Data samples

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

S. Ordoñez (UNAL-COL)

• Data collected in \(pp\) collisions at \(\sqrt{s} = 13\) TeV by LHCb in the years 2016-2018.
• 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 sample

The total data sample consists of appx. 30M candidates in the whole phase space.

In the region \(s_{low}^{DTF} < 1.18\) GeV\(^{2}\)  the number of candidates is reduced to appx. 14M.

February 22, 2023

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

S. Ordoñez (UNAL-COL)

Data sample

February 22, 2023

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

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

\(\phi(1020)\) 

Cloned tracks

Cloned tracks

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

\(\phi(1020)\) 

\(\phi(1020)\) 

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

S. Ordoñez (UNAL-COL)

Data sample

February 22, 2023

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

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

Cloned tracks

\(\phi(1020)\) 

Selection

Pre-selection

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

S. Ordoñez (UNAL-COL)

• On top of the trigger level cuts we also apply  offline pre-selection cuts.
• The total number of candidates in the 2016-2018 samples after the pre-selection is appx. 4.1M

• After pre-selection 29.5% of the candidates in the region \(s_{low}^{DTF} < 1.18\) GeV\(^2\) are kept.
• From the pre-selected sample an estimated 12.9% of the events correspond to potential signal events.

February 22, 2023

Selection

Pre-selection

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

February 22, 2023

S. Ordoñez (UNAL-COL)

• Comparison between the \(KKK\) mass distribution before and after the pre-selection for the region \(s_{low}^{DTF} < 1.18\) GeV\(^2\).

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

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

Selection

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

S. Ordoñez (UNAL-COL)

February 22, 2023

• \(KKK\) invariant mass distribution and Dalitz plots for one of the pre-selected subsamples

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

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

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

2016-Down

Pre-selection

Folding 

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

February 22, 2023

S. Ordoñez (UNAL-COL)

• Previous to the MVA it is necessary to prepare the MC samples that will be used as signal proxy.
• The data samples for each year and polarity are randomly divided into two reproducible sub-samples:

Monte Carlo reweighting

Fold 1

Fold 2

sWeights

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

S. Ordoñez (UNAL-COL)

• 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.

February 22, 2023

Monte Carlo reweighting

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

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

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

\(D^{+}\) candidate mass vs background weight

\(D^{+}\) candidate mass vs signal weight

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

Results for the sub-sample 2016-MagDown (Fold 1)

Dynamics correction

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

S. Ordoñez (UNAL-COL)

• 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, \(w_{nSPDHits}\).

February 22, 2023

Monte Carlo weighting

Reweight procedure

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

S. Ordoñez (UNAL-COL)

February 22, 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.

Monte Carlo weighting

Monte Carlo matching

Reweight procedure

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

S. Ordoñez (UNAL-COL)

February 22, 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.

gb_weight

Results for the KS test before the reweighting

2016-Down (Fold 2)

Monte Carlo matching

Reweight procedure

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

S. Ordoñez (UNAL-COL)

February 22, 2023

2016-Down (Fold 2)

Results for the KS test after the reweighting

Monte Carlo matching

Reweight procedure

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

S. Ordoñez (UNAL-COL)

February 22, 2023

• Variables after applying the gb_weights

MVA selection

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

February 22, 2023

S. Ordoñez (UNAL-COL)

• To further refine the candidate 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).

Selection

Fold 1

Fold 2

For each fold, 700k signal events are used for training and 100k for testing. Similarly, 370k bkg events are used for training, and 100k for testing.

MVA selection

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

February 22, 2023

S. Ordoñez (UNAL-COL)

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

MVA selection

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

February 22, 2023

S. Ordoñez (UNAL-COL)

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.

MVA selection

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

February 22, 2023

S. Ordoñez (UNAL-COL)

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

February 22, 2023

S. Ordoñez (UNAL-COL)

• 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

Selection

Fold 1

Fold 2

A sample with high purity is required for this analysis.

Figures of merit

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

February 22, 2023

S. Ordoñez (UNAL-COL)

• A cut on val_BDTG > 0.65 gives a purity of 92%, with a signal efficiency of around 50%.

Selection

Fold 1

Fold 2

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

February 22, 2023

S. Ordoñez (UNAL-COL)

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

• The final signal region corresponds to \(2\sigma_{eff}\) is: \([1860.38,1879.31]\) MeV
• Within the signal region there are: 237940 signal events and  21708 background events. 

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

February 22, 2023

S. Ordoñez (UNAL-COL)

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

Dalitz plot of the selected data

\(\phi(1020)\) 

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

February 22, 2023

S. Ordoñez (UNAL-COL)

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

Dalitz plot of the selected data

\(\phi(1020)\) 

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

February 22, 2023

S. Ordoñez (UNAL-COL)

Back up

Dynamics correction cross check

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

S. Ordoñez (UNAL-COL)

• To check if the weights were correctly calculated one can plot:

February 22, 2023

Monte Carlo weighting

MVA selection

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

February 22, 2023

S. Ordoñez (UNAL-COL)

Selection

MVA selection

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

February 22, 2023

S. Ordoñez (UNAL-COL)

Selection

• Application phase:
  • Application of the weights obtained from Fold 1 in Fold 2

Similar results are obtained for the application in Fold 1.

Figures of merit

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

February 22, 2023

S. Ordoñez (UNAL-COL)

Selection

Fold 1

Fold 2