Validation Regions for non-prompt background estimation in same charged \(W^{\pm}W^{\pm}\) scattering

(Status report)

Sebastian Ordoñez

jsordonezs@unal.edu.co

 

 

                                      18th of May 2021                                             

 

Outline

  • Introduction
  • Trilepton muon Validation Region
    • Evaluation
    • Closure Test within the muon Validation Region​
      • Data Closure Test
      • MC Closure Test
  • Trilepton electron Validation Region
  • Conclusion
  • Next steps

In the data-driven background estimation we use three orthogonal  regions:

  • Control Region: enriched in non-prompt background, there the fake factors \(F\) are extracted. In this study the \(F\) are extracted from a dilepton CR → Max master's thesis. 
VR
SR
CR

\(F\) application

\(F\) validation

  • Signal Region: phase space that is defined through selections on kinematic variables, enriched in potential signal of interest → ssWW
  • Validation Regions: regions in phase space orthogonal to CR and SR, where  the extrapolation is verified  → My work
  1. Validation Region for muons ​
  2. Validation Region for electrons

Introduction

\(F\) extraction

Trilepton muon Validation Region

In this Validation Region we apply the following selection flow:

We need to guarantee that fake muons have a \(p_{T}>27\) GeV in order to be able to apply the fake factor.

Definition

Composition of the non-prompt muons

Trilepton muon Validation Region

Evaluation

  1. Large number of total events and high purity in non-prompt muons.
  2. Good data modeling
  3. Agreement with the SR in the composition of non-prompt muons.

Composition of the non-prompt muons

Ana leptons

Trilepton muon Validation Region

Signal Region

Trilepton muon Validation Region

Evaluation

Statistics and data modeling

\(E_{T}^{miss}\) distribution for Non-Ana events

\(E_{T}^{miss}\) distribution for Ana events

Statistics and data modeling

  • The contribution of non-prompt muons in the trilepton muon Validation Region is almost  50%.
  • This represents an improvement in comparison to the Low dijet invariant mass Validation Region where it was about 25%.

\(E_{T}^{miss}\) dist. in the Low \(m_{jj}\) VR

Number of events for each MC category and data in the trilepton muon VR

Closure Test within the trilepton muon Validation Region

In order to test the Matrix Method, MC and data fake factors extracted from the dilepton Control Region are applied to  events with one non-prompt Non-Ana muon.

\boxed{ N_{A}-N_{A}^{prompt} = (N_{N}-N_{N}^{prompt})\cdot F}

?

     Monte Carlo Closure Test

  • The fake factor is extracted from MC in dilepton Control Region and then applied to MC in the Validation Region
  • What do we want to compare in this test?
\boxed{ N_{A}^{fake} = N_{N}^{fake}\cdot F}

\(N_{A}^{fake}\) estimated by the MC-data-driven method is compared to \(N_{A}^{fake}\) which are actually non-prompt according to the MC truth level information (Non-prompt MC).

Closure Test within the trilepton muon Validation Region

Data-driven Fake Factor Method

The method introduces the probability \(e_{i}\) (\(f_{i}\)) that a prompt (non-prompt) lepton passes the Ana requirements. The above equation is explicitly written as:

 

\boxed{N_{AA}-e_{1}e_{2}N_{PP}=(N_{NA}-\bar{e}_{1}e_{2}N_{PP})\frac{f_{1}}{\bar{f}_{1}}+(N_{AN}-e_{1}\bar{e}_{2}N_{PP})\frac{f_{2}}{\bar{f}_{2}}-(N_{NN}-\bar{e}_{1}\bar{e}_{2}N_{PP})\frac{f_{1}f_{2}}{\bar{f}_{1}\bar{f}_{2}}}

Where the bars mean the negation, i.e. the probability that a prompt (non-prompt) lepton does not pass the Ana selection. The fake factor is given by:

\boxed{F_{i}\equiv\frac{f_{i}}{\bar{f}_{i}}}

Closure Test within the trilepton muon Validation Region

     Data Closure Test

  • The fake factor is extracted from data in the dilepton Control Region and applied in data in the Validation Region.
  • What do we want to compare in this test?

Study how well the data corresponds to the sum of MC predictions  for all processes (Prompt MC) and Charge flip (Charge flip MC) and the non-prompt background estimated with the Matrix Method.

In an "ideal scenario" it would be expected that:

\boxed{\frac{\text{Data}}{\text{Prompt MC + Charge flip MC + Data-driven bkg}}=1}

Closure Test within the trilepton muon Validation Region

  • The number of non-prompt events in this Validation Region is underestimated, especiallly the fake muons with \(p_{T}>40\)GeV.
  • A perfect agreement is not expected here because of modelling differences among MC generators/samples.
  • It is acceptable to try the closure test on data. 

Fake muons \(p_{T}\) distribution

Monte Carlo Closure Test

  • The technical setup seems to work. 

Closure Test within the trilepton muon Validation Region

\(m_{lll}\) distribution

\(E_{T}^{miss}\) distribution

Monte Carlo Closure Test

Closure Test within the trilepton muon Validation Region

\(m_{jj}\) distribution

Leading jet \(p_{T }\) distribution

Monte Carlo Closure Test

Closure Test within the trilepton muon Validation Region

Subleading lepton \(p_{T }\) distribution

Leading lepton \(p_{T }\) distribution

Monte Carlo Closure Test

Closure Test within the trilepton muon Validation Region

Monte Carlo Closure Test

Third lepton \(p_{T }\) distribution

Subleading jet \(p_{T }\) distribution

Closure Test within the trilepton muon Validation Region

Data Closure Test

  • For several distributions, data is quite well modeled by the sum of the data-drivenly estimated non-prompt bkg and the prompt and charge flip contribution estimated by MC simulations.

\(m_{lll}\) distribution

Closure Test within the trilepton muon Validation Region

\(E_{T}^{miss}\) distribution

Leading lepton \(p_{T}\)

Data Closure Test

Closure Test within the trilepton muon Validation Region

Leading jet \(p_{T}\)

Subleading jet \(p_{T}\)

Closure Test within the trilepton muon Validation Region

\(m_{jj}\) distribution

Subleading lepton \(p_{T}\)

Closure Test within the trilepton muon Validation Region

Third lepton \(p_{T}\)

Conclusion

  • It was found a significant understimation of \(N_{A}^{fake}\) when using the Matrix Method in the Monte Carlo Closure Test. However, this is still acceptable and  within the expected. 
  • The Data Closure Test validate the Matrix Method and the dilepton Control Region employed for this study. 
  •  The closure tests confirms that the data-driven method described and the dilepton Control Region are suitable for the estimation of the non-prompt muon background within the signal region.

Next steps (muon VR)

  • Are we done yet?

Trilepton electron Validation Region

Definition

In order to get a composition of non-prompt electrons as close as possible to the composition of the Signal Region the following selection flow is employed:

Next steps: Change the \(p_{T}\) electron cut to the begining, change to \(m_{lll} < 300\)GeV 

Trilepton electron Validation Region

Composition of non-prompt electrons in the Signal Region

Non-prompt Ana electrons in the Signal Region come mainly from Light Flavor Decay associated to \(W+jets\) and also there is a significant contribution of B Hadron Decay from \(t\bar{t}\).

Trilepton electron Validation Region

 

Evaluation: Composition for all events > Ana and Non-Ana

Signal Region

Electron VR

Trilepton electron Validation Region

 

Evaluation: Composition for Ana events only

Trilepton electron Validation Region

 

Evaluation: Statistics (here only mc16a)

Electron \(p_{T}\) cut 

\(E_{T}^{miss}\) distribution for Ana

\(E_{T}^{miss}\) distribution for Non-Ana

Trilepton electron Validation Region

 

Evaluation: Statistics

Trilepton invariant mass cut 

Trilepton electron Validation Region

 

Evaluation: Statistics

Two muon invariant mass cut 

Trilepton electron Validation Region

 

Evaluation: Statistics

Charge muon cut 

Trilepton electron Validation Region

 

Evaluation: Statistics

Two muons Ana cut 

Trilepton electron Validation Region

 

Evaluation: Statistics

Lepton flavor cut 

Trilepton electron Validation Region

 

Evaluation: Statistics

Two Ana leptons cut 

Trilepton electron Validation Region

 

Evaluation: Statistics

Three leptons cut 

Back up

More distributions within current trilepton electron Validation Region

 

Electron \(p_{T}\) cut 

Back up

More distributions within current trilepton electron Validation Region

 

Trilepton invariant mass cut 

Back up

More distributions within current trilepton electron Validation Region

 

Two muon invariant mass cut 

Back up

More distributions within current trilepton electron Validation Region

 

Charge muon cut 

Back up

More distributions within current trilepton electron Validation Region

 

Two muons Ana cut 

Back up

More distributions within current trilepton electron Validation Region

 

Lepton flavor cut 

Back up

More distributions within current trilepton electron Validation Region

 

Two Ana leptons cut 

Back up

More distributions within current trilepton electron Validation Region

 

Three leptons cut 

Back up

More distributions within current trilepton electron Validation Region

 

Electron \(p_{T}\) cut 

Back up

More distributions within current trilepton electron Validation Region

 

Trilepton invariant mass cut 

Back up

More distributions within current trilepton electron Validation Region

 

Two muon invariant mass cut 

Back up

More distributions within current trilepton electron Validation Region

 

Charge muon cut 

Back up

More distributions within current trilepton electron Validation Region

 

Two muons Ana cut 

Back up

More distributions within current trilepton electron Validation Region

 

Lepton flavor cut 

Back up

More distributions within current trilepton electron Validation Region

 

Two Ana leptons cut 

Back up

More distributions within current trilepton electron Validation Region

 

Three leptons cut 

Back up

More distributions within current trilepton electron Validation Region

 

Electron \(p_{T}\) cut 

Back up

More distributions within current trilepton electron Validation Region

 

Trilepton invariant mass cut 

Back up

More distributions within current trilepton electron Validation Region

 

Two muon invariant mass cut 

Back up

More distributions within current trilepton electron Validation Region

 

Charge muon cut 

Back up

More distributions within current trilepton electron Validation Region

 

Two muons Ana cut 

Back up

More distributions within current trilepton electron Validation Region

 

Lepton flavor cut 

Back up

More distributions within current trilepton electron Validation Region

 

Two Ana leptons cut 

Back up

More distributions within current trilepton electron Validation Region

 

Three leptons cut 

Back up

More distributions within current trilepton electron Validation Region

 

Electron \(p_{T}\) cut 

Back up

More distributions within current trilepton electron Validation Region

 

Trilepton invariant mass cut 

Back up

More distributions within current trilepton electron Validation Region

 

Two muon invariant mass cut 

Back up

More distributions within current trilepton electron Validation Region

 

Charge muon cut 

Back up

More distributions within current trilepton electron Validation Region

 

Two muons Ana cut 

Back up

More distributions within current trilepton electron Validation Region

 

Lepton flavor cut 

Back up

More distributions within current trilepton electron Validation Region

 

Two Ana leptons cut 

Back up

More distributions within current trilepton electron Validation Region

 

Three leptons cut 

Back up

More distributions within current trilepton electron Validation Region

 

Electron \(p_{T}\) cut 

Back up

More distributions within current trilepton electron Validation Region

 

Trilepton invariant mass cut 

Back up

More distributions within current trilepton electron Validation Region

 

Two muon invariant mass cut 

Back up

More distributions within current trilepton electron Validation Region

 

Charge muon cut 

Back up

More distributions within current trilepton electron Validation Region

 

Two muons Ana cut 

Back up

More distributions within current trilepton electron Validation Region

 

Lepton flavor cut 

Back up

More distributions within current trilepton electron Validation Region

 

Two Ana leptons cut 

Back up

More distributions within current trilepton electron Validation Region

 

Three leptons cut