Sebastián Ordoñez-Soto

jsordonezs@unal.edu.co

Universidad Nacional de Colombia

Supervisors: Alberto C. dos Reis and Diego Milanés

Dalitz plot analysis of the \(D^{+}\rightarrow K^{-}K^{+}K^{+}\) decay

7th Colombian Meeting on High Energy Physics

December 2, 2022

Contents

  • Introduction
  • Data samples
  • Data selection
    • Initial data samples
    • Pre-selection
    • MVA 
    • Figures of Merit
  • Background model
  • Summary

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

Tree and annhihilation diagrams for the resonant decays of \(D^{+}\rightarrow K^{-}K^{+}K^{+}\) final state

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 selection: Initial data samples

Dalitz plot  of the \(D^{+}\) candidates

Invariant mass distribution (IMD)  of the \(D^{+}\) candidates

\(s_{12}\) (GeV)

\(s_{13}\) (GeV)

\(m_{K^{-}K^{+}K^{+}}\) (MeV)

\(D^{+}\) 

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}
  • Notation: \(s_{12} = m^{2}(K_{1} ^{-}K_{2}^{+})\) and \(s_{13} = m^{2}(K_{1}^{+}K_{3}^{+})\).

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 samples

2016-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: Initial data samples

\(s_{12}\)  projection of the Dalitz plot

\(s_{13}\)  projection of the Dalitz plot

2016-Up

\(s_{12}\) (GeV)

\(s_{13}\) (GeV)

Events / GeV\(^{2}\)

Events / GeV\(^{2}\)

Data selection: Initial data samples

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: Initial data samples

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: Initial data samples

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: Initial data samples

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: Initial data samples

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: Initial data samples

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: Initial data samples

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: Initial data samples

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\(^{2}\)

Data selection: Initial data samples

\(s_{12}\) (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 spectrum due to misidentification (mis-ID), e.g.,    \(D^{+}_{s} \rightarrow K^{-}K^{+}\pi^{+}\pi^{0}\), \(D^{+} \rightarrow K^{-}K^{+}\pi^{+}\pi^{0}\), \(\Lambda_{c}^{+}\rightarrow K^{-}K^{+}p\) and \(\Lambda_{c}^{+}\rightarrow K^{-}\pi^{+}p\).
  • Particle identification (PID) cuts are used to control the peaking background: probNNk\(_{1,2,3}\) > 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 specific contribution eliminated was that of cloned tracks of the \(K^{+}\) daughters.
  • To remove these events, the following two slope difference variables were used:

\(\phi\) (1020)

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 stages of the MVA are: training, testing and application.
  • For the training, a reweighted MC sample is used as signal and data sidebands are used as background.
  • These variables are chosen for the MVA training because of their discriminating power.

Data selection: Multivariate Analysis

MVA training results

  • 1M signal events and 900k background events were used for the training of the BDTG classifier.

MVA testing results

Overtraining check

Figures of merit

Data selection: Multivariate Analysis

  • 100k signal events and 100k background events were used for the testing of the BDTG classifier.

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 the BDTG_val variable  give us a higher signal purity with a loss in 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:

Fold 2

Data analysis: Figures of merit

Fits after BDTG cut

\(D^{+}\) 

\(D^{+}\) 

\(m_{K^{-}K^{+}K^{+}}\) (MeV)

Candidates / MeV

  • If the cut BDTG_val > 0.68 is applied,  a signal purity of 92.5% and a signal efficiency of 48% are reached.

IMD of the final \(D^{+}\) candidates

Fit to the final  mass distribution

Fold 2

Fold 2

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.

IMD of the final \(D^{+}\) candidates

Fit to the final  mass distribution

  • This is 4.55 times the statistics of the same analysis with the Run 1.

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

\(D^{+}\) 

IMD of the final \(D^{+}\) candidates in the signal region

Sidebands of the final data sample

  • 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)

Background Model

  • Work in progress: Study the composition of the remaining background.
  • Fits to the Dalitz projections are performed (slices of 9 MeV) and yields for the peaking and combinatorial background are obtained.

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.

Data and simulation samples

HLT2 selection criteria

Data selection: Initial data sample

Number of candidates before pre-selection

Data selection: Pre-selection

Summary of pre-selection cuts

Data selection: Pre-selection

Slope difference variables

Data selection: Multivariate Analysis

MVA training results

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