1. Towards a model independent PWA for pseudoscalar meson photoproduction
Lothar Tiator
NSTAR2011, Jefferson Lab, May 17-20, 2011 1

2. Towards a model independent PWA
Motivation
Polarization Observables - sign and frame issues short summary on theoretical issues of session B-I
Complete Experiments
Pseudo Data
Complete Amplitude Analysis
Complete Truncated Partial Wave Analysis 2

3. 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
The „new“ Complete Experiment aims directly on partial waves requires only 5 well selected observables 3

4. a model-independent pwa from complete experiments
our motivation
precise knowledge of meson photoproduction amplitudes is important for:
comparison with EFT, near threshold and near resonances
dispersion theoretical applications, as Compton scattering, 2g processes, various sum rules
baryon resonance analysis, besides pN the most important source
comparisons with quark models and lattice QCD, especially for N* physics
the best solution:
a model-independent pwa from complete experiments

5. studies on the complete experiment
earlier studies on the complete amplitude analysis
Barker, Donnachie, Storrow, Nucl. Phys. B95 (1975)
Fasano, Tabakin, Saghai, Phys. Rev. C46 (1992)
Keaton, Workman, Phys. Rev. C53 (1996)
Chiang, Tabakin, Phys. Rev. C55 (1997)
recent studies on PWA from complete experiments
Sandorfi, Hoblit, Kamano, Lee, J. Phys. G 38, (2011) [arXiv: [nucl-th]], parallel sess I-B-1&4
Dey, McCracken, Ireland, Meyer, [arXiv: [hep-ph]], parallel sess I-B-3
Workman, Paris, Briscoe, Tiator, Schumann, Ostrick, Kamalov, [arXiv: [nucl-th]], parallel sess I-B-4
Sarantsev, Anisovich, parallel sess I-B-2 5

6. model dependence in current PWA
compare 3 analyses from MAID/SAID/BOGA
for g,p : very similar in Watson region
large differences for W > 1700 MeV
for g,h : already large diff. near threshold
very large diff. for W > 1700 MeV
for g,K : already very large diff. near threshold
......

7. 4 helicity amplitudes

8. 4 helicity amplitudes

9. requirements for a complete experiment
set
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.

10. checking complete experiments
Mathematica can find exact solutions:

11. definitions from Barker, Donnachie, Storrow, 1975BT BR TR

12. coordinates and angles in the c.m. frame
linear photon polarization
in the x,y plane
reaction plane x,z or x´,z´
y,y‘ points towards you

13. definitions from Barker, Donnachie, Storrow, 1975BT BR TR

14. definitions from Fasano, Tabakin, Saghai, 1992
7 minus signs removed:
B. Dey et al.
and
A. Sarantsev et al.
use the same sign convention
a - sign
used here
by A. Sandorfi et al.

15. from Andy Sandorfi on the sign issues
obviously, different sign conventions are used by different groups

16. from Andy Sandorfi
table for conversion

17. same result from my own compilation:
now we have 2 options:
we go on as before and use these tables for translations
we try to find agreement on a common convention that everybody should use

18. frames used for recoil polarization

19. recoil polarization bases
also used by Dey et al.
for their
„longitudinal basis“
most common
„helicity basis“
however oriented
along the pion
don‘t miss the preprint
J.J. Kelly et al., Phys. Rev. C 75, (2007) and arXiv:nucl-ex/

20. recoil polarization bases
for a new convention, the better choices were 3 or 6

21. Coordinate Frames
There ought to be a law requiring ALL measurements be done in the cm frame!!!!!
Dick Arndt, July 2009

22. from Andrej Sarantsev, on the overall phase problem
even in the D region, no symmetry or theorem can tell us this phase f(W,q)

23. from Andrej Sarantsev, on the overall phase problem
this is the right way to go

24. partial wave expansion up to Lmax = 4
from Andrej Sarantsev
Lmax=3
Lmax=4

25. Summary 2 3-5 different sign conventions are being used
3-7 different coordinate frames can be found especially for recoil polarization in the lab frame
we have carefully compared those and can relate them in a unique way
now when experiments have started it would be the right time for an agreement among the different groups for a new convention before the data will be published
this is especially important for the experimental collaborations at JLab, Bonn and Mainz and for the people at GWU who run the world database 25

26. Complete Analysis
next I will demonstrate our analysis
from complete measurements with „pseudo data“
we have performed 2 kinds of analysis:
the amplitude analysis that leads to 4 amplitudes (but no partial waves)
the truncated partial wave analysis that leads
to 12 multipoles for Lmax=3

27. 2) truncated p.w. analysis up to ℓ=Lmax :
1) amplitude analysis:
4 complex amplitudes, e.g. F1, F2, F3, F4(W,q)
16 observables, ds/dW, S,... Tz´(W,q)
for each (W,q) we have 16 bilinear equations with 8 real parameters
at least 8 eq. = 8 obs. are needed for a unique solution up to 1 phase
e.g. with the following 8 obs: ds/dW,S,T,P,G,E,Ox´,Cx´ it works
but with the following 9 obs: ds/dW,S,T,P, G, E, F, H, Cx´ it doesn‘t
2) truncated p.w. analysis up to ℓ=Lmax :
4 Lmax complex multipoles E0+, E1+, M1+, M1-, E2+, E2-(W), ...
32 Lmax +8 measurable quantities A i k(W)
from 16 observables Oi(W,q) expanded in powers of cos q

28. already from the group S = { ds/dW, S, T, P }
we have almost enough information:
8 Lmax equations for 8 Lmax real numbers
but there remain discrete ambiguities, which can be resolved
with just one more observable, like F or G (but not E or H)
( Omelaenko, Sov. J. Nucl. Phys. 34, 406 (1981) )
so even with 5 observables we can get the complete information,
provided that the partial wave expansion converges !
g,p0 and g,h converge well
g,p converges well if p pole is treated explicitly
g,K should be similar, but problems may occur with large uncertainties in coupling constants of the pole terms and perhaps with high L t-channel Regge contributions

29. pseudo data
we have generated about 108 Monte-Carlo events with the MAID, SAID and BoGa models in steps of and angular bins of
we used:
beam pol.: PT=60% (linear polarization)
Pc=70% (circular polarization)
target pol.: P =80% (long. and trans., frozen spin butanol)
recoil pol.: A =20% (analyzing power, p-scatt on 12C)
the pseudo data have not yet been folded with a particular detector acceptance (will be our next step)

30. a sample of MAID pseudo data
for g,p0 at MeV and comparison with real data
MAID
pseudo data
real data

31. a sample of MAID pseudo data

32. 1. attempt MAID amplitude analysis with a
minimal complete set of 8 observables
MAID

33. 2. attempt
of 10 obs.
MAID

34. predicted target-recoil observables not simulated in the pseudo data
MAID

35. Chaos incomplete amplitude analysis
results for an incomplete set of 8 observables
with very high precision (numbers directly from MAID)
dσ/dΩ, Σ, T, P, G, H, E, F
Chaos

36. truncated partial wave analysis (TPWA)
second approach: truncated partial wave analysis TPWA
in practice all PWA are truncated to a certain Lmax
for g,p it means L = 0, ... Lmax being analyzed
L > Lmax taken from Born terms
we will use Lmax = 3 (SPDF waves)
-> 12 complex multipoles
-> 23 real fit parameters and 1 fixed phase
from experiment we get
24 numbers from each set S, BT
28 numbers from each set BR, TR
104 numbers in total from 16 observables
finally the overall phase can be obtained by the p-pole term for p+
and by a small model dependence for p0 (Grushin‘s method, 1988) 36

37. first in the Watson region at E = 340 MeV
ED and SE fits are indistinguishable
also BT and TR obs are described very well
single energy fit to 4 obs dσ/dΩ, Σ, T, P
Maid
pseudo data
p(g,p0)p

38. beam-target double pol. obs. at E = 340 MeV
energy dependent fit to 4 obs
predictions
single energy fit to 4 obs
E(q)
F(q)
Maid
pseudo data
p(g,p0)p
G(q)
H(q)

39. Ox´ double pol. obs. at E = 600 MeV
dσ/dΩ, P, Σ, T = 4
p(g,p0)p
Prediction compared to a fit of double-polarization observable
+ E, F, G, H = 8
+ Ox , Oz , Cx , Cz = 12

40. Multipole: predicted vs input E0+

41. Multipole: predicted vs input M1-

42. Summary 3 all of this work is still in progress
From a complete experiment of pion photoproduction with pseudo data we have obtained a good truely model independent amplitude analysis with 10 observables but these amplitudes do not give us the desired partial waves because of the missing overall phase f(E,q)
Therefore we have done a truncated partial wave analysis directly from the data and got very good results with only 6-8 observables from only 2 sets of polarization observables (S + BT)
in a truncated partial wave analysis presented by they were plagued with multiple minima
and only with 16 observables and good precision they obtained satisfactory results (also in pseudo data simulations)
Sam Hoblit on KL
all of this work is still in progress 45