Sebastián Ordoñez-Soto
Universidad Nacional de Colombia
Analysis supervisors: Alberto C. dos Reis and Diego Milanés
Internship tutor: Patrick Robbe
November 23, 2022
Dalitz plot analysis of the \(D^{+}\rightarrow K^{-}K^{+}K^{+}\) decay
Internship report
Introduction
- Decays of \(D\) mesons into three final state hadrons are an important tool for studies of low energy QCD.
- These decays proceed dominantly through intermediate resonances, in particular, scalar states which are still poorly understood.
- The scalar states with mass below 1.7 GeV couple to \(\pi\pi\), \(K\pi\) and \(K\bar{K}\) and are produced in decays with a pair of identical particles in the final state, e.g., \(D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}\), \(D^{+}_{(s)}\rightarrow \pi^{-}\pi^{+}\pi^{+}\) and \(D^{+}\rightarrow K^{-}K^{+}K^{+}\).
Data and simulation samples
- Data collected in \(pp\) collisions at \(\sqrt{s} = 13\) TeV by LHCb in the Run 2 (2016-2018), which in total corresponds to 5.6 fb\(^{-1}\) of integrated luminosity.
-
Exclusive HLT2 Turbo lines Hlt2CharmHadDpToKmKpKp select the \(D^{+}\rightarrow K^{-}K^{+}K^{+}\) candidates.
-
- Monte Carlo (MC) simulated data is available. Similar configurations for each year but with different trigger settings.
Data and simulation samples
HLT2 selection criteria
Data selection: Initial data set
Dalitz plot of the \(D^{+}\) candidates
Invariant mass distribution of the \(D^{+}\) candidates
\(s_{12}\) (GeV)
\(s_{13}\) (GeV)
\(m_{K^{-}K^{+}K^{+}}\) (MeV)
\(D^{+}\)
Clone tracks
Left sideband
Right sideband
\(1869.66 \pm0.05\) MeV
Signal region
Events / MeV
- Mass distributions and Dalitz plots for the 2016-Down data before the pre-selection.
- The data samples have high levels of background: combinatorial and specific backgrounds
d\Gamma = \frac{1}{(2\pi)^{3}}\frac{1}{32M^{3}}|\mathcal{M}|^{2}dm_{12}^{2}dm_{13}^{2}
2016-Down
\(s_{12}\) projection of the Dalitz plot
\(s_{13}\) projection of the Dalitz plot
\(s_{12}\) (GeV)
\(s_{13}\) (GeV)
Clone tracks
Clone tracks
Events / GeV\(^{2}\)
Events / GeV\(^{2}\)
Data selection: Initial data set
2016-Up
Data selection
Dalitz plot of the \(D^{+}\) candidates
Invariant mass distribution of the \(D^{+}\) candidates
\(m_{K^{-}K^{+}K^{+}}\) (MeV)
\(s_{12}\) (GeV)
\(s_{13}\) (GeV)
Events / MeV
\(s_{12}\) projection of the Dalitz plot
\(s_{13}\) projection of the Dalitz plot
Data selection
2016-Up
\(s_{12}\) (GeV)
\(s_{13}\) (GeV)
Events / GeV\(^{2}\)
Events / GeV\(^{2}\)
Data selection
2017-Down
Dalitz plot of the \(D^{+}\) candidates
Invariant mass distribution of the \(D^{+}\) candidates
\(m_{K^{-}K^{+}K^{+}}\) (MeV)
\(s_{12}\) (GeV)
\(s_{13}\) (GeV)
Events / MeV
Data selection
2017-Down
\(s_{12}\) projection of the Dalitz plot
\(s_{13}\) projection of the Dalitz plot
\(s_{13}\) (GeV)
\(s_{12}\) (GeV)
Events / GeV\(^{2}\)
Events / GeV\(^{2}\)
Data selection
2017-Up
Dalitz plot of the \(D^{+}\) candidates
Invariant mass distribution of the \(D^{+}\) candidates
\(m_{K^{-}K^{+}K^{+}}\) (MeV)
\(s_{12}\) (GeV)
\(s_{13}\) (GeV)
Events / MeV
Data selection
2017-Up
\(s_{12}\) projection of the Dalitz plot
\(s_{13}\) projection of the Dalitz plot
\(s_{12}\) (GeV)
\(s_{13}\) (GeV)
Events / GeV\(^{2}\)
Events / GeV\(^{2}\)
Data selection
2018-Down
Dalitz plot of the \(D^{+}\) candidates
Invariant mass distribution of the \(D^{+}\) candidates
\(m_{K^{-}K^{+}K^{+}}\) (MeV)
\(s_{12}\) (GeV)
\(s_{13}\) (GeV)
Events / MeV
Data selection
2018-Down
\(s_{12}\) projection of the Dalitz plot
\(s_{13}\) projection of the Dalitz plot
\(s_{12}\) (GeV)
\(s_{13}\) (GeV)
Events / GeV\(^{2}\)
Events / GeV\(^{2}\)
Data selection
2018-Up
Dalitz plot of the \(D^{+}\) candidates
Invariant mass distribution of the \(D^{+}\) candidates
\(m_{K^{-}K^{+}K^{+}}\) (MeV)
\(s_{12}\) (GeV)
\(s_{13}\) (GeV)
Candidates / MeV
Data selection
2018-Up
\(s_{12}\) projection of the Dalitz plot
\(s_{13}\) projection of the Dalitz plot
\(s_{12}\) (GeV)
\(s_{13}\) (GeV)
Events / GeV\(^{2}\)
Events / GeV\(^{2}\)
\(s_{12}\) (GeV)
\(s_{13}\) (GeV)
\(m_{K^{-}K^{+}K^{+}}\) (MeV)
Dalitz plot of the \(D^{+}\) pre-selected candidates
Mass distribution of the \(D^{+}\) pre-selected candidates
Events / MeV
\(D^{+}\)
Data selection: Pre-selection
- Mass distributions and Dalitz plots for the 2016-Down data after the pre-selection.
- There is charm background in the \(K^{-}K^{+}K^{+}\) mass spectra due to misidentification (mis-ID), e.g., \(D^{+}_{s} \rightarrow K^{-}K^{+}\pi^{+}\pi^{0}\) and \(D^{+} \rightarrow K^{-}K^{+}\pi^{+}\pi^{0}\).
- Particle identification (PID) cuts are used to control the peaking background: probNNk\(_{all}\) > 0.6 cut
\(m_{K^{-}K^{+}K^{+}}\) (MeV)
\(s_{12}\) (GeV)
\(s_{12}\) projection of the Dalitz plot
\(s_{13}\) projection of the Dalitz plot
Events / MeV
Events / MeV
\(D^{+}\)
Data selection: Pre-selection
\text{difTX23} = \left|\frac{p_{x_{2}}}{p_{z_{2}}} - \frac{p_{x_{3}}}{p_{z_{3}}} \right|
\text{difTY23} = \left|\frac{p_{y_{2}}}{p_{z_{2}}} - \frac{p_{y_{3}}}{p_{z_{3}}} \right|
- The next contribution eliminated was that of cloned tracks of the \(K^{+}\) daughters.
- To remove these events, the following two slope difference variables were used:
Data selection: Pre-selection
Slope difference variables
Data selection: Multivariate Analysis
2016-Down (Fold 1)
Sidebands from data
Input data for training
\(m_{K^{-}K^{+}K^{+}}\) (MeV)
\(m_{K^{-}K^{+}K^{+}}\) (MeV)
Invariant mass distribution of the \(D^{+}\) simulated candidates
Events / MeV
Events / MeV
\(D^{+}_{MC}\)
2016-Down (Fold 1)
- A MultiVariate Analysis (MVA) is used to reduce the combinatorial contribution to the \(D^{+}\rightarrow K^{-}K^{+}K^{+}\).
- The three main staged of the MVA are: training, testing and application.
- For the training, a reweighted MC sample is used as signal ad data sidebands are used as background.
Discriminant variables
- These variables are chosen for the MVA training because of their discriminating power.
Data selection: Multivariate Analysis
MVA testing results
Overtraining check
Figures of merit
Data selection: Multivariate Analysis
BDTG application on Data
Events
Events
MVA application results
BDTG application on MC
Fold 2
Fold 2
- The last step of the MVA is to apply the resulting BDTG classifier in non-labeled data
- A tighter cut on this variables give us a higher signal purity with a cost on the signal efficiency.
Data selection: Multivariate Analysis
Data selection: Figures of merit
Signal efficiency and purity
- In Dalitz plot analysis high purity samples are required.
\text{P}_{i} = \frac{S_{i}}{S_{i}+B_{i}}
- Purity is defined as:
\epsilon_{i}^{MC} = \frac{N_{i}^{MC}}{N_{0}^{MC}}
- Signal efficicency is calculated as:
Data analysis: Figures of merit
Fits after BDTG cut
BDTG_val > 0.7
\(D^{+}\)
\(D^{+}\)
\(m_{K^{-}K^{+}K^{+}}\) (MeV)
Candidates / MeV
Data selection: Final sample
\(m_{K^{-}K^{+}K^{+}}\) (MeV)
\(m_{K^{-}K^{+}K^{+}}\) (MeV)
Candidates / MeV
Candidates / (1.3 MeV)
\(D^{+}\)
\(D^{+}\)
- The final sample contains 505 thousand candidates in the signal region, of which (92.52 \(\pm\) 0.07 )% correspond to signal.
- Next step: Study the remaining background, specially obtain the fraction of \(\phi\) background in the signal region.
Invariant mass distribution of the final \(D^{+}\) candidates
Fit of the final mass distribution
Data selection: Final sample
Candidates / GeV\(^{2}\)
\(s_{12}\) (GeV)
\(s_{12}\) (GeV)
\(s_{13}\) (GeV)
Dalitz plot of the \(D^{+}\) candidates
\(s_{12}\) projection of the Dalitz plot
- Dalitz plot and one of its projections for events in the full \(K^{-}K^{+}K^{+}\) spectrum
\(\phi\) (1020)
Data selection: Final sample
\(m_{K^{-}K^{+}K^{+}}\) (MeV)
\(m_{K^{-}K^{+}K^{+}}\) (MeV)
Events / MeV
Events / MeV
\(D^{+}\)
Invariant mass distribution of the final \(D^{+}\) candidates in the signal region
Invariant mass distribution of the final sidebands
- Let us consider separately the signal region and the sidebands.
Data selection: Final sample
Candidates / GeV\(^{2}\)
\(s_{12}\) (GeV)
\(s_{12}\) (GeV)
\(s_{13}\) (GeV)
Dalitz plot of the \(D^{+}\) candidates in the signal region
\(s_{12}\) projection of the Dalitz plot from the signal region
Signal region
\(\phi\) (1020)
Data selection: Final sample
Candidates / GeV\(^{2}\)
\(s_{12}\) (GeV)
\(s_{12}\) (GeV)
\(s_{13}\) (GeV)
Dalitz plot of the sidebands events
\(s_{12}\) projection of the Dalitz plot from the sidebands
Sidebands
\(\phi\) (1020)
Summary
Thank you!
- The 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.
- Different figures of merit were estimated aiming to find the optimal cut in the resulting MVA classifier output.
- A final sample with 505 thousand \(D^{+}\rightarrow K^{-}K^{+}K^{+}\) candidates and with a purity of (92.52 \(\pm\) 0.07) % was obtained.
IJCLab internship report
By Sebastian Ordoñez
