Status of Higgs Combination ATLAS Higgs MeetingCERN/phone, 7 November, 2008Glen Cowan, RHULEilam Gross, Weizmann Instutite

OutlineOverview of HG11 goals, people involved, documentsReview of combination methodValidation of approximations usedResults of combinationSummary

CSC HG11 OverviewDescribes statistical methods for combination of search channels.Applies combination to (a subset of) Higgs channels: WWenmn (0-jet and 2-jet), gg, tt, ZZ(*)4lTreats systematics by means of profile likelihood method.Considers fixed-mass hypothesis; look-elsewhere-effect mustbe 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,...)

CSC HG11 PeopleEditors: Eilam Gross, Glen CowanContacts for individual channels:WWBill QuayleggYaquan FangttKyle Cranmer4lAndrea Di SimoneNote referee:Fabiola GianottiChapter referees:Fabio Cerutti, Bruno MansoulieChapter editors:Rachid Mazini, Bill Murray+ e.g. Louis Fayard, Aleandro Nisati, Karl Jakobs, Dave Charlton, Ofer Vitells...

HG11 DocumentsSource of note in CVS:http://atlas-sw.cern.ch/cgi-bin/viewcvs-atlas.cgi/groups/StatForumAFS 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=25831higgs_combo_csc_3nov08.pdfThe draft note (new WW numbers) 4 November 2008 version:http://indico.cern.ch/conferenceDisplay.py?confId=25831higgs_combo_csc_4nov08.pdf

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

Profile likelihood ratioTo test hypothesized value of m, construct profile likelihood ratio:Maximized L for given mMaximized LEquivalently use qm = - 2 ln l(m):data agree well with hypothesized m qm smalldata disagree with hypothesized m qm large

p-value / significance of hypothesized mTest hypothesized m by giving p-value, probability to seedata with compatibility with m compared to data observed:Equivalently use significance:

Sampling distribution of qmTo 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.Wilks theorem: in large sample limit f (qm|m) should approachwith w = . (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).

Example from validation exercise: ZZ(*) 4l5s level(One minus)cumulativedistributions.Band gives 68%CL limits.c2c2c2c2Distributions of q0 for 2, 10 fb-1 from MC compared to c2

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

Special treatment for WW+0j discovery (2)So for WW0j discovery (m=0), the p-values were determinedby toy MC and transformed to effective q0 values according towhich was then used in the formula for the median significance.

SensitivityDiscovery: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 expectationvalues (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.

Combined discovery sensitivityNo WW0j spin correlations With WW0j spin correlations

Combined discovery sensitivityNo WW0j spin correlations With WW0j spin correlations

Combined discovery sensitivityNo WW0j spin correlations With WW0j spin correlations Shaded band below 2 fb-1 indicates this region not accurate(but expected to be conservative).

p-value of m =1 (SM) versus mHNo WW0j spin correlations With WW0j spin correlations

p-value of m =1 (SM) versus mHNo WW0j spin correlations With WW0j spin correlations

1 - p-value of m =1 (SM) versus L, mHNo WW0j spin correlations With WW0j spin correlations Shaded band below 2 fb-1 indicates this region not accurate(but expected to be conservative).

Median 95% CL limit on m assuming no Higgs

SummaryCombination method based on developed and applied to:WWenmn (0-jet and 2-jet), gg, tt, ZZ(*)4lSystematics incorporated using profile likelihood ratio.Work represents a snapshot of combination activities; other areasstill 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 ofa Higgs in the mass range between 143 and 179 GeV;expected upper limit at 95% CL on mH is 121 GeV.

Summary (2)Many comments by referees (and others) -- led to importantimprovements:More thorough explanation of mathematical approximationsused 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 inbasic conclusions.

Extra slides

Expected discovery significance from WW0jwith spin correlationsno spin correlations

Luminosity for 5s discovery assuming SM Higgs

Luminosity for 95% CL exclusion

Median 95% CL limit on m assuming no Higgs