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

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Presentation transcript:

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? ● 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?

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

Pole vs BW widths very different for S 11 and P 11 | R π | different from current values

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

SAID model for pion photoproduction ( 1990 ) T ππ gives phase (Watson’s Thm) Phase determined by T ππ (smooth connection to Watson’s Thm)

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

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

Dominant pieces for E2 and M1

A 1/2, A 3/2 for Δ(1232) at the pole

Some comparative results for A 1/2, A 3/2 Breit-Wigner values extracted using a form similar to MAID Agreement with pole values is reasonable even for cases with R π = Γ π / 2 being a poor approximation

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

Kamano et al., Dyn CC model Large differences

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

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

Laurent Padé Pietarinen (Pere Masjuan) (A. Svarc)

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

Z0Z0 ZCZC Zagreb-Tuzla form Z Compare to:

F 15 SAID πN SP06 ( A. Svarc )

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

Other material

πNπN For next speaker: 2 fits with 1 or 2 D 13 states

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