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Multichannel Partial-Wave Analysis of Scattering

Multichannel Partial-Wave Analysis of Scattering. Hongyu Zhang Tallahassee, FL October 12, 2005. Outline. Introduction Database Formalism for Partial-Wave Analysis Fitting Procedures Results of Single-Energy Partial-Wave Analysis Summary. Introduction.

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Multichannel Partial-Wave Analysis of Scattering

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  1. Multichannel Partial-Wave Analysisof Scattering Hongyu Zhang Tallahassee, FL October 12, 2005

  2. Outline • Introduction • Database • Formalism for Partial-Wave Analysis • Fitting Procedures • Results of Single-Energy Partial-Wave Analysis • Summary

  3. Introduction • Since 1998, the Crystal Ball Collaboration at the BNL AGS has measured precise new data for several important reactions. These data have motivated a new partial-wave analysis (PWA) that is the subject of this research. • Ultimate goal is to obtain more reliable information about properties of Λ* and Σ* resonances. • This can be done by improvements in the experimental database and/or by improved partial-wave analysis techniques. Goal

  4. Introduction • Our current knowledge of strangeness -1 hyperons is derived almost entirely from energy-dependent PWAs of scattering data. • Energy-dependent PWAs assume a simple parametrization for the partial-wave amplitudes, which introduces a model-dependent bias and often results in a violation of unitarity of the S-matrix. • One objective of our work is to reduce this bias as much as possible by carrying out a constrained energy-independent partial-wave analysis. Partial-Wave Analyses

  5. Database • Nuclear Physics B 6 (1968) 273-324 8 (1968) 233-264 20 (1970) 476-492 21 (1970) 15-76, 515-527 24 (1970) 417-440 29 (1971) 413-430 34 (1971) 41-70 67 (1973) 125-156 85 (1975) 289-310 90 (1975) 349-383 93 (1975) 189-216 96 (1975) 54-66 105 (1976) 189-221 • Physical Review D 12 (1975) No. 1, 6-14 14 (1976) No. 1, 13-27 17 (1978) No. 9, 2226-2240 • Numerical Data and Functional Relationships in Science and Technology Group I: Nuclear and Particle Physics, Vol. 12, Subvolume a • Crystal Ball Collaboration (Private Communication) Journals

  6. Database Momentum Range and Statistics

  7. Formalism for Partial-Wave Analyses • Unitarity Relations • Previous Partial-Wave Analyses

  8. Formalism for Partial-Wave Analyses Types of Unitarity Violation Observed: Unitarity Violation in Prior PWAs

  9. Fitting Procedures • Analysis Method • Unitarization of selected “best” published amplitudes • Constrained single-energy fits of world data for:

  10. Fitting Procedures • Constraints • Small amplitudes (|T|<0.05) held fixed using unitarized solution • Selected data bins of typically 30 MeV width • Parameterize each amplitude in bin by: T(E)≈T(E0)+T’(E0)(E-E0) where E is the CM energy of the data point in bin, E0 is the center energy in bin, T(E0) is the complex T-matrix amplitude at CM energy E0, T’(E0) is the “slope parameter” which is fixed at value from unitarized solution

  11. Results of Single-Energy Partial-Wave Analysis

  12. Results of Single-Energy Partial-Wave Analysis

  13. Results of Single-Energy Partial-Wave Analysis

  14. Results of Single-Energy Partial-Wave Analysis

  15. Results of Single-Energy Partial-Wave Analysis

  16. Summary What has been done: • The available world database of dσ/dΩ, total cross sections, and polarization up to ~2 GeV, has been compiled, involving the reactions • Initialized with a set of unitarized partial-wave amplitudes, after obtaining a reasonably smooth set of single-energy solutions for the amplitudes, an energy-dependent fit was carried out to ensure that the final results are consistent with unitarity. What remains to be done: • Perform a unitarized fit based on our single-energy results • Extract resonance parameters in a consistent manner for all channels

  17. Acknowledgments • D. Mark Manley, John Tulpan from Kent State University • Crystal Ball Collaboration • U. S. Department of Energy, grant DE-FG02-01ER41194

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