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

• 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 the Babar collaboration in \(D^{0}\) decays and \(D^{+}_{s}\) decays:
  • 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.
• 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.

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

Sebastian Ordoñez

December 4, 2023

Data samples

• 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

• 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

Cloned tracks

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

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

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

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

Sebastian Ordoñez

December 4, 2023

Data samples

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

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

• 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.

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

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.

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:

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.

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

• 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

• 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

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

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

Sebastian Ordoñez

December 4, 2023

Data Offline Selection

• 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

• 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

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 \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)

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

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

• 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

\(K^{-}K^{+}K^{+}\) 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.