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From (photo) data to poles

From (photo) data to poles. Ron Workman Data Analysis Center Institute for Nuclear Studies George Washington University. Baryons 2013 University of Glasgow. Some thoughts on N* photo-couplings. ● How do Breit -Wigner and pole photo-couplings compare?

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From (photo) data to poles

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  1. From (photo) data to poles Ron Workman Data Analysis Center Institute for Nuclear Studies George Washington University Baryons 2013 University of Glasgow

  2. Some thoughts on N* photo-couplings ● How do Breit-Wigner and pole photo-couplings compare? ● E2/M1 values are clearly different ● Some old pole values (VT) differ from more recent Bonn-Gatchina values. ● Is the similarity of Bonn-Gatchina pole/BW results dependent on model details?

  3. A.V. Anisovich et al., EPJ A48 (2012) 15 Pole and Breit-Wigner values similar apart from a phase

  4. Pole vs BW widths very different for S11 and P11 | Rπ | different from current values

  5. Photo-decay amplitudes from multipoles Quantities (real) evaluated at BW resonance energy Quantities (complex) evaluated at pole position C: isospin factor

  6. SAID model for pion photoproduction ( 1990 ) Tππgives phase (Watson’s Thm) Phase determined by Tππ (smooth connection to Watson’s Thm)

  7. Simple case: Δ(1232) 3/2+ 0.054 phase: -115o BG: ~ 0.052 phase: -125o

  8. Pole vs BW contributions for Δ(1232) Largest contribution: E2 (pole) RLW, R.A. Arndt, PRC 59, 1810 (1999) 0 ~ linear Largest contribution: M1 (pole) Term → 0for W = 1232 MeV ( no contribution to BW + background approach ) Don’t expect approaches to be similar for E2/M1

  9. Dominant pieces for E2 and M1

  10. A1/2 , A3/2 for Δ(1232) at the pole

  11. Some comparative results for A1/2 , A3/2 Breit-Wigner values extracted using a form similar to MAID Agreement with pole values is reasonable even for cases with Rπ = Γπ / 2 being a poor approximation

  12. Some other background forms plus Crawford/Morton ‘83 Berends/Donnachie ‘78 Arai/Fujii ‘82 Resonance Background

  13. Kamanoet al., Dyn CC model Large differences

  14. Kamanoet al., arXiv 1305.4351 ( May 2013) Program is ambitious Difficult to determine source of differences in photo-couplings: Fit quality vs DCC

  15. Obtaining the residues ● analytic continuation / contour integrals ● speed plots ● Padé approx ● regularization method ● ‘Pietarinen expansion’ Zagreb/Tuzla BW: technically simple – but model dependent Pole: model independent – but new technical issues may arise

  16. Laurent Padé (PereMasjuan) Pietarinen (A. Svarc)

  17. Cut plane f b c a e See, for example, H. Burkhardt Dispersion Relation Dynamics, Ch. A9 Z Unit circle e a c μ b f

  18. Zagreb-Tuzla form Z0 ZC Z Compare to:

  19. F15 SAID πN SP06 ( A. Svarc )

  20. Interesting results when applied to SES, with no analytic form available to determine poles ( A. Svarc ) Application to multipoles is being studied

  21. Other material

  22. For next speaker: 2 fits with 1 or 2 D13 states πN

  23. Characteristic forward peaking in charged-pion photoproduction Feature is absent in this plot from arXiv: 1305.4351v1

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