From (photo) data to polesRon Workman

Data Analysis CenterInstitute for Nuclear Studies

George Washington University

Baryons 2013University 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 andBreit-Wignervalues similarapart from aphase

Pole vs BW widthsvery different forS11 and P11

| Rπ | differentfrom current values

Quantities (real) evaluated at BW resonance energy

Quantities (complex) evaluatedat pole position

Photo-decay amplitudes from multipoles

C: isospin factor

SAID model for pion photoproduction ( 1990 )

Tππ gives phase (Watson’s Thm)

Phase determined by Tππ (smooth connection to Watson’s Thm)

0.054 phase: -115o

Simple case: Δ(1232) 3/2+

BG: ~ 0.052 phase: -125o

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

A1/2 , A3/2 for Δ(1232) at the pole

Some comparative results for A1/2 , A3/2

Breit-Wigner values extracted usinga form similar to MAID

Agreement with pole valuesis reasonable even for caseswith Rπ = Γπ / 2 being a poor approximation

plus

Some other background forms

Crawford/Morton ‘83Berends/Donnachie ‘78

Resonance Background

Arai/Fujii ‘82

Kamano et al., Dyn CC model

Large differences

Kamano et al., arXiv 1305.4351( May 2013)

Program is ambitious

Difficult to determinesource of differences inphoto-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 dependentPole: model independent – but new technical issues may arise

Laurent

Padé

Pietarinen

(Pere Masjuan)

(A. Svarc)

f b c ea

ae

c

f

Cut plane

Unit circle

See, for example,H. BurkhardtDispersion RelationDynamics, Ch. A9

Z

μb

Z0 ZC

Zagreb-Tuzla form

Z

Compare to:

F15

SAIDπNSP06

( A. Svarc )

Interesting results when applied to SES, with no analytic form available to determine poles

( A. Svarc )

Application tomultipoles isbeing studied

Other material

πN

For next speaker:2 fits with 1 or 2 D13 states

Characteristic forward peakingin charged-pion photoproduction

Feature is absent in this plot fromarXiv: 1305.4351v1