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Motivation Partial Wave Analysis Up to know: worked on + with - - PowerPoint PPT Presentation

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Study to Determine the Quantum Numbers of Resonances with PAWIAN th 2019| P ANDA CM 19/3 GSI | Jenny Ptz November 6 Motivation Partial Wave Analysis Up to know: worked on + with analysis of

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Study to Determine the Quantum Numbers

  • f Ξ Resonances with PAWIAN

November 6

th 2019| ഥ

PANDA CM 19/3 GSI | Jenny Pütz

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Motivation

  • Up to know: worked on

analysis of ҧ 𝑞𝑞 → ത 𝛰+𝛰∗− with 𝛰∗− → 𝛭𝐿− (& c.c.)

1)

  • Quantum number of most

𝛰 resonances unknown or

  • nly estimated
  • No experimental data and

theoretical predictions

  • PWA: possibility to determine

those quantum numbers

Partial Wave Analysis

  • 6. November 2019

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1) See plenary talk and talk in Hyperon Session at CM 18/3 PDG2014

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What is PAWIAN?

  • PArtial Wave Interactive ANalysis software
  • Different spin formalisms and dynamics
  • Event-based maximum likelihood fit (MINUIT2)
  • Generates events based on user-defined decay model or on

fit results obtained with real data

  • 6. November 2019

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For further information: https://panda-wiki.gsi.de/foswiki/bin/view/PWA/PawianPwaSoftware

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Strategy

  • Is it possible to reconstruct the input values?
  • Event Generation:
  • 1 data set of 10000 events for ത

ΞΛ𝐿−

  • 2 data sets of 3000 events for each resonance
  • 𝑞 ҧ

𝑞= 4.6 GeV/c and 𝑀𝑛𝑏𝑦=0,1 for each data set

  • Different quantum numbers generated for Ξ(1690)− and Ξ(1820)−

Τ

1 2−, Τ 1 2+ , Τ 3 2−, Τ 3 2 +

  • Fit all hypotheses to each generated data set
  • At later stage: included crossed channel ത

pp → ഥ Λ 1890 Λ

  • 6. November 2019

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How are Results Compared?

  • Different criteria used: BIC and AIC
  • BIC: Bayesian information criterion
  • model selection among a finite set of models
  • AIC: Akaike information criterion
  • Estimates quality of model relative to set of models
  • In both cases, model with lowest value is preferred
  • Final selection based on : ΔAIC = AIC𝑗 − AIC𝑛𝑗𝑜
  • ΔAIC < 2: evidence for the model; ΔAIC > 10 : model unlikely
  • Special case: AIC and BIC show different tendencies => AIC+BIC
  • 6. November 2019

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  • 6. November 2019

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Single Resonances

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Ξ(1690)− (𝑴𝐧𝐛𝐲= 𝟏)

  • 6. November 2019

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Fitted ½+ Sample Generated ½+ Sample

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Ξ(1690)− (𝑴𝐧𝐛𝐲= 𝟏)

  • 6. November 2019

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In all tested cases: generated hypothesis preferred by fit!

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Ξ(1690)− (𝑴𝐧𝐛𝐲= 𝟏)

  • 6. November 2019

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Generated 1/2+ & fitted 3/2+ Generated 1/2+ & fitted 1/2−

not caused by statistical effects

Generated 3/2+ & fitted 1/2+ Generated 3/2− & fitted 1/2−

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  • True hypothesis preferred by fit in each case
  • Similar fitted angular distributions as for 𝑀max = 0

Ξ(1690)− (𝑴𝐧𝐛𝐲= 𝟐)

  • 6. November 2019

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Generated 1/2− & fitted 3/2− Generated 1/2− & fitted 3/2−

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Ξ(1820)− (𝑴𝐧𝐛𝐲= 𝟏)

  • 6. November 2019

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Fitted 3/2− Sample Generated 3/2− Sample

For 𝑀max = 1 even harder to distinguish

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  • 6. November 2019

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Crossed Channel

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  • 6. November 2019

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Ξ(1690)− (𝑀MAX = 1)

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Ξ(1820)

− (𝑀MAX = 𝟏)

  • 6. November 2019

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  • Performed test to reproduce quantum numbers
  • “Single” resonances: promising
  • Included crossed channel: ത

pp → ഥ Λ 1890 Λ

  • Statistics is limiting factor
  • Systematic studies with higher statistics needed
  • Combined sample for both Ξ resonances
  • Same test should be done for charge conjugate particles
  • 6. November 2019

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Summary & Outlook

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  • 6. November 2019

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Thank you for your attention

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  • 6. November 2019

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Backup

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Reminder

  • Partial Wave Analysis (PWA): tool to extract complex amplitudes
  • f process
  • In case of low energies → process dominated by resonances
  • PWA gives possibility to determine:
  • Mass & width
  • Spin & Parity

Partial Wave Analysis

  • 6. November 2019

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ത p p K− ∧ ത Ξ+

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Event Generation

  • Beam momentum of 4.6 GeV/c² corresponds to a momentum in

center-of-mass frame of:

  • 𝑞cm ≈ 600 MeV/c for Ξ 1690 − → 𝑀max = 3
  • 𝑞cm ≈ 410 MeV/c for Ξ 1820 − → 𝑀max = 2

Maximum Angular Momentum of ഥ 𝐪𝐪

  • 6. November 2019

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BIC and AIC

  • Bayesian information criterion (BIC):

is a criterion for model selection among a finite set of models; the model with the lowest BIC is preferred. 𝐶𝐽𝐷 = 2 ∙ −𝑀𝐼𝐼 + 𝑙 ∙ ln(𝑜) with LHH: maximal loglikelihood value, k: number of free fit parameters and n: number of events in the sample

  • Akaike information criterion (AIC):

is a measure of the relative quality of statistical models for a given set of data. Given a collection of models for the data, AIC estimates the quality of each model, relative to each of the other models 𝐵𝐽𝐷 = 2𝑙 + 2 ∙ (−𝑀𝑀𝐼)

  • 6. November 2019

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Helicity Frame

  • 6. November 2019

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Image from Bertram Kopf

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Gottfried-Jackson Frame

  • 6. November 2019

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Image from Bertram Kopf

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Ξ(1690)−

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Ξ(1690)− (𝑴𝐧𝐛𝐲= 𝟏)

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Ξ(1690)− (𝑴𝐧𝐛𝐲= 𝟐)

  • 6. November 2019

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Ξ(1820)− (𝑴𝐧𝐛𝐲= 𝟏)

  • 6. November 2019

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Ξ(1820)− (𝑴𝐧𝐛𝐲= 𝟐)

  • 6. November 2019

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Ξ(1690)− (𝑴𝐧𝐛𝐲= 𝟐) cross channel

  • 6. November 2019

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Ξ(1820)− (𝑴𝐧𝐛𝐲= 𝟏) crossed channel

  • 6. November 2019

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