Fits to W final states

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Fits to W final states
L. R. Flores-Castillo, B. Mellado, S. Padhi, Sau
Lan Wu University of Wisconsin-Madison Exotics
Meeting
Feb 21st, 2007
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Motivation

• Computing the significance using a sliding cut
  strategy can overestimate it (look-elsewhere
  effect).
• A global likelihood fit can take this into
  account see, e.g., talks by Y. Gao in the Higgs
  meeting.
• Counting the number of events on a MT window does
  not take into account shape information
• In the case of W, the MT distribution may also
  depend on tails on the missing ET reconstruction.
  A global fit can use them as sidebands, instead
  of relying on MC.
• At 100 pb-1
• How significant is this?

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Samples, selection

• Fortran Atlfast for
• W?l nu
• 5 samples to cover a large kinematic range
• W ?l nu
• 1,2,3,4,5,6 TeV
• Selection
• Exactly one lepton in ?
• Pt(lepton)50GeV
• 90 lepton rec. eff. applied
• MET 50GeV
• No cut on MT

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Background model

• The function exp( p0 - p1(mT)p2 ) does a good
  job over the full range (8 orders of magnitude).
• Some variations due to the joining of background
  samples

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Signal Model
Derivative discontinuity
p0 p1(mT)p2
Double exponential tail

• The same model works fine for all m(W) values
• The sharp peak needs to be softened
• Related to resolution
• Brings some headaches when fitting

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Signal template. Fits
No need to model the turn on (completely
swallowed by the background)
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Signal template. Fits

• The highest-mass W samples (5, 6 TeV) have a
  negative slope before the drop this is still
  well described by the model, but brings a problem
  later.

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Signal template. Parameterization

• Once we have a model for each W mass value, we
  can find a model for each parameter as a function
  of the true mass of the W
• Result a one-parameter family of functions that
  describes the shape of the transverse mass for
  each W mass

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• The previously mentioned negative slope of the
  highest two W masses produces a sign change in
  one parameter
• The change is smooth (because the weight of the
  corresponding term vanishes), but it is not clear
  how to interpolate
• For now, will use only up to 4TeV

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Toy MC

• Single experiment with a 2TeV W signal over the
  W background, corresponding to 100pb-1

• Unbinned maximum likelihood fits
• Left BG model, floating all three background
  parameters
• Right SB model, floating also the mass of the
  W, and the fraction (dashed
  background component solid line total)

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Delta Log Likelihood

• Estimate the probability of a background-only
  experiment to produce a typical signal (one with
  a ?NLL in the median of the distribution).
• Behaves as expected, but too low statistics
  (very slow fits in the bg-only case)
• Still, seems unlikely that it would reach 5
  sigma
• (fitter or look-elsewhere?)

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Outlook and plans

• Preliminary parameterization of the signal and
  background shapes for the W analysis.
• First look at the delta log likelihood.
• Machinery working, but too low statistics as of
  now
• To do
• Increase the statistics, refine the model
  (mainly suppress the kink)
• Compare with shapes obtained from full simulation
• Study the dependence of the parameters on
  instrumental uncertainties
• Toy MC studies of Z significance

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• BACKUP

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The remaining parameters

• Only modeled up to 4TeV