, (and systematic uncertainties as suggested) would not be possible to place limits on the exclusion of the Higgs with the ttH channel.

  17. ttH, H-> Combination Results Looks like adding the systematics makes H-> more favourable on its own… Is this really the case?

  18. Back Up

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