Multidimensional fits to 1lepton background CSC Note 1

1
Multidimensional fits to 1-lepton backgroundCSC
Note 12 ATLAS SUSY WG

• A. Koutsman W. Verkerke, NIKHEF
• 18-06-2007

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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
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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

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

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Are ET,MT correlated in signal/bkg?

• First step investigate possible correlations in
  more detail
• Procedure
• Slice signal, bkg samples in bins of MT and look
  at ET distribution
• Make fit to distribution in each slice, see if
  fit parameter changes vs MT

SUSY SU3
TTBar 2l
Wn jets
TTBar 1l
MT
ET
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Are ET,MT correlated in signal/bkg?

• Conclusion assumption that ET, MT are
  uncorrelated is good for background (not for
  signal, SU3)
• Now add observable
• reconstructed hadronic top mass mtop
• Defined as inv. mass of 3 jet system
• with highest sum pT
• Also looked at correlations between (mtop,MT) and
  (mtop,ET)
• No correlation observed for backgrounds

TTbar-1l
mtop vs MT
mtop vs ET
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Fitting the background

• In absence of correlations, we can construct
  relatively simple multi-dimensional models to
  describe background data
• E.g. Fttbar(MT,ET,mtop) F1(MT)?F2(ET)?F3(mtop)
• Next step Write model that describes combined
  background in control region and use that to
  extrapolate to signal region
• Fbkg(MT,ET,mtop) Ntt1l Ftt1l(MT,ET,mtop)
  Ntt2l
  Ftt2l(MT,ET,mtop)
  Nwnj Fwnj(MT,ET,mtop) Nsusy
  Fsusy(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

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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
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First iteration of combined background fit

• 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
235 25 229 Nsemi 1074 63
1072 Nwjets 401 61 408
PARAMETER CORRELATION COEFFICIENTS NO.
GLOBAL 1 2 3 1 0.38044
1.000 -0.041 -0.231 2 0.75591 -0.041
1.000 -0.725 3 0.77041 -0.231 -0.725
1.000
OK!
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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 w/o SUSY comp Truth Nsemi 979
61 1072 Ndi 623 38
229 Nwjets 484 64
408 Nsu3 0 (fixed) 378
Fit with SUSY comp. Truth Nsemi 1127 67
1072 Ndi 158 39
229 Nwjets 382 68 408 Nsu3
420 36 378
OK
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Next iteration of combined background fit

• Cross check fit model with floating SUSY
  component to
• data w/o SUSY
• More checks 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
• Fit with SUSY in data and model

Fit Truth Nsemi
1080 64 1072 Ndi 219 31
229 Nwjets 396 61
408 Nsu3 14 18 0
NB plots on 1.8 fb-1
PULL DISTRIBUTION mean -0.0006 0.051 s
0.958 0.032
OK.
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How well does the generic SUSY shape work?

• In the fit we have taken a generic shape for SUSY
  as our observation
• was that the distribution of SUSY data in
  MT,ET in the control region
• is usually fairly flat, independent of the
  SUSY point
• Check Run fit with SUSY background from multiple
  SUSY point and indentical ansatz SUSY component
  in fit

Fit to pull distributionsof SUSY in 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
OK
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Summary

• Have looked at possibility to determine amount of
  SM backgroundto SUSY from a fit to MT,ET,mtop
• 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
• Next increase realism of procedure
• Need to exclude signal region from fit (technical
  issue only).
• Do not expect this to cause major changes as most
  information that separates background components
  is in control region
• See if we can also release some or all of the
  background shape parameters in the fit
• Verify that control region ? signal region
  extrapolation procedure works OK.