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

2. basic questions from our conveners:
What are the the common grounds and differences between contemporary approaches like MAID, SAID, BnGa, Jülich, EBAC, Giessen ? common grounds: Born terms, vector meson exchanges, D(1232), Watson’s theorem differences: 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 today b) 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 waves in a similar way as we have mostly done it for pN scattering in the last 30 years.
How to combine the knowledge from two body coupled channels approaches and various production processes ? Coupled channels approaches will profit enormously, when they will get model-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+ -> p g
most recent entries: A1/2 (10-3 GeV-1/2 )
Anisovich A BnGa
Dugger JLab
Arndt SAID
Drechsel MAID -61
Penner D 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. But a 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 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. mainly only ds/dW and S which count !
currently in CNS-DAC data base for g + p -> p0 + p for W< 2 GeV:
ds/dW G Ox‘ 7 Tx‘ 0
S H Oz‘ 7 Tz‘ 0
T E Cx‘ 0 Lx‘ 0
P F Cz‘ 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, (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 to 4 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 group
observables
single S
ds/dW T P
beam-target BT G H E F
beam-recoil BR
Ox´
Oz´
Cx´
Cz´
target-recoil TR
Tx´
Tz´
Lx´
Lz´
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: group observables
single S
ds/dW T P
beam-target BT G H E F
beam-recoil BR
Ox´
Oz´
Cx´
Cz´
target-recoil TR
Tx´
Tz´
Lx´
Lz´
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 group
observables
single S
ds/dW T P
beam-target BT G H E F
beam-recoil BR
Ox´
Oz´
Cx´
Cz´
target-recoil TR
Tx´
Tz´
Lx´
Lz´
Omelaenko (1981)
for a truncated partial wave analysis with Lmax waves only 5 observables are necessary, e.g. the 4 from group S and 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: group observables
single S
ds/dW T P
beam-target BT G H E F
beam-recoil BR
Ox´
Oz´
Cx´
Cz´
target-recoil TR
Tx´
Tz´
Lx´
Lz´
Omelaenko (1981)
for a truncated partial wave analysis with Lmax waves only 5 observables are necessary, e.g. the 4 from group S and 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 MeV and comparison with real data
MAID
pseudo data
real data 16

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 waves due 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 observables these can be: ds, S, T, P, F or: ds, S, T, F, G or: ds, S, Ox‘, Oz‘, Cz‘ or many more 19