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Toward a Model Independent Determination of Resonance Parameters

Explore commonalities and differences between MAID, SAID, BnGa, and more approaches. Learn about constraints in analyzing resonance data and the impact of complete experiments in understanding baryon resonance spectrum. Discover how polarization observables influence analysis tools. Discover how various groups perform model-independent analyses and unitarize amplitudes.

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Toward a Model Independent Determination of Resonance Parameters

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  1. Toward a Model IndependentDetermination of Resonance Parameters Lothar Tiator Johannes Gutenberg Universität Mainz in collaboration with CB@MAMI, Dubna and GWU CRC 1044 Analysis Tools for Next Generation Hadron Spectroscopy Camogli, Italy, 2012

  2. basic questions from our conveners: • What are the the common grounds and differences between contemporaryapproaches like MAID, SAID, BnGa, Jülich, EBAC, Giessen ?common grounds: Born terms, vector meson exchanges, D(1232), Watson’s theoremdifferences: channel coupling, unitarity treatments above pp threshold, parametrization of background beyond B+V • Do presently used analysis tools use sufficient input to constrain the output ?Or are there constraints that can be/should be added ?We should always distinguish between 2 kinds of analyses:a) the Partial Wave Analysis of the measured data: ds/dW, S, T, P, E, F,G, H, Cx,... (few constraints) - this I am addressing todayb) the Baryon Resonance Analysis from the PWA amplitudes usually done with BW models or Dynamical models with/without coupl. channels (many more constraints)

  3. basic questions from our conveners: • How to reach agreement on particular resonances from various approaches ?First we need reliable (truly model independent) partial waves from analysis with complete sets of polarization observables.Then we will need resonance analysis tools and methods starting from partial wavesin a similar way as we have mostly done it forpN scattering in the last 30 years. • How to combine the knowledge from two body coupled channelsapproaches and various production processes ?Coupled channels approaches will profit enormously, when they will getmodel-independent partial waves for (g, p) , (g, h)and(g, K)then, they no longer have to fit large data bases of polarization observables. • To which extent will complete experiments disentangle the resonance spectrum ?It will optimize the database and will allow us to generate model-independent partial wave amplitudes.It will not completely determine the resonance spectrum! - main part of this talk today

  4. from new baryon resonance tables 2012 photon decay amplitudes N(1440) 1/2+-> pg most recent entries: A1/2 (10-3 GeV-1/2 ) Anisovich 12A BnGa -61 +- 8 Dugger 07 JLab -51 +- 2 Arndt 96 SAID -63 +- 5 Drechsel 07 MAID -61 Penner 02D Gießen -81 3 PWA are easily accessible on the web: MAID unitary isobar model SAID model independent partial wave analysis (but with incomplete data) BnGa coupled-channel partial wave analysis with similar results for dominant N* properties • MAID/SAID/BnGa: • independent analyses by independent groups • different ways to parametrize background • different ways to unitarize amplitudes above pp threshold

  5. Buta closer look in the partial wave amplitudes (photoproduction multipoles) shows large differences among the different analyses, which use mainly the same data from the world data base CNS-DAC @ GWU strong model dependence in the pw amplitudes due to an incomplete data base: mainly ds/dW and S, some T, P,very few G, H

  6. 16 Polarization Observables in Pion Photoproduction

  7. currently in CNS-DAC data base for g + p -> p0 + p for W< 2 GeV: ds/dW9382G 28Ox‘ 7Tx‘ 0 S1885H 24Oz‘ 7Tz‘ 0 T 353 E 0 Cx‘ 0 Lx‘ 0 P 556 F 0 Cz‘ 0 Lz' 0 mainly only ds/dW and S which count!

  8. comparison of multipoles: MAID – SAID - BonnGatchina from Anisovich et al., Eur. Phys. J. A. 44, 203-220 (2010) Re Re Re Re no problems for M1+ surprisingly large differences, even though the world data is equally well described

  9. with newly measured polarization observables solutions will move closer MAID, SAID, BnGa and new fits()with extra T and F data (MAMI, preliminary) E0+ E2- BnGa MAID SAID in our analysis we see large changes in E0+, E2- and M1-

  10. what is a complete experiment ? a complete experiment is a set of polarization observables that is sufficient to exactly determine all underlying (complex) amplitudes up to 1 phase it does not give us a guarantee to completely determine the baryon resonance spectrum and this is not so much the problem with the phase it is the model dependence of the approaches and dynamical models or isobar models, etc., which subsequently have to analyze the amplitudes in order to find the resonances and their properties.

  11. Complete Analysis • we must distinguish between 2 kinds of complete analyses: • the amplitude analysis that leads to4 amplitudes:Fi(W,q)(but no partial waves) • the truncated partial wave analysis that leads • for Lmax = 1 to 4 multipoles: Mi(W) i.e. E0+, E1+, M1+, M1- • for Lmax = 2 to 8 multipoles • for Lmax = 3 to 12 multipoles • etc. function of energy and angle function of energy only

  12. requirements for the 1. kind of a complete experiment Barker,Donnachie,Storrow (1975): „In order to determine the amplitudes uniquely (up to an overall phase of course) one must make five double polarization measurements in all, provided that no four of them come from the same set.“ Keaton, Workman (1996) and Chiang,Tabakin (1997): a carefully chosen set of 8 observables is sufficient.

  13. one possible solution for the 1. kind is: Barker,Donnachie,Storrow (1975): „In order to determine the amplitudes uniquely (up to an overall phase of course) one must make five double polarization measurements in all, provided that no four of them come from the same set.“ Keaton, Workman (1996) and Chiang,Tabakin (1997): a carefully chosen set of 8 observables is sufficient.

  14. requirements for the 2. kind of a complete experiment Omelaenko (1981) for a truncated partial wave analysis with Lmax wavesonly 5 observables are necessary, e.g. the 4 from group Sand 1 additional from any other group Grushin (1989)applied it for a PWA in the D(1232) region with only S+P waves (Lmax= 1)

  15. one possible solution for the 2. kind is: Omelaenko (1981) for a truncated partial wave analysis with Lmax wavesonly 5 observables are necessary, e.g. the 4 from group Sand 1 additional from any other group Grushin (1989)applied it for a PWA in the D(1232) region with only S+P waves (Lmax= 1)

  16. a sample of MAID pseudo data based on 108 Monte-Carlo events for g,p0 at 320-340 MeV and comparison with real data MAID pseudo data real data

  17. S11(E0+) multipole: predicted vs. input

  18. P11(M1-) multipole: predicted vs. input

  19. Summary • The „classical“ Complete Experiment requires 8 well selected observables but it can not give us information on N* physics because it does not give us partial wavesdue to an unknown angle-dependent overall phase f(W,q) • The „new“ Complete Experiment aims directly on partial waves and requires only 5 well selected observablesthese can be: ds, S, T, P, For: ds, S, T, F, Gor: ds, S, Ox‘, Oz‘, Cz‘or many more

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