[PPT] - (Tentative) Summary of the different methods to measure the spin in PowerPoint Presentation

SLIDE 1

(Tentative) Summary of the different methods to measure the spin in H→γγ

J. Schaarschmidt, JB. de

Vivie (LAL),

S. Laplace (LPNHE)

HSG1 meeting, September 13th 2012

1

jeudi 13 septembre 2012

SLIDE 2

Introduction

2

Steps to measure spin in H→γγ:
Variable to disentangle the background: diphoton mass. Different methods

to exploit it:

1D fit on mass:
either to obtain S and B yields, for all events or in cosθ* bins
r to compute sWeights for cosθ* sPlots
2D fit on mass + cosθ*
Angular variable to measure the spin: cosθ*
3 possible definitions: boost axis, Collins Soper (used here), beam axis
test spin0/spin2 hypotheses using likelihood ratios:
«Tevatron style» L0/L2: test spin0 versus spin2 hypotheses - what has been

investigated so far and in this talk

«LHC style» L2/Lmin (see HSG7 meeting on Sept. 12): fit the fraction of spin0/spin2

components - not yet investigated

correlations between mass and cosθ* need to be known for some of the methods

jeudi 13 septembre 2012

SLIDE 3

Samples and technical points

3

Samples:
Signal (dN/dcosθ*∼const): official HSG1 D3PDs
Background: Wisconsin fast sim (thanks to them !)
Spin 2: unofficial D3PDs from J. Albert/F. Bernlochner of Pythia6 Graviton-

like mH=125 GeV (thanks to him !)

production modes available : gg (dN/dcosθ*∼1+6cos2θ*+cos4θ*) and qq

(dN/dcosθ*∼1-cos4θ*) (VBF not treated here)

note: J. Albert and JB de

Vivie noticed some weird differences for spin2 between Pythia6 and Pythia8. Anyway, official samples will be made with JHU generator...

Technical points:
workspace similar to official one, but with 2D pdf of mass and cosθ* (so

far non-correlated)

here, use Collins-Soper definition of cosθ* (note: this definition does

not «suffer» from the asymmetric kinematic cutoffs present in the Boost Axis definition mentionned by Wisconsin in HSG1 Sept. 6)

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SLIDE 4

cosθ* distributions

background

4

*)|

|Cos(

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Collins-Soper Frame Boost Axis Beam Axis Background

*)

Cos(
1
0.8 -0.6 -0.4 -0.2

0.2 0.4 0.6 0.8 1 0.01 0.02 0.03 0.04 0.05 0.06

Collins-Soper Frame Boost Axis Leading Boost Axis Subleading Beam Axis Background

(plots: M. Kuna)

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SLIDE 5

*)|

|Cos(

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Collins-Soper Frame Boost Axis Beam Axis Spin 0 Signal

cosθ* distributions

spin0/spin2

5

*)|

|Cos(

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Collins-Soper Frame Boost Axis Beam Axis Spin 2 qq

*)|

|Cos(

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Collins-Soper Frame Boost Axis Beam Axis Spin 2 gg

(plots: M. Kuna)

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SLIDE 6

cosθ* distributions

6

(plots: M. Kuna)

*)|

|Cos(

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Background Spin 0 Signal Spin 2 gg Spin 2 qq Collins-Soper

*)|

|Cos(

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

Background Spin 0 Signal Spin 2 gg Spin 2 qq Beam Axis

*)|

|Cos(

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Background Spin 0 Signal Spin 2 gg Spin 2 qq Boost Axis

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SLIDE 7

Likelihood ratios definition

7

f S

c (cos θ∗ e|0, 2gg) = 0f S 0 (cos θ∗ e) + S 2gg(cos θ∗ e) + (1 − 0 − 2gg)f S 2qq(cos θ∗ e)

cosθ* pdf for signal: sum of spin0, spin2 (gg and qq - vbf not included yet) pdfs with

fractions ε0, ε2gg and ε2qq=(1-ε0-ε2gg) - so far, used ε2gg =1 for spin2 hypothesis

the likelihood is given by:

−lnLS[+B]

c,[m] (0, 2gg) = (ˆ

nS+ˆ nB)−

e

ln

ˆ

nSf S

c (cos θ∗ e|0, 2gg)

f S

m(me|mH)

+ˆ nBf B

c (cos θ∗ e)

f B

m(me)

where one includes the background component or not, and the correlations or not

(here, without... )

the likelihood ratios are defined by:

−2lnΛ = −2lnL0 L2 = −2lnL(1, 0) L(0, 1)

«Tevatron way»: fixed fractions «LHC way»: floating fractions (χ2 behavior) not investigated yet (Gaussian behavior)

−2lnΛ = −2ln L2 Lmin = −2ln L(0, 1) L (ˆ 0, ˆ 2gg)

jeudi 13 septembre 2012

SLIDE 8

Methods

No Events used Signal extraction Mass-cos correlation LR for Hypo

r Hypothesis testing

No Events used extraction correlation needed ? binned ? content 1 S+B small mass window 1D fit on mass no(*) no 1D(c)[x1D(m)] S+B 2 S+B full mass window 2D fit on mass,cos yes no 2D(m,c) S+B 3 S 1D fit on mass in cos bins no(*) yes 1D(c) S 4 S sPlots yes yes 1D(c) S

8

J. Albert,
F. Bernlochner

(a bit different) Wisconsin

M. Fanti,

Wisconsin

S. Laplace, N. Rhone,

JB de Vivie

(*): remaining correlations within a mass or cosθ* bin is a systematic uncertainty → Goal of this presentation: comparison of statistical power of all these methods using inclusive toys

Previous work

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SLIDE 9

Statistical interpretation

9

asymmetric: usual type II error β symmetric: at q(α=β) Expected significance of spin0 hypothesis («N(σ)»): Probability to exclude spin 2 hypothesis if spin 0 is true («Pexcl»)

P(95%CL) = q(α2=0.05)

−∞

fS0(q)dq

without any a priori belief in spin0/spin2 with prejudice that spin0 is favored

Find q for spin2 excl. @ 95%CL (α2=0.05) «How often will we find a value of q that allows to exclude spin 2?»:

drawings: courtesy Jana

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SLIDE 10

Method #1

10

studies performed by M. Fanti (HSG1 Aug. 9 and Sep. 6) and Wisconsin (Sep. 6) + this study
1D fit of mass to get S and B, use LR(S+B)(c,m)
advantage:
events outside the signal mass window do not contribute to the spin0/spin2 separation:

the LR is effective only in a small mass window, and thus background correlations can be mostly ignored (still need to assess residual effect)

background pdf either from MC (Wisconsin, this study) or data (Fanti: narrow sideband)

L=10.7 fb-1, μ= 1.85, N(toys) = 10k spin2 L μ N(σ)

asym

Pexcl this study pythia6, 125 GeV 10.7 32.1 1.85 1.8 2.9 57 % 94 % Fanti pythia6, 300 GeV 5.9 30 ∼1.53

17 %

39 % Wisconsin JHU, 126.5 GeV 5.9 30 1.41 0.52 1.14

hard to compare results given the different L/

μ/spin2 samples used and the different ways of quoting results: should agree on benchmark values/stat. interpretation...

still: our result looks way too good ! More

checks needed

(1D fit on mass)

almost Gaussian behavior (not exactly so cannot rely on analytical formulae to derive significances)

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SLIDE 11

Method #2

11

studies performed by J. Albert, F. Bernlochner (HSG1 Apr. 12) + this study
advantage:
make use of full satistical power (cosθ* in fit: improved significance)
drawbacks:
need to correctly modelize mass-cosθ* correlations
hard to fit a 2D pdf in the data directly...

L=10.7 fb-1, μ= 1.85, N(toys) = 2k

L μ N(σ)

asym

Pexcl this study 10.7 1.85 1.9 61 %

J. Albert, F.

Bernlochner «up to with up to 90% CL with 15-25 CL exclus 15-25 fb-1» exclusion fb-1» (2D fit on mass-cosθ*) 5% «only» improvement over 1D fit in this ideal case without correlations: not worth the complication of a 2D fit ! here, without correlations

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SLIDE 12

Method #3

12

studies performed by Wisconsin (HSG1 Jun. 21) + this study (Jana)
advantages:
obtain the cosθ* distribution of signal events without a priori knowledge
do not need the background cosθ* pdf (only the signal pdf enters the LR)
correlations are less an issue in each cosθ* bins (residual effect to be quantified)

(1D mass fit in bins of cosθ*)

S+B fit in the data in each cosθ* bin toys :

bkg pdfs are obtained from B-only fit of

the data (different than slides 7, 8 where MC is used for bkg pdf)

obtain S per cosθ* bin → 10-bins histo
build binned likelihood ratio from histo

More details in Jana’s slides on the sharepoint:

https://espace.cern.ch/atlas-phys-higgs-htogamgam/Lists/ 2012%20HCP/Attachments/6/spin_from_signalyield.pdf

jeudi 13 septembre 2012

SLIDE 13

Method #3

13

Results:

L μ N(σ)

asym

Pexcl 10.7 1.3 41 % this study 21.4 1.85 1.7 58 % 32.1 2.1 66 %

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SLIDE 14

Method #4

14

(sPlots)

Study put on sharepoint in june, based on a simple inclusive toy not using the

workspace of the other studies in this talk - no precise significance computation yet

Advantages:
obtain the cosθ* distribution of signal events without a priori knowledge using

ALL events (in principle, more powerfull than method #3)

do not need the background cosθ* pdf (only the signal pdf enters the LR)
Drawback: basic sPlots assume no correlations. Extensions exist to handle them,

though...

Reminders on sPlots technique:
Likelihood fit on a control variable (mγγ)
Get covariance matrix from likelihood:
Compute sweights:
Apply sweight to each event to obtain SPlot of test variable (cosθ*) to obtain,
n average, the «true» signal distribution...

jeudi 13 septembre 2012

SLIDE 15

15

(sPlots)

Warning: spin2 distribution is from 300 GeV graviton here

more realistic case: L=20 fb-1, S/B=0.1

hSPlotSignal

Entries 13522

! cos 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Weighted signal events 50 100 150 200

hSPlotSignal

Entries 13522

sPlot spin 0, p=0.99 spin 2, p=0.00 background, p=0.99 250 ± = 1296

s

N 301 ± = 12078

bg

N

s-plot for signal

hSPlotSignal

Entries 13403

! cos 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Weighted signal events

100
50

50 100 150 200 250 300

hSPlotSignal

Entries 13403

sPlot spin 0, p=0.00 spin 2, p=0.00 background, p=0.00 106 ± = 1282

s

N 321 ± = 12106

bg

N

s-plot for signal

hSPlotSignal

Entries 190284

! cos 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Weighted signal events 2000 4000 6000 8000 10000

hSPlotSignal

Entries 190284

sPlot spin 0, p=0.00 spin 2, p=0.00 background, p=0.00 429 ± = 128834

s

N 737 ± = 60555

bg

N

s-plot for signal

hSPlotSignal

Entries 189465

! cos 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Weighted signal events 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

hSPlotSignal

Entries 189465

sPlot spin 0, p=0.96 spin 2, p=0.00 background, p=0.00 899 ± = 128837

s

N 738 ± = 60705

bg

N

s-plot for signal

ideal case: L=100 fb-1, S/B=2

no correlations with correlations: much wider spread

f sdata !

example toys

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SLIDE 16

Method #4:

Dealing with correlations

16

(sPlots)

hSPlotSignal Entries 165

! cos 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Weighted signal events 20 40 60 80 100 120 140 160 180

hSPlotSignal Entries 165

sPlot spin 0, p=0.68 spin 2, p=0.00 background, p=0.32 106 ± = 1285

s

N 295 ± = 12097

bg

N

s-plot for signal

hSPlotSignal

Entries 13403

! cos 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Weighted signal events

100
50

50 100 150 200 250 300

hSPlotSignal

Entries 13403

sPlot spin 0, p=0.00 spin 2, p=0.00 background, p=0.00 106 ± = 1282

s

N 321 ± = 12106

bg

N

s-plot for signal

Can compute the sweights using the knowledge of correlations taken from MC or

(better..) data sidebands:

Here: use another dataset generated with the same model as «MC»

neglecting correlations in SPlot SPlot including background correlations from «MC» modified sweight without cross-terms between signal and bkg data background sample (includes correlations) with

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SLIDE 17

Statistical Power of the different methods

17

No Events used Fit LR N(σ) spi σ) spin0

Prob. excl

spin2 @ No used Fit LR asym. sym. spin2 @ 95%CL 1 S+B (range) 1D(m) 1D(c) x1D(m) 1.84 0.93 57.1 % 2 S+B 2D (m,c) 2D(m,c) 1.9 0.98 61.1 % 3 S 1D(m) in cos bins 1D(c) 1.3 0.6 41 % 4 S sPlots 1D(c)

ngoing...

ng... mH = 126.5 GeV, L=10.7 fb-1, μ=1.85, N(toys) = 1000 no correlations spin2: gg only, mH=125 GeV

these numbers should not be taken litteraly for the moment

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SLIDE 18

Systematics to be investigated

(not exhaustive)

18

Background cosθ* pdf:
Wisconsin fast sim MC ?
Interpolation from sidebands in data ?
correlations with mass
Spin 2 model: common systematics for all channels
pT is not well predicted at all: hard to go beyond inclusive

analysis...

fractions of production modes (gg, qq, vbf) is not known: this

enters the model definition

...

jeudi 13 septembre 2012

SLIDE 19

Conclusions

19

Several methods available to measure the spin in H→γγ:
common points: input variables (m and cosθ*)
differences:
some require the knowledge of the background cosθ* distribution,
thers do not
some require the knowledge of correlations
some allow to *see* the signal cosθ*, which might be more convincing

eventually than only relying on the result of a statistical test (people like to actually see the bumps !)

f course, more knowledge given in input means more statistical power, but

larger systematics

ther methods could also be investigated (see e.g. hep-ph/1209.1037: use

center-edge asymmetrie instead of LR, claimed to be less sensitive to systematics)

bvious: need to define benchmark lumi/mu/spin2 models and agree on way of

quoting results (=quote both significances and exclusions)

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SLIDE 20

Backup

20

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SLIDE 21

Method #3: more results

21

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SLIDE 22

costhetastar distributions

22

*)

Cos(
1
0.8 -0.6 -0.4 -0.2

0.2 0.4 0.6 0.8 1 0.01 0.02 0.03 0.04 0.05 0.06

Background Spin 0 Signal Spin 2 gg Spin 2 qq Collins-Soper

*)

Cos(
1
0.8 -0.6 -0.4 -0.2

0.2 0.4 0.6 0.8 1 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

Background Spin 0 Signal Spin 2 gg Spin 2 qq Beam Axis

*)

Cos(
1
0.8 -0.6 -0.4 -0.2

0.2 0.4 0.6 0.8 1 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

Background Spin 0 Signal Spin 2 gg Spin 2 qq Boost Axis

jeudi 13 septembre 2012