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Status of Higgs Combination

Status of Higgs Combination. ATLAS Higgs Meeting CERN/phone, 7 November, 2008. Glen Cowan , RHUL Eilam Gross, Weizmann Instutite. Outline. Overview of HG11 goals, people involved, documents Review of combination method Validation of approximations used Results of combination Summary.

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Status of Higgs Combination

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  1. Status of Higgs Combination ATLAS Higgs Meeting CERN/phone, 7 November, 2008 Glen Cowan, RHUL Eilam Gross, Weizmann Instutite Status of Higgs combination

  2. Outline • Overview of HG11 goals, people involved, documents • Review of combination method • Validation of approximations used • Results of combination • Summary Status of Higgs combination

  3. CSC HG11 Overview Describes statistical methods for combination of search channels. Applies combination to (a subset of) Higgs channels: WW→enmn (0-jet and 2-jet), gg, tt,ZZ(*)→4l Treats systematics by means of profile likelihood method. Considers fixed-mass hypothesis; look-elsewhere-effect must be studied separately. NB gg and WW CSC notes describe floating-mass fits. Some approximations used for discovery/exclusion significance. Valid for L > 2 fb-1. For lower L need toy MC methods. Does not represent final word on methods -- other developments ongoing (Bayesian, CLs, look-elsewhere-effect,...) Status of Higgs combination

  4. CSC HG11 People Editors: Eilam Gross, Glen Cowan Contacts for individual channels: WW Bill Quayle gg Yaquan Fang tt Kyle Cranmer 4l Andrea Di Simone Note referee: Fabiola Gianotti Chapter referees: Fabio Cerutti, Bruno Mansoulie Chapter editors: Rachid Mazini, Bill Murray + e.g. Louis Fayard, Aleandro Nisati, Karl Jakobs, Dave Charlton, Ofer Vitells... Status of Higgs combination

  5. HG11 Documents Source of note in CVS: http://atlas-sw.cern.ch/cgi-bin/viewcvs-atlas.cgi/groups/StatForum AFS area for combination inputs: /afs/cern.ch/atlas/project/statistics/ The draft note circulated to collaboration (old WW numbers): ATL-COM-PHYS-2008-203, http://cdsweb.cern.ch/record/1137608 , http://indico.cern.ch/conferenceDisplay.py?confId=25831 higgs_combo_csc_3nov08.pdf The draft note (new WW numbers) 4 November 2008 version: http://indico.cern.ch/conferenceDisplay.py?confId=25831 higgs_combo_csc_4nov08.pdf Status of Higgs combination

  6. Reminder of combination method The single-channel likelihood function uses Poisson model for events in signal and control histograms: q represents all nuisance parameters, e.g., background rate, shapes m =1 is SM. m =0 is background only. There is a likelihood Li(m,qi) for each channel, i = 1, …, N. The full likelihood function is Status of Higgs combination

  7. Profile likelihood ratio To test hypothesized value of m, construct profile likelihood ratio: Maximized L for given m Maximized L Equivalently use qm = - 2 ln l(m): data agree well with hypothesized m→qm small data disagree with hypothesized m→qm large Status of Higgs combination

  8. p-value / significance of hypothesized m Test hypothesized m by giving p-value, probability to see data with ≤ compatibility with m compared to data observed: Equivalently use significance: Status of Higgs combination

  9. Sampling distribution of qm To compute p-value of hypothesized m, need distribution f (qm|m). For 5s discovery we need a p-value of 2.8 × 10-7; To estimate this using MC needs > 108 events. Wilk’s theorem: in large sample limit f (qm|m) should approach with w = ½. (a “half-chi-square” distribution). Validation exercise shows approximation OK for L≥ 2 fb-1. We use the half-chi-square approximation in the current note; for lower luminosities we will need MC to get f (qm|m) (feasible for exclusion limits at 95% CL). Status of Higgs combination

  10. Example from validation exercise: ZZ(*)→ 4l Distributions of q0 for 2, 10 fb-1 from MC compared to ½c2 ½c2 ½c2 (One minus) cumulative distributions. Band gives 68% CL limits. ½c2 ½c2 5s level Status of Higgs combination

  11. Special treatment for WW+0j discovery For WW (→ Bill Quayle), further systematic studies were carried out that went beyond profile likelihood method. Parameter variations were considered to minimize the sensitivity of the qm distribution to variations in other fixed parameters such as QCD scale. For WW0j discovery (m=0), the parameter alterations led to a distribution of q0 significantly different from expected form. original parameters altered parameters Status of Higgs combination

  12. Special treatment for WW+0j discovery (2) So for WW0j discovery (m=0), the p-values were determined by toy MC and transformed to effective q0 values according to which was then used in the formula for the median significance. Status of Higgs combination

  13. Sensitivity Discovery: Generate data under s+b (m = 1) hypothesis; Test hypothesis m = 0 →p-value →Z. Exclusion: Generate data under background-only (m = 0) hypothesis; Test hypothesis m = 1. If m = 1 has p-value < 0.05 exclude mH at 95% CL. Estimate median significance by setting data equal to expectation values (Asimov data) or by using MC. For median, can combine significances of individual channels. For significance of e.g. a real data set, need global fit. Status of Higgs combination

  14. Combined discovery sensitivity No WW0j spin correlations With WW0j spin correlations Status of Higgs combination

  15. Combined discovery sensitivity No WW0j spin correlations With WW0j spin correlations Status of Higgs combination

  16. Combined discovery sensitivity No WW0j spin correlations With WW0j spin correlations Shaded band below 2 fb-1 indicates this region not accurate (but expected to be conservative). Status of Higgs combination

  17. p-value of m =1 (SM) versus mH No WW0j spin correlations With WW0j spin correlations Status of Higgs combination

  18. p-value of m =1 (SM) versus mH No WW0j spin correlations With WW0j spin correlations Status of Higgs combination

  19. 1 - p-value of m =1 (SM) versus L, mH No WW0j spin correlations With WW0j spin correlations Shaded band below 2 fb-1 indicates this region not accurate (but expected to be conservative). Status of Higgs combination

  20. Median 95% CL limit on m assuming no Higgs Status of Higgs combination

  21. Summary Combination method based on developed and applied to: WW→enmn (0-jet and 2-jet), gg, tt,ZZ(*)→4l Systematics incorporated using profile likelihood ratio. Work represents a “snapshot” of combination activities; other areas still ongoing activity (Bayesian, CLs, look-elsewhere-effect…) Approximations used expected to be valid for L ≥ 2 fb-1. For 2 fb-1: expected (median) sensitivity is ≥5s for discovery of a Higgs in the mass range between 143 and 179 GeV; expected upper limit at 95% CL on mH is 121 GeV. Status of Higgs combination

  22. Summary (2) Many comments by referees (and others) -- led to important improvements: More thorough explanation of mathematical approximations used and of their limitations. Comparison with methods used at LEP (appendix). Careful formulation of conclusions, e.g., results conservative as only subset of channels used; caveats concerning approximations; L < 2 fb-1 will need toy MC studies. Draft circulated to collaboration does not yet have WW spin correlations; these give improved sensitivity but no change in basic conclusions. Status of Higgs combination

  23. Extra slides Status of Higgs combination

  24. Expected discovery significance from WW0j with spin correlations no spin correlations Status of Higgs combination

  25. Luminosity for 5s discovery assuming SM Higgs Status of Higgs combination

  26. Luminosity for 95% CL exclusion Status of Higgs combination

  27. Median 95% CL limit on m assuming no Higgs Status of Higgs combination

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