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

Sebastián Ordoñez-Soto

Universidad Nacional de Colombia

 

Supervisors: Alberto C. dos Reis and Diego Milanés

 

March 30th, 2022

 

Charm WG Meeting

Outline

 

  1. Introduction
  2. State of the Art
  3. Results from Run 1
  4. Analysis strategy
  5. Outlook

Introduction

  • Decays of \(D\) mesons into three pseudoscalars are excellent laboratories to study light-meson spectroscopy.
  • No tools for a description from first principles.

Motivation

Problem

  • In a \(D\rightarrow K^{-}K^{+}K^{+}\) decay, the \(K\bar{K}\) scattering amplitudes can be determined.
    • Need phenomenological models.
  • The challenge:
    • Dynamics: Heavy-quark weak transitions, hadron formation and final-state interactions (FSI)
    • Strong part: effects of coupled channels, three-body interactions and isospin.

S. Ordoñez (UNAL-COL)

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

March 30, 2022

  • Model based on chiral effective Lagrangians.

The Multi-meson model

  • Model parameters have transparent physical meaning.
  • The Triple-M  has been developed to describe the \(D^{+}\rightarrow K^{-}K^{+}K^{+}\) decay.
  • It has been already used in a Dalitz plot fit with data from the Run 1.
  • It allows to obtain the \(K\bar{K}\) scattering amplitudes.

Introduction

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

March 30, 2022

S. Ordoñez (UNAL-COL)

State of the Art

http://dx.doi.org/10.1103/PhysRevD.98.056021

[1]. [2018] First version of the model.

[2]. [2018] (PAPER-2018-039) Dalitz plot fit using the Multi-meson model decay amplitude. 

http://dx.doi.org/10.1007/JHEP04(2019)063

[3]. [2020] Improved version of the Multi-meson model.

http://dx.doi.org/10.1103/PhysRevD.102.076012

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

March 30, 2022

S. Ordoñez (UNAL-COL)

Results from Run 1

Figures taken from Ref. [2] (PAPER-2018-039)

http://dx.doi.org/10.1007/JHEP04(2019)063

Invariant-mass spectrum of the \(K^{-}K^{+}K^{+}\) candidates.

  • 111 thousand candidates, of which \(90.45 \pm 0.07 \%\) correspond to signal

(left) Dalitz plot of the selected sample, including background. (right) Dalitz plot projections for candidates from regions I (blue) and II (red), above and below \(s_{K^{-}K^{+}}= 1.5\) GeV \(^{2}\).

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

March 30, 2022

S. Ordoñez (UNAL-COL)

Figure and table taken from Ref. [2] (PAPER-2018-039)

Results from Run 1

Relative fractions (%) of the various components of the Triple-M amplitude. The uncertainties correspond to the combined statistical and systematic uncertainties.

Projections of the Dalitz plot with the fit result with the Triple-M amplitude superimposed.

http://dx.doi.org/10.1007/JHEP04(2019)063

March 30, 2022

March 30, 2022

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

S. Ordoñez (UNAL-COL)

Figure taken from Ref. [2] (PAPER-2018-039)

Results from Run 1

(top) Phase-shifts \(\delta_{K^{+}K^{-}}^{0I}\) and (bottom) inelasticities \(\eta^{0I}\) as a function of the  \(K^{+}K^{-}\) invariant mass, for both isospin states.

http://dx.doi.org/10.1007/JHEP04(2019)063

March 30, 2022

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

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

S. Ordoñez (UNAL-COL)

Analysis strategy

Perform a Dalitz plot analysis of the \(D^{+}\rightarrow K^{-}K^{+}K^{+}\) decay channel using the much larger data set of Run 2 and the improved version of the Multi-meson model.

Methodology

  • GooFit
    • Code the new version of the Triple-M amplitude
    • Perform test with toys
  • Simulations
    • Large MC samples available
    • Need to match data and MC distributions \(\rightarrow\) GB-Reweighting
  • Data
    • Sample used for the CPV search in  \(D^{+}\rightarrow K^{-}K^{+}K^{+}\) has low purity: not adequate for DP analysis.
      • New selection to be made

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

March 30, 2022

S. Ordoñez (UNAL-COL)

Outlook

  • GooFit
    • Use existing GooFit classes to perform a DP fit of the \(D^{+}\rightarrow K^{-}K^{+}K^{+}\) decay.
    • Next: Create a GooFit class corresponding to the first version of the Triple-M.
  • Data
    • Perform first tests with a small sample (2016) 
      • MVA selection
      • Fits 
      • Significance and purity study
    • Next: Pre-selection  
  • Simulations
    • Next: weights and GB-reweighting

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

March 30, 2022

S. Ordoñez (UNAL-COL)

Thank you!