G. Cowan RHUL Physics Status of Higgs combination page 1 Status of Higgs Combination ATLAS Higgs...

G. CowanRHUL Physics Status of Higgs combination page 1

Status of Higgs Combination

ATLAS Higgs Meeting

CERN/phone, 7 November, 2008

Glen Cowan, RHUL

Eilam Gross, Weizmann Instutite

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Outline

1) Overview of HG11 goals, people involved, documents

2) Review of combination method

3) Validation of approximations used

4) Results of combination

5) Summary

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CSC HG11 OverviewDescribes statistical methods for combination of search channels.

Applies combination to (a subset of) Higgs channels:

WW→e(0-jet and 2-jet), , ,ZZ(*)→4l

Treats systematics by means of profile likelihood method.

Considers fixed-mass hypothesis; look-elsewhere-effect mustbe studied separately.

NB and WW CSC notes describe floating-mass fits.

Some approximations used for discovery/exclusion significance.

Valid for L > 2 fb. For lower L need toy MC methods.

Does not represent final word on methods -- other developments ongoing (Bayesian, CLs, look-elsewhere-effect,...)

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CSC HG11 PeopleEditors: Eilam Gross, Glen Cowan

Contacts for individual channels:WW Bill Quayle Yaquan Fang Kyle Cranmer4l 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...

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HG11 DocumentsSource 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=25831higgs_combo_csc_3nov08.pdf

The draft note (new WW numbers) 4 November 2008 version:http://indico.cern.ch/conferenceDisplay.py?confId=25831higgs_combo_csc_4nov08.pdf

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Reminder of combination method

represents all nuisance parameters, e.g., background rate, shapes =1 is SM.

=0 is background only.

The single-channel likelihood function uses Poisson modelfor events in signal and control histograms:

There is a likelihood Li(,i) for each channel, i = 1, …, N. The full likelihood function is

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Profile likelihood ratioTo test hypothesized value of , construct profile likelihood ratio:

Maximized L for given

Maximized L

Equivalently use q = 2 ln ():

data agree well with hypothesized → q small

data disagree with hypothesized → q large

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p-value / significance of hypothesized

Test hypothesized by giving p-value, probability to seedata with ≤ compatibility with compared to data observed:

Equivalently use significance:

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Sampling distribution of q

To compute p-value of hypothesized , need distribution f (q|).

For 5discovery we need a p-value of 2.8 × 10;

To estimate this using MC needs > 108 events.

Wilk’s theorem: in large sample limit f (q|) should approach

with w = ½. (a “half-chi-square” distribution).

Validation exercise shows approximation OK for L ≥ 2 fb.

We use the half-chi-square approximation in the current note;for lower luminosities we will need MC to get f (q|)(feasible for exclusion limits at 95% CL).

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Example from validation exercise: ZZ(*) → 4l

5 level

(One minus)cumulativedistributions.Band gives 68%CL limits.

½2

½2

½2

½2

Distributions of q0 for 2, 10 fb from MC compared to ½2

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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 q distribution to variations in other fixed parameterssuch as QCD scale.For WW0j discovery (=0), the parameter alterations led toa distribution of q0 significantly different from expected form.

original parameters altered parameters

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Special treatment for WW+0j discovery (2)

So for WW0j discovery (=0), the p-values were determinedby toy MC and transformed to effective q0 values according to

which was then used in the formula for the median significance.

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SensitivityDiscovery:

Generate data under s+b (= 1) hypothesis;Test hypothesis = 0 → p-value → Z.

Exclusion:Generate data under background-only (= 0) hypothesis;Test hypothesis .If = 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.

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Combined discovery sensitivity

No WW0j spin correlations With WW0j spin correlations

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Combined discovery sensitivity

No WW0j spin correlations With WW0j spin correlations

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Combined discovery sensitivity

No WW0j spin correlations With WW0j spin correlations

Shaded band below 2 fb indicates this region not accurate(but expected to be conservative).

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p-value of =1 (SM) versus mH

No WW0j spin correlations With WW0j spin correlations

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p-value of =1 (SM) versus mH

No WW0j spin correlations With WW0j spin correlations

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p-value of =1 (SM) versus L, mH

No WW0j spin correlations With WW0j spin correlations

Shaded band below 2 fb indicates this region not accurate(but expected to be conservative).

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Median 95% CL limit on assuming no Higgs

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SummaryCombination method based on developed and applied to:

WW→e(0-jet and 2-jet), , ,ZZ(*)→4l

Systematics 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.

For 2 fb:

expected (median) sensitivity is ≥5 for discovery ofa Higgs in the mass range between 143 and 179 GeV;expected upper limit at 95% CL on mH is 121 GeV.

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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 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.

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Extra slides

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Expected discovery significance from WW0j

with spin correlations

no spin correlations

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Luminosity for 5 discovery assuming SM Higgs

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Luminosity for 95% CL exclusion

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Median 95% CL limit on assuming no Higgs