G. Cowan RHUL Physics Status of Higgs combination page 1 Status of Higgs Combination ATLAS Higgs Meeting CERN/phone, 7 November, 2008 Glen Cowan, RHUL

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


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


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,...)


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...


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


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


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


p-value / significance of hypothesized

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

Equivalently use significance:


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).


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


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


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.


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.


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).


p-value of =1 (SM) versus mH



p-value of =1 (SM) versus mH



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


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


Median 95% CL limit on assuming no Higgs


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.


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.


Extra slides


Expected discovery significance from WW0j

with spin correlations

no spin correlations


Luminosity for 5 discovery assuming SM Higgs


Luminosity for 95% CL exclusion


Median 95% CL limit on assuming no Higgs