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A Genetic Algorithm Analysis of N* Resonances

This analysis explores the contribution of N* resonances to K+L and examines how using a genetic algorithm can enhance the data analysis. The results provide insights into the current understanding of these resonances.

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A Genetic Algorithm Analysis of N* Resonances

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  1. A Genetic Algorithm Analysisof N* Resonances Outline:- • Analysis of N* contribution to gp → K+L • How does using a Genetic Algorithm help? • How much can an analysis of the data currently tell us? • Conclusions and Outlook D. G. Ireland Department of Physics and Astronomy University of Glasgow

  2. With D13 Without D13 “Evidence” of missing D13 resonance Mart & Benhold, Phys. Rev. C 61 012201(R) (1999) Analysis of “World” data (1999)

  3. Hadrodynamical Model of Janssen, et al. • Coupling constants and other parameters have to be determined by fits to data. • The “fit” is an optimisation involving 20 – 30 free parameters. • [This is a single channel model, more complete descriptions require coupled channel analyses.] • Strategy: Genetic Algorithm (GA) + Minuit

  4. GA components... A “population” of encoded trial solutions Each solution has a “fitness” Evolution of population, consisting of ... Crossover Selection Mutation + iteration towards convergence...

  5. Comparison: GA vs. MINUIT

  6. Janssen, Ireland & Ryckebusch, Phys. Lett. B 562 (2003) 51 Phase 1: Calculation with additional D13 Many sets of fitted parameters = many calculations with equal goodness-of-fit

  7. Each calculation has a different set of fitted coupling constants. Distributions of Fitted Parameters

  8. Large ambiguities, even within one model Predictions for Unmeasured Observables

  9. Phase 2: Systematic Study with more experimental data points... To address two questions:- • Is there more evidence of an extra resonance in the reaction? • What are the quantum numbers of this extra resonance? Each model:- • contains a “core” set of resonances: S11(1650), P11(1710) and P13(1720) • contains an extra resonance of mass 1895 MeV, with different quantum numbers: S11, P11, P13, D13 • used 100 calculations (GA + MINUIT) • New photon beam polarisation (SPRing-8), and electroproduction data (Jlab Hall C) used in fit.

  10. Core S11 Total Cross-Section P11 P13 D13 Photon Beam Asymmetry Results:

  11. “Pluralitas non est ponenda sine necessitate” - plurality should not be posited without necessity For models A and B, calculate ratio of posterior probabilities:- William of Occam (or Ockham, ca. 1285-1349) Occam's Razor ←ratio of likelihoods Occam factor (approximate) Best fit to data

  12. Table of Results • Raw scores indicate D13 most likely • More sophisticated comparison favours P11 • Data support hypothesis of extra resonance • Situation still not clear

  13. Linear Core S11 P11 P13 D13 Circular Beam – recoil polarisation Model Predictions – New Measurements

  14. Phase 3: Lots more data! e.g. J.W.C. McNabb et al., PRC 69 (2004) 042201 Two approaches:- • Use parameters obtained in previous fit for Core, S11, P11, P13, D13 models • Re-fit, but with two models: Core and S11+P11+P13+D13 (all hypothetical resonances together)

  15. Angular Distributions Data: J.W.C. McNabb et al., PRC 69 (2004) 042201 (CLAS)

  16. Differential Cross Sections Data: J.W.C. McNabb et al., PRC 69 (2004) 042201 (CLAS)

  17. Beware many parameters! • Full calculation penalised for many parameters. • Occam factor calculation very approximate! • Situation inconclusive • “Full” evaluation of integrals necessary → MCMC

  18. Conclusions • Genetic Algorithm: potentially powerful addition to analysis toolbox. • Must do many calculations – study parameter space. • Current data indicates poor agreement with (tree-level) model and no extra resonances • Adding resonances does not necessarily improve agreement…

  19. Outlook • Harness fitting strategy to coupled-channels calculations. • Improve evaluation of Occam factors. • Monte Carlo integration of likelihoods P(D|A) over parameter space → theoretical error bars (c.f. lattice QCD simulations). • Experiment: polarisation observables crucial.

  20. Comparing Different Models How do we quantify the intuitive feeling that some models are better?

  21. Typical correlation matrix for the fitted free parameters Chi-Squared surface very complicated Difficulty of Problem

  22. Polarisation transfer data from CLAS D. Carman et al., PRL 90 (2003) 131804 Core S11 P11 P13 D13 Model Predictions - Electroproduction p(e,e’k+)L

  23. Recoil Polarisation Data: J.W.C. McNabb et al., PRC 69 (2004) 042201 (CLAS)

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