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
- 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:
- 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 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
andBDTG. A
similar performance is observed, there is no strong motivation for a specific choice \(\rightarrow\) TheBDTG
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:
and


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
andBDTG.
- 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.
- 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.

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
- 278