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Why D 0 K 0 S + ? What is the LHCb experiment? Data Analysis Conclusions Separating Signal from Background in D 0 K 0 S + Raymond Tat 1 Angelo Di Canto 2 Mark Williams 3 1 University of California, Berkeley 2 CERN 3

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SLIDE 1

What is the LHCb experiment? Why D0 → K0

S π+π−?

Data Analysis Conclusions

Separating Signal from Background in D0 → K 0

Sπ+π−

Raymond Tat1

Angelo Di Canto2 Mark Williams3

1University of California, Berkeley 2CERN 3University of Manchester

August 2018

Tat University of California, Berkeley CERN University of Manchester Separating Signal from Background in D0 → K0

S π+π−

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SLIDE 2

What is the LHCb experiment? Why D0 → K0

S π+π−?

Data Analysis Conclusions

Table of Contents

1 What is the LHCb experiment? 2 Why D0 → K 0

Sπ+π−?

3 Data Analysis 4 Conclusions

Tat University of California, Berkeley CERN University of Manchester Separating Signal from Background in D0 → K0

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SLIDE 3

What is the LHCb experiment? Why D0 → K0

S π+π−?

Data Analysis Conclusions

Section 1 What is the LHCb experiment?

Tat University of California, Berkeley CERN University of Manchester Separating Signal from Background in D0 → K0

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SLIDE 4

What is the LHCb experiment? Why D0 → K0

S π+π−?

Data Analysis Conclusions

CP Violation

The universe is mostly matter. But why? Standard Model CP violation is not enough to explain the

  • bserved asymmetry.

So, we search for CP violation beyond what is predicted by the Standard Model. This will be a sensitive probe of new physics.

Tat University of California, Berkeley CERN University of Manchester Separating Signal from Background in D0 → K0

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SLIDE 5

What is the LHCb experiment? Why D0 → K0

S π+π−?

Data Analysis Conclusions

Large Hadron Collider beauty (LHCb)

LHCb’s main goal is to investigate CP violation. LHCb’s design is specially suited to study b and c quarks.

Tat University of California, Berkeley CERN University of Manchester Separating Signal from Background in D0 → K0

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SLIDE 6

What is the LHCb experiment? Why D0 → K0

S π+π−?

Data Analysis Conclusions

Section 2 Why D0 → K 0

Sπ+π−?

Tat University of California, Berkeley CERN University of Manchester Separating Signal from Background in D0 → K0

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SLIDE 7

What is the LHCb experiment? Why D0 → K0

S π+π−?

Data Analysis Conclusions

CP Violation and Mixing with Neutral Charm Mesons

No CP violation measured in the charm sector to date. Two phenomena described by four parameters:

CP Violation

Described by |q/p| and φ

Mixing: D0 → ¯ D0

Described by x and y

D0 → K 0

Sπ+π− allows us to measure all 4 parameters.

Tat University of California, Berkeley CERN University of Manchester Separating Signal from Background in D0 → K0

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SLIDE 8

What is the LHCb experiment? Why D0 → K0

S π+π−?

Data Analysis Conclusions

The Current State of Affairs

x (%) −0.6 −0.4 −0.2 0.2 0.4 0.6 0.8 1 1.2 y (%) −0.6 −0.4 −0.2 0.2 0.4 0.6 0.8 1 1.2

CPV allowed σ 1 σ 2 σ 3 σ 4 σ 5

!"#$%

&!$'()*+,-

|q/p| 0.6 0.8 1 1.2 1.4 1.6 Arg(q/p) [deg.] −60 −40 −20 20 40 60

σ 1 σ 2 σ 3 σ 4 σ 5

!"#$%

&!$'()*+,-

Tat University of California, Berkeley CERN University of Manchester Separating Signal from Background in D0 → K0

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SLIDE 9

What is the LHCb experiment? Why D0 → K0

S π+π−?

Data Analysis Conclusions

Section 3 Data Analysis

Tat University of California, Berkeley CERN University of Manchester Separating Signal from Background in D0 → K0

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SLIDE 10

What is the LHCb experiment? Why D0 → K0

S π+π−?

Data Analysis Conclusions

Analysis of D0 → K 0

Sπ+π− Candidates

Input: D0 → K 0

Sπ+π− candidates from LHCb (Run 2,

2016-2017) Eventual goal: Perform an analysis of the decay time versus the Dalitz coordinates Goal of this project: Improve signal significance (↓ σstat) while avoiding large biases or correlations (↓ σsyst)

Tat University of California, Berkeley CERN University of Manchester Separating Signal from Background in D0 → K0

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What is the LHCb experiment? Why D0 → K0

S π+π−?

Data Analysis Conclusions

Delta Mass Plot with Backgrounds

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 22000

Candidates

0.29 ± B = 3.84 0.16 ± C = 2.64 0.073 ± cut = -0.7359 0.0041 ± mean = 145.4313 1626 ± nbkg = 502869 1518 ± nsig = 151485 0.014 ± sigma0 = 0.541 0.025 ± sigma1 = 0.307 0.021 ± sigma2 = 0.979 0.065 ± threshold = 138.962 0.026 ± var1 = 0.513 0.021 ± var2 = 0.796

140 145 150 155 160 ) [MeV] D ( m δ 4 − 2 − 2 4

data

σ (data - model)/

Tat University of California, Berkeley CERN University of Manchester Separating Signal from Background in D0 → K0

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SLIDE 12

What is the LHCb experiment? Why D0 → K0

S π+π−?

Data Analysis Conclusions

Multivariate Analysis (MVA)

Combines information from many weakly discriminating variables into a more powerful discriminator Test multiple MVA methods using a combination of the libraries TMVA, sklearn, and hep ml. Ex: BDT, neural network, Fischer discriminant analysis

Tat University of California, Berkeley CERN University of Manchester Separating Signal from Background in D0 → K0

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SLIDE 13

What is the LHCb experiment? Why D0 → K0

S π+π−?

Data Analysis Conclusions

The sPlot technique

sPlot is a data-driven method to extract signal and background distributions for variables Fit signal and backgrounds distributions to the delta mass. Also allows us to choose input variables based on signal-background separation.

Tat University of California, Berkeley CERN University of Manchester Separating Signal from Background in D0 → K0

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What is the LHCb experiment? Why D0 → K0

S π+π−?

Data Analysis Conclusions

MVA Performance Evaluation

We can assess MVA performance with a Receiver Operating Characteristic (ROC) curve. Area under the ROC curve can be used as a metric for MVA performance

0.0 0.2 0.4 0.6 0.8 1.0 False Positive Rate 0.0 0.2 0.4 0.6 0.8 1.0 True Positive Rate

Receiver operating characteristic

uGB_bin_tau (area = 0.77) GradBoost (area = 0.78) MLP (area = 0.83) AdaBoost (area = 0.78) uGB_bin_dalitz (area = 0.77) Luck

Tat University of California, Berkeley CERN University of Manchester Separating Signal from Background in D0 → K0

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What is the LHCb experiment? Why D0 → K0

S π+π−?

Data Analysis Conclusions

Results

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 22000

Candidates

0.29 ± B = 3.84 0.16 ± C = 2.64 0.073 ± cut = -0.7359 0.0041 ± mean = 145.4313 1626 ± nbkg = 502869 1518 ± nsig = 151485 0.014 ± sigma0 = 0.541 0.025 ± sigma1 = 0.307 0.021 ± sigma2 = 0.979 0.065 ± threshold = 138.962 0.026 ± var1 = 0.513 0.021 ± var2 = 0.796

140 145 150 155 160 ) [MeV] D ( m δ 4 − 2 − 2 4

data

σ (data - model)/ 2000 4000 6000 8000 10000

Candidates

0.59 ± B = 1.72 0.30 ± C = 1.93 0.12 ± cut = -1.230 0.0042 ± mean = 145.4398 378 ± nbkg = 35924 440 ± nsig = 86195 0.072 ± sigma0 = 0.652 0.017 ± sigma1 = 0.417 0.10 ± sigma2 = 1.04 0.13 ± threshold = 139.39 0.15 ± var1 = 0.61 0.051 ± var2 = 0.635

140 145 150 155 160 ) [MeV] D ( m δ 4 − 2 − 2 4

data

σ (data - model)/

Signal efficiency: 57% Background rejection: 93%

Tat University of California, Berkeley CERN University of Manchester Separating Signal from Background in D0 → K0

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SLIDE 16

What is the LHCb experiment? Why D0 → K0

S π+π−?

Data Analysis Conclusions

Boosting to Uniformity

For analysis, we want our MVA to have uniform efficiency in decay time and Dalitz coordinates. We can force this to be the case with Uniform Gradient Boosting (uGB)

Tat University of California, Berkeley CERN University of Manchester Separating Signal from Background in D0 → K0

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What is the LHCb experiment? Why D0 → K0

S π+π−?

Data Analysis Conclusions

Section 4 Conclusions

Tat University of California, Berkeley CERN University of Manchester Separating Signal from Background in D0 → K0

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What is the LHCb experiment? Why D0 → K0

S π+π−?

Data Analysis Conclusions

Summary

When a signal peak is clearly visible over a background, sPlot and MVA can help to reduce backgrounds. This analysis is data-driven: no Monte Carlo necessary. Multilayer perception achieves highest performance, but uniform boosting may reduce systematic uncertainty. Eventually, this will help us to perform a decay-time analysis

  • f D0 → K 0

Sπ+π−.

Tat University of California, Berkeley CERN University of Manchester Separating Signal from Background in D0 → K0

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What is the LHCb experiment? Why D0 → K0

S π+π−?

Data Analysis Conclusions

Image Credits

Decision Tree: https://indico.scc.kit.edu/event/48/contributions/ 3410/attachments/1690/2312/BDT_KSETA_Freudenstadt.pdf LHCb image: https://home.cern/about/updates/2013/02/ proton-lead-run-brings-new-physics-reach-lhcb Crab Nebula: https://home.cern/topics/antimatter/ matter-antimatter-asymmetry-problem

Tat University of California, Berkeley CERN University of Manchester Separating Signal from Background in D0 → K0

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SLIDE 20

Bonus Content

Section 5 Bonus Content

Tat University of California, Berkeley CERN University of Manchester Separating Signal from Background in D0 → K0

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SLIDE 21

Bonus Content

Input Variables Used

D0 end vertex χ2 Sum of transverse momenta of π+ and π− Cosine of helicity angle Soft pion transverse momentum Soft pion primary vertex χ2 K 0

S vertex z error

D0 momentum π+ track χ2 probability K 0

S transverse momentum

Tat University of California, Berkeley CERN University of Manchester Separating Signal from Background in D0 → K0

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SLIDE 22

Bonus Content

Variable Correlations

100 − 80 − 60 − 40 − 20 − 20 40 60 80 100

D0_ENDVERTEX_CHI2 pi_sum_PT helicity Dst_pi_PT Dst_pi_OWNPV_CHI2 D0_KS_ORIVX_ZERR D0_P D0_KS_PT D0_pip_TRACK_PCHI2 D0_ENDVERTEX_CHI2 pi_sum_PT helicity Dst_pi_PT Dst_pi_OWNPV_CHI2 D0_KS_ORIVX_ZERR D0_P D0_KS_PT D0_pip_TRACK_PCHI2

Correlation Matrix (signal)

100 7

  • 1

6 4 2

  • 1

7 100

  • 40

81

  • 2

4 42 15 4

  • 1
  • 40

100

  • 8
  • 17
  • 9

51

  • 5

6 81

  • 8

100

  • 3
  • 1

41 55 2

  • 2
  • 3

100

  • 2
  • 3
  • 2
  • 3

4

  • 17
  • 1
  • 2

100 70

  • 9
  • 6

4 42

  • 9

41

  • 3

70 100 25

  • 4

2 15 51 55

  • 2
  • 9

25 100

  • 3
  • 1

4

  • 5

2

  • 3
  • 6
  • 4
  • 3

100

Linear correlation coefficients in %

Tat University of California, Berkeley CERN University of Manchester Separating Signal from Background in D0 → K0

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