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

Sebastián Ordoñez, Alberto Reis, Diego Milanés

jsordonezs@unal.edu.co

Universidad Nacional de Colombia

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

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

S. Ordoñez (UNAL-COL)

October 29, 2023

• The \(K^{-}K^{+}\) \(S\)-wave amplitude has not been well studied yet. There is a lack in the understanding of the scalar states involved, such as the controversial \(f_{0}(980)\) and the \(a_{0}(980)\).
• Previous studies have been performed by Babar:
  • Amplitude analysis of the decay \(D^{0}\rightarrow K^{-}K^{+}\pi^{0}\)
  • Dalitz plot analysis of  \(D^{+}_{s}\rightarrow K^{+}K^{-}\pi^{+}\)
• The \(D^{+}\rightarrow K^{-}K^{}K^{+}\) can shed light in the study  of the \(K^{-}K^{+}\) \(S\)-wave. There are large and pure data samples available coming from LHCb.
• Results of this analysis can be useful for CPV studies in decays of \(B\) mesons.

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.

Data samples

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

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\(^{2}\)]

\(\phi(1020)\) 

\(\phi(1020)\) 

Cloned tracks

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

Cloned tracks

\(\phi(1020)\) 

Data samples

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\(^{2}\)]

\(\phi(1020)\) 

Cloned tracks

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

Data samples

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

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

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

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:

and

Selection

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

S. Ordoñez (UNAL-COL)

October 29, 2023

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:

Selection

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

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

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

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

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

S. Ordoñez (UNAL-COL)

October 29, 2023

Selection

Results for the KS test after the reweighting

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

S. Ordoñez (UNAL-COL)

October 29, 2023

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).

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.

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

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.

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

Selection

• Performance results for the BDTG classifier.

Similar results are obtained for Fold 2.

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

• 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

• 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...