SUSY 1lepton background multidimensional fits CSC Note 1

1
SUSY 1-lepton background multidimensional fits
CSC Note 12 ATLAS SUSY WG

• A. Koutsman W. Verkerke, NIKHEF
• 23 augustus 2007

2
One lepton mode SUSY
1 fb-1
Effective mass (GeV)

• Dominant backgrounds
• Top pair
• Wjets
• QCD
• Zjets

• GOAL estimate and understand backgrounds from
  data
• TARGET Develop methods to discover/exclude SUSY
  with 1 fb-1

3
Multidimensional method

• MT Method
• extrapolate Wjets/ttbar bkg from control region
  (low MT) to signal region (high MT)
• Main Idea Improve MT method
• Try to use additional observables for
  extrapolation (e.g. mtop)
• Explicitly account for SUSY contamination in
  control region

Overestimated by factor 2.5
Key issues to understand - Amount of
correlations between observables and type
of correlation - Amount and shape of SUSY
in control region
4
Fitting the background w/o correlations

• In absence of correlations, we can construct
  relatively simple multi-dimensional models to
  describe background data
• E.g. Pttbar(MT,ET,mtop) P1(MT)?P2(ET)?P3(mtop)
• New observable reconstructed hadronic top mass
  mtop
• Defined as invariant mass of 3 jet system with
  highest sum pT
• Next step Write model that describes combined
  background in control region and use that to
  extrapolate to signal region
• Ptotal(MT,ET,mtop) Ntt1l Ptt1l(MT,ET,mtop)
  Ntt2l
  Ptt2l(MT,ET,mtop)
  Nwnj Pwnj(MT,ET,mtop)
  Nsusy Psusy(MT,ET,mtop) (Ansatz model)
• Idea Hope for improved determination of SM
  backgrounds due to
• Additional observables used in procedure
• Generic SUSY component included in fit to account
  for non-zero SUSY contamination in control region

5
First iteration of combined background fit

• Start out with simplest exercise Shapes of
  components fixed
• Determined from fits to individual background MC
  samples
• Shapes chosen for various
• backgrounds
• TTbar Semileptonic
• (11214110 parameters)
• exponential in missing ET
• exponentialgauss in mtrans
• landaugaus in mtop
• TTbar Dileptonic
• (1225 parameters)
• exponential in missing ET
• gauss in mtans
• landau in mtop
• Wjets
• (112127 parameters)
• exponential in missing ET
• exponentialgauss in mtrans
• landau in mtop

TTbar Semileptonic
TTbar Dileptonic
Wjets
6
First iteration of combined background fit w/o
SUSY

• Now fit model for combined background with fixed
  shapes to mix of background samples and see if
• We have enough information in fit to constrain
  various fractions
• If we find back the fractions of background that
  went into the fit (no bias etc)
• Fits on 1 fb-1 of data

Fit Truth Ndi
123 17 141 Nsemi 567
40 578 Nwjets 168 35
140
OK!
7
Next iteration of combined background fit

• Include generic SUSY contribution in fit (flat in
  ET, gentle slope in MT,
• landau in mtop) and fit to data with SUSY
  SU3 contamination
• Combined fit with SUSY on 1 fb-1 of data

Fit Truth Ndi
146 25 141 Nsemi 557
43 578 Nwjets 168 43
140 Nsu3 216 24 228
OK
8
Combined background fit cross checks

• Cross check 1 fit model with floating SUSY
  component to data w/o SUSY
• Cross check 2 fit model w/o SUSY component to
  data with SUSY contamination

Fit
Truth Ndi 125 18
141 Nsemi 565 40
578 Nwjets 172 35
140 Nsu3 -3 4.7 0
OK
Fit
Truth Ndi 331 26
141 Nsemi 427 37
578 Nwjets 329 37
140 Nsu3 0(fixed) 228
OK
9
How well does the generic SUSY shape work?

• Are we sure the fit is not biased? Run fit 1000
  times on toy MC samples drawn from combined
  background p.d.f. fitted to MC-data and look at
  pull distributions
• In the fit we have taken a generic shape for SUSY
  component. How well does it portray other SUSY
  points?
• Fit to pull distributions offraction SUSY in
  combined fit
• SU1
• mean -0.027 0.052
• s 0.993 0.037
• SU2
• mean -0.067 0.057
• s 1.040 0.037
• SU3
• mean -0.0006 0.051
• s 0.958 0.032

1000 toy MCs output
Fits are unbiased
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Summary simple fit with generic SUSY component

• Have enough information in MT,ET,mtop to
  constrain individual background components
  (tt1l,tt2l,Wjets)
• Can account for unknown SUSY contribution in
  control region with generic SUSY component in fit
• In current simplified approach the generic SUSY
  component in fit allows unbiased determination of
  amount of SM background in presence of unknown
  amount of SUSY in data
• Have checked with multiple SUSY data points that
  procedure essentially works for all SUSY points

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How to deal with correlations?

• 2D histograms give a clue, but no quantative
  account
• In the previous iteration we dealt with simple
  factorizable PDFs
• What if ET and MT have a small correlation?
  How can we understand it?
  How do we model it?
• CONDITIONAL PDFs
• Model the dependence of ET and MT and functions
  of each other

12
Are ET, MT correlated in signal/bkg?

• Procedure
• Slice sample in bins of MT and look at ET
  distribution
• Make fit to distribution in each slice, see if
  fit parameter changes vs MT
• Make sure fits model
• can describe data in
• every slice

Wjets
0ltMT10
20ltMT30
30ltMT40
10ltMT20
40ltMT50
50ltMT60
60ltMT70
70ltMT80
110ltMT120
80ltMT90
100ltMT110
90ltMT100
missing ET
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Model the correlation

• First Look at ET slope dependence vs MT slice
• Conclusion
• There is a correlation because
• slope is not constant

• Next step try to model this dependence by
  replacing
• with slope of ET expressed as polynomial in
  MT
• Fit 2D distribution with 2D conditional product
  PDF and see if ET slope dependence on MT is
  correctly described

For MTgt160 statistics is the bottle neck and
fits are not trustworthy
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Fit the 2D distribution

• Now fit the 2D model with conditional dependence
• Wjets
• conditional exponential in ET
• exponentialgauss in MT
• Check the results of the fit by
• comparing the conditional PDF
• with data ? very good agreement
  

2D fit result Sliced data
OK
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Alternate correlation coordinates

• What if we turn the observables around?
• Slice sample in bins of ET and look at MT
  distribution
• Wjets exponentialgauss in MT
• 4 parameters slope(1) of the exponential
  mean(2),sigma(3) and fraction (4) of gaussian
• Multiple parameters cause
• more difficulty, low statistics
• make fits unstable

80ltET90
90ltET100
100ltET110
110ltET120
120ltET130
130ltET140
140ltET150
150ltET160
160ltET170
180ltET190
170ltET180
190ltET200
Thus we set the mean of the gaussian constant and
float all other parameters
200ltET210
230ltET240
220ltET230
210ltET220
MT peak portrays W-mass
MT
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Is MT dependent on ET?

• Make a plot of each parameter of MT as a function
  of ET

• Statistics insufficient for
• ETgt300 (less than 20 events)
• Sigma gaussian constant (no dependence)
• Fraction gaussian gentle slope
• Exponential slope very gentle slope

Now we can fit

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Double conditional pdf (Wjets)

• But were really after
• Shape of MT depends on ET and shape ET depends on
  MT
• Wjets try-out
• Model the development of
• the shapes by polynomials
• Fit the Wjets in ET,MT to the
• data with two simple conditional
• dependences
• Check if correlations come out of the fit
  correctly
• conditional exponential in ET

N.B. binned fits shown here

• conditional exponentialgauss in MT

OK
18
Triple conditional dependence

• Now double conditional fit works for ET,MT we
  studied also the correlations with 3rd variable
  mtop using same procedure
• Idea once we have studied all the correlations,
  we want to fit our model in all three variables
  (ET, MT, mtop). If necessary every parameter from
  the plain model gets fashioned with a correlation
  to other variables. So we get a triple
  conditional pdf to describe each individual
  background sample.
• Example
• How well does the triple conditional correlations
  model fit our data?
• Checks done for every background sample
• Make sure that all correlation coefficients are
  significant
• Global correlation of each coefficient should be
  reasonable
• Keep all the correlations that pass the checks
  and on to combined fit

OK
Wjets
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Combined background fit

• Summary
• for every background sample (Wjets,
  tt?lnln, tt?lnqq) we
• have now a conditionally dependent
  multi-dimensional
• model that fits the data
• Next step
• Construct a combined model that describes
  combined background and a non-zero contamination
  from SUSY in control region
• Pdata(MT,ET,mtop) Ntt1l Ptt1l(MT,ET,mtop)
  Ntt2l
  Ptt2l(MT,ET,mtop)
  Nwjets Pwjets(MT,ET,mtop)
  Nsusy Psusy(MT,ET,mtop) (Ansatz model)
• How well does the new correlated model fit the
  data?
• Is it better than the simplified model?

20
First iteration of correlated combined bkg fit

• Start out with simplest exercise Shapes of
  components fixed
• Determined from fits to individual background MC
  samples
• Shapes chosen for various backgrounds
• TTbar Semileptonic
• Correlated model
• 15 parameters
• Simple model
• 10 parameters
• TTbar Dileptonic
• Correlated model
• 7 parameters
• Simple model
• 5 parameters
• low statistics make
• correlation studies difficult
• Wjets
• Correlated model
• 15 parameters

TTbar Semileptonic
TTbar Dileptonic
Wjets
SU3
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Combined background fit w/o SUSY

• First fit model for combined background w/o SUSY
  component with fixed shapes to mix of background
  samples
• Do we find back the fractions of background that
  went into the fit?
• How are the fractions compared to fit with the
  simplified model?
• Fit on 1fb-1 of background data

Correlated Fit Plain Fit
Truth Ndi 220 26
235 25 229 Nsemi 1073
62 1074 63
1072 Nwjets 416 61 401
61 408
OK
N.B. following results shown for release-11, but
comparable with release-12
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Combined background fit with SUSY

• Now we include SU3 contamination into our data
  and a generic SUSY contribution into our model (
  Ansatz model SUSY flat in ET,
• gentle slope in MT, landau in mtop)
• Fit with shapes of components fixed on 1fb-1 of
  data

Correlated Fit Plain Fit
Truth Ndi 180 42
158 39 229 Nsemi
1095 65 1127 67
1072 Nwjets 434 66 382
68 408 Nsu3 379 36
420 36 378
Correlated fit a bit better
23
Combined background fit cross checks

• Cross check 1 fit model with floating SUSY
  component to data w/o SUSY
• Cross check 2 fit model w/o SUSY component to
  data with SUSY contamination

Correlated Fit Plain Fit
Truth Ndi 239 32
219 31 229 Nsemi
1066 62 1080 64
1072 Nwjets 421 61 396
61 408 Nsu3 -17 16
14 18 0
OK
Correlated Fit Plain Fit
Truth Ndi 592 38
623 38 229 Nsemi
972 61 979 61
1072 Nwjets 524 64 484
64 408 Nsu3 0(fixed)
0(fixed) 378
OK
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How well does the generic SUSY shape work?

• Are we sure the correlated fit is not biased?
  Again run fit 1000 times on toy MC samples drawn
  from combined background p.d.f. fitted to MC-data
  and look at pull distributions
• How well does the combined correlated fit
  portray other SUSY points?
• Fit to pull distributions offraction SUSY in
  combined fit
• SU1
• mean -0.096 0.056
• s 1.005 0.036
• SU2
• mean -0.021 0.055
• s 1.031 0.037
• SU3
• mean -0.023 0.055
• s 1.030 0.036

1000 toy MCs output
Fits are unbiased
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Summary on fits with correlations

• Shown that we can determine the amount of
  individual background components and a generic
  SUSY contamination correctly using a simplified
  model w/o correlations in a multidimensional fit
• Possible correlations of parameters in ET,MT and
  mtop have been studied for all background samples
• Non-negligible correlations between variables
  have been introduced into the our model using
  triple conditional pdfs
• The correlated model has enough information in
  MT,ET,mtop to constrain individual background
  components (tt1l,tt2l,Wjets) and account for
  unknown SUSY contamination in control region
• Effect of correlations is not huge ? Aim to
  introduce a subset of most important correlations
  in final model
• Next
• Exclude signal region from fit and test the
  procedure
• of extrapolation from control region

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Extrapolation control region ? signal region

• Have shown that we can distinguish amounts of
  Wjets, tt(1l) and tt(2l) background from data
  using full observables space
• Now repeat exercise without signal region
• Fit Wtt(1l)tt(2l)genericSUSY background to
  data in control region
• Extrapolate amount of W,tt(1l),tt(2l) to signal
  region
• Compare predicted amounts in signal region to MC
  truth
• Shapes still fixed (releasing shape parameters
  last step of whole exercise)

27
First iteration fit extrapolation

• Define two sidebands in MT, ET
• Example
• SB1 0 lt MT lt 120
• ET full range
• SB2 120 lt MT lt 300
• 0 lt ET lt 300
• Fit the combined model in both ranges
• While extrapolating make sure fractions are
  correctly defined

28
Combined fit extrapolation

• First try-out do extrapolation only in MT
• SB1 0 lt MT lt 70
• SB2 70 lt MT lt 150
• Do extrapolation in both observables
• SB1 0 lt MT lt 70
• 100 lt ET lt 200
• SB2 70 lt MT lt 150
• 200 lt ET lt 250

Fit Truth Ndi
51 12 49 Nsemi 4.6
0.7 4 Nwjets 4.5 1.2
3 Nsu3 114 12 118
OK
Fit Truth Ndi
2.6 2 5 Nsemi
0.1 0.04 0 Nwjets 1e-4 0.03
1 Nsu3 67 2 64
OK
29
Summary and outlook

• We can correctly determine the amount of
  background in the control region using only a
  part of the observables space
• The extrapolation to the signal region works
  accurately using fit results from the control
  region
• ? Control region is enough to determine
  the amounts of W, tt(1l) and tt(2l) background
• ? We do no need the signal region to
  determine the amount of SUSY contamination in the
  control region
• LAST STEP float as many shape parameters of the
  
• distribution as possible
  and show that fitting
• procedure still works

30
Back-up slides
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Method-1 (S.Asai, K.Oe) CSC Note1/2

• Main idea separate data in two sets
• MTgt100 signal region
• MTlt100 control region
• Assumption-1 the shape of BG in control region
  is same as shape of BG in signal region ? Just
  need to scale with events
• Assumption-2 SUSY is negligible in control region

Top Wnjets
Top Wnjets SUSY
Estimated signal region X scaling
Works without SU3 in the game ?Assumption 1
is fairly good
Actual BG can be estimated correctly
Estimated BG over- estimated by factor 2
Problems with SU3 ?Assumption 2 is no
good
(Kenta Oe Shoji Asai)
(Kenta Oe Shoji Asai)
32
Release 12 Samples

• W0,1,2,3,4,5 partons
• WenunJets (n2..5) 5223-5226
• WmununJets (n3..5) 8203-8205
• WtaununJets (n2..5) 8208-8211
• T1 (MC_at_NLO) 5200
• separate at truth-level between
• semi-leptonic (e, mu, tau)
• di-leptonic (ee, mumu, tautau, emu,
  etau, mutau)
• SUSY
• SU1 5401
• SU2 5402
• SU3 5403
• SU4 6400
• SU6 5404
• SU8 5406

• All samples normalized to 1 fb-1
• All following plots for ELECTRONS

33
Top mass correlation
top sliced in ET

• Studying the correlations we came
• across one unexpected result
• concerning the reconstructed
• hadronic top mass. It seemed
• to have a dependence on ET
• To see if this was an effect of reconstruction
  software, we repeated the study with an extra
  feature
• the reconstructed hadronic top had
• to match a truth top (?R lt 0.2)
• The result of this study shows that
• the top mass is indeed dependent
• of ET, even if you match to truth
• MORE STUDIES NEED TO BE DONE
• BEFORE A CONCLUSION CAN BE DRAWN!!!

matched top sliced in ET
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Are ET, mtop correlated?

• See if mtop shape depends on ET
• mtop is described by a landau in our model ? 2
  parameters

mtop sliced in ET
-Sigma landau mtop has a very gentle slope
-Mean landau mtop is correlated -Model
correlation as polynomial 1st order
35
Are ET, mtop correlated?

• Procedure as before
• Slice 2D sample in bins of mtop and look at ET
  distribution
• Make fit to distribution in each slice, see if
  fit parameter changes vs mtop

Fitted slope per slice vs. mtop
- Clear correlation between slope of exponential
in ET and mtop, as the slope is not constant vs
mtop - Model correlation as a polynomial of 2nd
order