Status of Higgs Combination ATLAS Higgs Meeting CERNphone

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

Outline 1) Overview of HG 11 goals, people involved, documents 2) Review of combination method 3) Validation of approximations used 4) Results of combination 5) Summary G. Cowan RHUL Physics Status of Higgs combination 2

CSC HG 11 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(*)→ 4 l 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, . . . ) G. Cowan RHUL Physics Status of Higgs combination 3

CSC HG 11 People Editors: Eilam Gross, Glen Cowan Contacts for individual channels: WW Bill Quayle gg Yaquan Fang tt Kyle Cranmer 4 l 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. . . G. Cowan RHUL Physics Status of Higgs combination 4

HG 11 Documents Source of note in CVS: http: //atlas-sw. cern. ch/cgi-bin/viewcvs-atlas. cgi/groups/Stat. Forum 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/conference. Display. py? conf. Id=25831 higgs_combo_csc_3 nov 08. pdf The draft note (new WW numbers) 4 November 2008 version: http: //indico. cern. ch/conference. Display. py? conf. Id=25831 higgs_combo_csc_4 nov 08. pdf G. Cowan RHUL Physics Status of Higgs combination 5

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 G. Cowan RHUL Physics Status of Higgs combination 6

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 G. Cowan RHUL Physics Status of Higgs combination 7

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: G. Cowan RHUL Physics Status of Higgs combination 8

Sampling distribution of qm To compute p-value of hypothesized m, need distribution f (qm|m). For 5 s 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). G. Cowan RHUL Physics Status of Higgs combination 9

Example from validation exercise: ZZ(*) → 4 l Distributions of q 0 for 2, 10 fb-1 from MC compared to ½c 2 G. Cowan RHUL Physics ½c 2 Status of Higgs combination (One minus) cumulative distributions. Band gives 68% CL limits. 5 s level 10

Special treatment for WW+0 j 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 WW 0 j discovery (m=0), the parameter alterations led to a distribution of q 0 significantly different from expected form. G. Cowan RHUL Physics original parameters altered parameters Status of Higgs combination 11

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

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 m. H 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. G. Cowan RHUL Physics Status of Higgs combination 13

Combined discovery sensitivity No WW 0 j spin correlations G. Cowan RHUL Physics With WW 0 j spin correlations Status of Higgs combination 14

Combined discovery sensitivity No WW 0 j spin correlations G. Cowan RHUL Physics With WW 0 j spin correlations Status of Higgs combination 15

Combined discovery sensitivity No WW 0 j spin correlations With WW 0 j spin correlations Shaded band below 2 fb-1 indicates this region not accurate (but expected to be conservative). G. Cowan RHUL Physics Status of Higgs combination 16

p-value of m =1 (SM) versus m. H No WW 0 j spin correlations G. Cowan RHUL Physics With WW 0 j spin correlations Status of Higgs combination 17

p-value of m =1 (SM) versus m. H No WW 0 j spin correlations G. Cowan RHUL Physics With WW 0 j spin correlations Status of Higgs combination 18

1 - p-value of m =1 (SM) versus L, m. H No WW 0 j spin correlations With WW 0 j spin correlations Shaded band below 2 fb-1 indicates this region not accurate (but expected to be conservative). G. Cowan RHUL Physics Status of Higgs combination 19

Median 95% CL limit on m assuming no Higgs G. Cowan RHUL Physics Status of Higgs combination 20

Summary Combination method based on developed and applied to: WW→enmn (0 -jet and 2 -jet), gg, tt, ZZ(*)→ 4 l 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 ≥ 5 s for discovery of a Higgs in the mass range between 143 and 179 Ge. V; expected upper limit at 95% CL on m. H is 121 Ge. V. G. Cowan RHUL Physics Status of Higgs combination 21

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. G. Cowan RHUL Physics Status of Higgs combination 22