Study of the \(K^{+}K^{-}\) S-wave amplitude near threshold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

Group meeting

Sebastián Ordoñez, Alberto Reis, Diego Milanés

jsordonezs@unal.edu.co

Universidad Nacional de Colombia

October 29 , 2023

Outline

  • Introduction
  • Analysis strategy
  • Data samples
    • Data
    • Monte Carlo
  • Selection
    • Pre-selection
    • MC reweighting
    • MVA
    • Figures of merit
  • \(K^{-}K^{+}K^{+}\) Invariant mass fit
    • Dalitz plot final sample
  • Outlook

Introduction

Motivation

Study of the \(K^{-}K^{+}\)  S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

S. Ordoñez (UNAL-COL)

October 29, 2023

Perform a study of the \(K^{-}K^{+} S\)-wave amplitude in the \(D^{+}\rightarrow K^{-}K^{+}K^{+}\) decay channel using the data set of Run 2.

Main objective

Data samples

Data sample

Study of the \(K^{-}K^{+}\)  S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

S. Ordoñez (UNAL-COL)

October 29, 2023

  • Data was collected at the LHCb detector between 2016 and 2018. Specifically, the data come from \(pp\) collisions at \(\sqrt{s} = 13\) TeV, corresponding to a total of 5.b fb\(^{-1}\).
  • The candidates are required to pass any of the L0 hardware trigger lines.
  • The data set comes from HLT2 Turbo line: Hlt2CharmHadDpToKmKpKp
  • Statistics of the data samples after trigger level cuts:

Data samples

Data sample

Study of the \(K^{-}K^{+}\)  S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

S. Ordoñez (UNAL-COL)

October 29, 2023

Notation: \(s_{12} = s_{K^{-}K^{+}} = m_{K^{-}K^{+}}^{2}\) and \(s_{13} = s_{K^{-}K^{+}} = m_{K^{-}K^{+}}^{2}\)

\(s_{12}\) [GeV\(^{2}\)]

\(s_{13}\) [GeV\(^{2}\)]

\(\phi(1020)\) 

\(\phi(1020)\) 

Cloned tracks

\(s_{12}\) [GeV\(^{2}\)]

Cloned tracks

\(\phi(1020)\) 

Events

Data samples

Data sample

Study of the \(K^{-}K^{+}\)  S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

S. Ordoñez (UNAL-COL)

October 29, 2023

\(s_{12}\) [GeV\(^{2}\)]

\(s_{13}\) [GeV\(^{2}\)]

\(\phi(1020)\) 

Cloned tracks

Events

\(m(K^{-}K^{+}K^{+})\) [MeV]

Data samples

Monte Carlo

Study of the \(K^{-}K^{+}\)  S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

S. Ordoñez (UNAL-COL)

October 29, 2023

  • Large Monte Carlo (MC) samples are available for each year and polarity (here only used a sub-sample).
  • MC data is used for the extraction of the PDF parameters employed in fits.
  • MC (reweighted) is used as signal proxy in the MVA selection and the calculation of the efficiency map.

Configurations used to simulate the data per year

Selection

Pre-selection

Study of the \(K^{-}K^{+}\)  S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

S. Ordoñez (UNAL-COL)

October 29, 2023

  • On top of the trigger level cuts, offline pre-selection cuts are also applied.

Selection

Specific backgrounds: Charm background

Study of the \(K^{-}K^{+}\)  S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

S. Ordoñez (UNAL-COL)

October 29, 2023

  • The background in the \(K^{-}K^{+}K^{+}\) mass spectrum coming from other charm decays is controlled by specific requirements based on PID
  • Possible sources of contamination to \(D^{+}\rightarrow K^{-}K^{+}K^{+}\) from mis-ID are \(\Lambda_{c}^{+}\rightarrow K^{-}K^{+}p\) and      \(\Lambda_{c}^{+}\rightarrow K^{-}\pi^{+}p\), where the proton and the pion are misidentified as kaons.

Selection

Specific backgrounds: Clone tracks

Study of the \(K^{-}K^{+}\)  S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

S. Ordoñez (UNAL-COL)

October 29, 2023

  • The cloned tracks originate when a track associated to one of the \(K^{+}\) is doubled to the other.
  • The slope difference variables on the \(x\) and \(y\) directions are considered:
\text{difTX}_{23}=\left|\frac{p_{x_{2}}}{p_{z_{2}}}-\frac{p_{x_{3}}}{p_{z_{3}}}\right|
\text{difTY}_{23}=\left|\frac{p_{y_{2}}}{p_{z_{2}}}-\frac{p_{y_{3}}}{p_{z_{3}}}\right|

and

Selection

Offline selection before MVA: summary

Study of the \(K^{-}K^{+}\)  S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

S. Ordoñez (UNAL-COL)

October 29, 2023

Monte Carlo reweighting: Folding

Study of the \(K^{-}K^{+}\)  S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

S. Ordoñez (UNAL-COL)

October 29, 2023

  • It is necessary to prepare the MC samples that will be used as signal proxy in the MVA.
  • The samples are randomly divided into two reproducible sub-samples:

After the folding, it is ensured that each fold has the same number of events coming from each sub-sample.

Selection

Monte Carlo reweighting: SPlot

Study of the \(K^{-}K^{+}\)  S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

S. Ordoñez (UNAL-COL)

October 29, 2023

  • To obtain signal weights via sPlot technique which are required for the reweight procedure, a fit to the invariant \(K^{-}K^{+}K^{+}\) mass is performed for each sub-sample.

Selection

Monte Carlo reweighting: Dynamics correction

Study of the \(K^{-}K^{+}\)  S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

S. Ordoñez (UNAL-COL)

October 29, 2023

  • The MC sample is generated as phase space, therefore the dynamics is emulated by applying a resonant structure weight \(w_{data}\).
  • A correction in the number of SPDHits is applied as a weight, \(w_{nSPDHits}\).

Selection

Monte Carlo reweighting: Reweight procedure

Study of the \(K^{-}K^{+}\)  S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

S. Ordoñez (UNAL-COL)

October 29, 2023

  • The \(w_{nSPDHits}\) and \(w_{data}\) are insufficient to match data and MC, a third weight is required.
  • Inputs for the MVA reweighting are: MC sample weighted (PID, SPDhits correction, phase space dynamics) and the data sample with background subtracted from sPlot.

Selection

Monte Carlo reweighting: Reweight procedure

Study of the \(K^{-}K^{+}\)  S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

S. Ordoñez (UNAL-COL)

October 29, 2023

  • The Kolgomorov-Smirnov test is employed to estimate how different data and MC are.
  • The output of the reweight procedure is a gb_weight.

Selection

Results for the KS test before the reweighting

gb_weight

Monte Carlo reweighting: Reweight procedure

Study of the \(K^{-}K^{+}\)  S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

S. Ordoñez (UNAL-COL)

October 29, 2023

  • The matching between the data and MC variables is said to be successful, confirmed by the KS test and ROC curve.

Selection

Results for the KS test after the reweighting

Monte Carlo reweighting: Reweight procedure

Study of the \(K^{-}K^{+}\)  S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

S. Ordoñez (UNAL-COL)

October 29, 2023

  • Variables after applying the gb_weights.

Selection

Multivariate Analysis Selection

Study of the \(K^{-}K^{+}\)  S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

S. Ordoñez (UNAL-COL)

October 29, 2023

Selection

  • A BDT is trained and applied using the TMVA package.
  • Fold 1 is used for training and the resulting BDT weights are applied to Fold 2, and vice versa.
  • A single BDT is trained with all of the sub-samples (year and polarities).
  • Training phase:
    • MC samples are used as signal proxy, all weights are applied.
    • The data sidebands are used as background: \([1820,1840]\) MeV and \([1900,1920]\) MeV.

Fold 1

Fold 2

N. Background events N. Signal events
753313 2064370
N. Background events N. Signal events
752618 2064377

For each fold, 2M signal events are used for training and 50k for testing. Similarly, 690k bkg events are used for training, and 50k for testing.

Multivariate Analysis Selection

Study of the \(K^{-}K^{+}\)  S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

S. Ordoñez (UNAL-COL)

October 29, 2023

Selection

  • The set of variables is chosen based on their discriminant power and not having a significant efficiency variation across the Dalitz plot.

Fold 1

Training variables for BDT classifier
D_IP_CHI2
log(D_FD_CHI2)
DIRA
D_ENDVERTEX_CHI2
logIP
D_BPVTRPOINTING

Multivariate Analysis Selection

Study of the \(K^{-}K^{+}\)  S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

S. Ordoñez (UNAL-COL)

October 29, 2023

Selection

  • Testing phase:
    • To perform the selection, two classifiers were tested: BDT and BDTG.
    • From the ROC curves a similar performance is observed, there is no strong motivation for a specific choice. The BDTG is used for the application.
Condition BDT BDTG
NTrees 700 700
MinNodeSize 2.5% 2.5%
MaxDepth 4 4
BoostType AdaBoost Grad
AdaBoostBeta 0.5 none
Shrinkage none 0.1
UseBaggedBoost true true
BaggedSampleFraction 0.5 0.5
SeparationType GinIndex none
nCuts 20 20

TMVA configurations for the training of BDT classifiers.

Multivariate Analysis Selection

Study of the \(K^{-}K^{+}\)  S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

S. Ordoñez (UNAL-COL)

October 29, 2023

Selection

  • Performance results for the BDTG classifier.

Similar results are obtained for Fold 2.

Figures of merit

Study of the \(K^{-}K^{+}\)  S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

S. Ordoñez (UNAL-COL)

October 29, 2023

  • From a fit to the MC sample with the cut val_BDTG > 0, a \(\sigma_{eff} = 4.34\) MeV was estimated.
  • The signal window used will be \(2\sigma_{eff}\), which corresponds to: \([1861.41,1878.77]\) MeV

Fold 1

Fold 2

Selection

  • A cut on val_BDTG > 0.57 gives a purity of 92.5%, with a signal efficiency of around 54%.

Study of the \(K^{-}K^{+}\)  S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

S. Ordoñez (UNAL-COL)

October 29, 2023

\(K^{-}K^{+}K^{+}\) Invariant mass fit

  • The final signal region corresponds to \(2\sigma_{eff}\) is: \([1860.38,1879.31]\) MeV
  • Within the signal region there are: 516392 signal events and  43600 background events.

Study of the \(K^{-}K^{+}\)  S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

S. Ordoñez (UNAL-COL)

October 29, 2023

\(K^{-}K^{+}K^{+}\) Invariant mass fit

Dalitz plot of the selected data

  • Considering events within the signal region the Dalitz plot below is obtained.
  • A clear interference between the \(S\)-wave and the \(\phi(1020)\) resonance is observed.

Study of the \(K^{-}K^{+}\)  S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

S. Ordoñez (UNAL-COL)

October 29, 2023

\(K^{-}K^{+}K^{+}\) Invariant mass fit

Dalitz plot of the selected data

  • Taking events in the regions \([1805,1850]\) MeV and \([1890,1935]\) MeV the Dalitz plot below is obtained.
  • The remaining background is composed by two components: combinatorial and a peaking background at the \(\phi(1020)\) mass.

Study of the \(K^{-}K^{+}\)  S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

S. Ordoñez (UNAL-COL)

October 29, 2023

Background model

To be continued...

Group meeting

By Sebastian Ordoñez

Group meeting

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