Study of the \(K^{+}K^{-}\) S-wave amplitude near threshold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)
Sebastian Ordoñez*, Alberto Reis, Diego Milanés
jsordonezs@unal.edu.co
Universidad Nacional de Colombia
Charm WG meeting
February 22 , 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
S. Ordoñez (UNAL-COL)
Study of the \(K^{-}K^{+}\) S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)
February 22, 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:
- 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.
Analysis strategy
Study of the \(K^{-}K^{+}\) S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)
S. Ordoñez (UNAL-COL)
February 22, 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.
Methodology
- Data
- Sample used for the CPV search in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\) is not adequate for DP analysis \(\rightarrow\) New selection to be made.
- Only a small region of the phase space will be used \(\rightarrow\) Dalitz folded
- Given that there is no interference between the two \(K^{-}K^{+}\) channels in the region of interest, it is possible to use the Dalitz plot folded.
- Simulations
- Large Monte Carlo (MC) samples available
- Need to match data and MC distributions \(\rightarrow\) GB-Reweighting
This analysis follows a similar strategy to that used in the analysis of \(D_{(s)}^{+}\rightarrow \pi^{-}\pi^{+}\pi^{+}\)
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\(^{2}\)]
\(s_{13}\) [GeV\(^{2}\)]
\(\phi(1020)\)
Cloned tracks
Cloned tracks
- Notation: \(s_{12} = s_{K^{-}K^{+}} = m_{K^{-}K^{+}}^{2}\) and \(s_{13} = s_{K^{-}K^{+}} = m_{K^{-}K^{+}}^{2}\)
\(\phi(1020)\)
\(\phi(1020)\)
Events
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\(^{2}\)]
\(s_{high}^{DTF}\) [GeV\(^{2}\)]
Cloned tracks
\(\phi(1020)\)
Events
Data samples
Study of the \(K^{-}K^{+}\) S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)
S. Ordoñez (UNAL-COL)
Monte Carlo
February 22, 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)
- 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]
Events
Events
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\(^{2}\)]
\(s_{13}\) [GeV\(^{2}\)]
\(s_{low}^{DTF}\) [GeV\(^{2}\)]
\(s_{high}^{DTF}\) [GeV\(^{2}\)]
2016-Down
Pre-selection
Events
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
After the folding, it is ensured that each fold has the same number of events coming from each sub-sample.
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
- The matching between the data and MC variables is said to be successful, confirmed by the KS test and ROC curve.
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
| N. Background events | N. Signal events |
|---|---|
| 477845 | 802422 |
Fold 1
| N. Background events | N. Signal events |
|---|---|
| 480365 | 800592 |
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.
-
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.
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
| Training variables for BDT classifier |
| D_IP_CHI2 |
| log(D_FD_CHI2) |
| DIRA |
| D_ENDVERTEX_CHI2 |
| logIP |
| D_BPVTRPOINTING |
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:
BDTandBDTG. - From the ROC curves a similar performance is observed, there is no strong motivation for a specific choice. The
BDTGis used for the application.
- To perform the selection, two classifiers were tested:
| 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.
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
BDTGclassifier.
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 > 0.65gives 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
\(\phi(1020)\)
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
- 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
\(\phi(1020)\)
Events
Study of the \(K^{-}K^{+}\) S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)
February 22, 2023
S. Ordoñez (UNAL-COL)
Outlook
-
Background study
- Determine the fractions of the two components of the remaining background: combinatorial and \(\phi(1020)\).
- Next: Produce the background model using a toys with the computed background fractions.
-
Efficiency
- Next: Calculate the efficiency map using the Monte Carlo samples and the final selection
Study of the \(K^{-}K^{+}\) S-wave amplitude near treshhold in \(D^{+}\rightarrow K^{-}K^{+}K^{+}\)
February 22, 2023
S. Ordoñez (UNAL-COL)
Thank you!
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
