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

8th ComHEP

Universidad del Tolima, Ibagué, Colombia

December 4th, 2023

Sebastián Ordoñez*, Alberto Reis, Diego Milanés

 

Outline

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

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

Sebastian Ordoñez

December 4, 2023

Introduction

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

Sebastian Ordoñez

December 4, 2023

Motivation

Main objective

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.

p
p
\boxed{D^{+}}
K^{+}
K^{+}
K^{-}

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

Sebastian Ordoñez

December 4, 2023

Data samples

Data sample

  • Data were 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 and come from HLT2 Turbo line: Hlt2CharmHadDpToKmKpKp
  • Statistics of the data samples after trigger level cuts for all years and polarities:
    • Whole phase space: 30131550 candidates
    • Region near threshold (\(s_{low}^{DTF} < 1.16672\)): 13193548 candidates

Monte Carlo

  • Large phase space Monte Carlo (MC) samples are available for each year and polarity.
  • 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.

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

Sebastian Ordoñez

December 4, 2023

Data samples

Dalitz plot of the initial sample

Cloned tracks

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

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

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

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

Events

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

Sebastian Ordoñez

December 4, 2023

Data samples

Dalitz plot folded and Invariant mass of the three reconstructed candidates

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

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

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

Candidates/1.3 Mev 

\(\phi(1020)\) 

Cloned tracks

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

Sebastian Ordoñez

December 4, 2023

Data Offline Selection

Pre-selection

  • Charm background: 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 \(\Lambda_{c}^{+}\rightarrow K^{-}\pi^{+}p\)
  • 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 used: difTX23 and difTY23

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

Sebastian Ordoñez

December 4, 2023

Data Offline Selection

  • Statistics of the pre-selected sample
  • \(K^{-}K^{+}K^{+}\) invariant mass spectrum fit and Dalitz plot of the pre-selected sample

Monte Carlo reweighting

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

Sebastian Ordoñez

December 4, 2023

  • Sample preparation: The samples are randomly divided into two reproducible sub-samples.
  • Signal weights: Fits to the invariant \(K^{-}K^{+}K^{+}\) mass are performed in order to obtain signal weights via sPlot technique.
  • A correction in the number of SPDHits is applied as a weight, \(w_{nSPDHits}\).

  • The MC sample is generated as phase space, therefore the dynamics is emulated by applying a resonant structure weight \(w_{data}\)

  • The \(w_{nSPDHits}\) and \(w_{data}\) are insufficient to match data and MC, a third weight is required: \(w_{gb}\)

Monte Carlo reweighting

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

Sebastian Ordoñez

December 4, 2023

  •  Background subtracted data (SPlot) in blue and MC simulation after the applying all weights (\(w_{nSPDHits},w_{data},w_{gb}\)) in orange.

Variables distributions after MVA reweighting

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

Sebastian Ordoñez

December 4, 2023

  • The data sidebands are used as background: \([1820,1840]\) MeV and \([1900,1920]\) MeV.

  • A single 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.

Data Offline Selection: MVA

Training phase

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

Fold 1

Fold 2

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

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

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

Sebastian Ordoñez

December 4, 2023

  • To perform the selection, two classifiers were tested: BDT and BDTG. A similar performance is observed, there is no strong motivation for a specific choice \(\rightarrow\) The BDTG is used for the application
  • Performance results for the BDTG classifier:

Testing phase

Data Offline Selection: MVA

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

Sebastian Ordoñez

December 4, 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

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

Data Offline Selection: Figures of merit

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

Sebastian Ordoñez

December 4, 2023

Final sample

  • 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.
  • A clear interference between the \(S\)-wave and the \(\phi(1020)\) resonance is observed.

\(K^{-}K^{+}K^{+}\) invariant mass spectrum fit and Dalitz plot of the final sample

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

Sebastian Ordoñez

December 4, 2023

Background model and Efficiency map

Background model

  • Slices of 9 MeV are taken from the sidebands and a fit is performed to the \(s_{low}\) distribution in order to estimate the fractions of each background component: \(\phi(1020)\) and combinatorial.
  • From extrapolation, a fraction of 24.5%  \(\phi(1020)\) background and a 75.5% of combinatorial are estimated for the signal region.
  • A large toy MC is generated with these contributions and a  final histogram is obtained as background model.

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

Sebastian Ordoñez

December 4, 2023

Background model and Efficiency map

Efficiency map

  • In order to perform the Dalitz plot fit we need to take into account the variation of the detection efficiency across the phase space. A map of the efficiency is computed as a function of the Dalitz plot coordinates.

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

Sebastian Ordoñez

December 4, 2023

Summary and Outlook

Summary

Outlook

Thank you!

  • A pre-selection of the \(D^{+}\rightarrow K^{-}K^{+}K^{+}\) candidates was successfully performed, removing most of the charm background and cloned tracks.
  • A Multivariate Analysis was carried out in order to reject the remaining combinatorial background in the \(D^{+}\rightarrow K^{-}K^{+}K^{+}\) mass spectrum.
  • A final sample with 560 thousand \(D^{+}\rightarrow K^{-}K^{+}K^{+}\) candidates and a purity of 92.5  was obtained.
  • A background model and a efficiency model were calculated.
  • Dalitz plot fits are now being performed using the isobar model and a Quasi-Model-Independent Partial Wave Analysis (QMIPWA).
  • First tests for the extraction of the \(K\bar{K}\) S-wave using the QMIPWA method are under study. 

Back up

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

Sebastian Ordoñez

December 4, 2023

Data samples

Statistics of the initial samples

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

Sebastian Ordoñez

December 4, 2023

Data Offline Selection

Specific backgrounds: Charm background

  • 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 \(\Lambda_{c}^{+}\rightarrow K^{-}\pi^{+}p\)

Optimal cut: ProbNNk\(_{1,2,3} > 0.6\)

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

Sebastian Ordoñez

December 4, 2023

Data Offline Selection

Specific backgrounds: Clone tracks

  • 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|

and

\text{difTY}_{23}=\left|\frac{p_{y_{2}}}{p_{z_{2}}}-\frac{p_{y_{3}}}{p_{z_{3}}}\right|

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

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

Sebastian Ordoñez

December 4, 2023

  • The data sidebands are used as background: \([1820,1840]\) MeV and \([1900,1920]\) MeV.

  • A single 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.

Data Offline Selection: MVA

Training

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

Fold 1

Fold 2

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

  • 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.

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.

COMHEP 8: KK S-wave D2KKK

By Sebastian Ordoñez

COMHEP 8: KK S-wave D2KKK

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