1. Model-independent partial-wave analysis for pion photoproduction Lothar Tiator

2. Motivation Complete Experiments Pseudo Data from Monte-Carlo events Complete Amplitude Analysis Complete Truncated Partial Wave Analysis Summary and Conclusion Motivation Complete Experiments Pseudo Data from Monte-Carlo events Complete Amplitude Analysis Complete Truncated Partial Wave Analysis Summary and Conclusion

3. in collaboration with Michael Ostrick and Sven Schumann Institut für Kernphysik, Johannes Gutenberg Universität Mainz, Germany Sabit Kamalov Bogoliubov Laboratory for Theoretical Physics, JINR Dubna, Russia Ron Workman and Mark Paris Center for Nuclear Studies, Department of Physics, GWU Washington, DC, USA arXiv:1102.4897

4. 3 recent partial wave analyses for S 11 SAID, Arndt et al. 2006 Dubna-Mainz-Taipei, Chen et al. 2007 Regensburg, Bonn, Bruns et al. 2010 1. resonance: S 11 (1535) Re Wp-2 Im Wp|res|  [°] Said 15029516-16 DMT 14997814-45 Bruns 1506280 2. resonance: S 11 (1650) Re Wp-2 Im Wp|res|  [°] Said 16488014-69 DMT 163112035-83 Bruns 169292

5. how can this be improved ? more precise piN data not possible in near future coupled channels analysesnecessary, but database still very limited J/  decays very helpful if statistics can be improved high-precision analyses of  and  photoproduction currently at Mainz, Bonn and JLab: „complete experiments“ are in preparation for  using linearly and circularly polarized photon beams longitudinal and transverse polarized targets measuring recoil polarization of outgoing nucleon

6. studies on the complete experiment Barker, Donnachie, Storrow, Nucl. Phys. B95 (1975) 347-356 Fasano, Tabakin, Saghai, Phys. Rev. C46 (1992) 2430-2455 Keaton, Workman, Phys. Rev. C53 (1996) 1434-1435 Chiang, Tabakin, Phys. Rev. C55 (1997) 2054-2066 Sandorfi, Hoblit, Kamano, Lee, J. Phys. G 38, 053001 (2011) [arXiv:1010.4555 [nucl-th]] Dey, McCracken, Ireland, Meyer, [arXiv:1010.4978 [hep-ph]] Workman, Paris, Briscoe, Tiator, Schumann, Ostrick, Kamalov, [arXiv:1102.4897 [nucl-th]] Sarantsev, Anisovich earlier studies on the complete amplitude analysis recent studies on PWA from complete experiments

7. What is a complete experiment? a set of polarization observables which allow us to exactly predict all other possible experiments (if experimental errors are neglected) in pion nucleon scattering: 4 observables are possible 4 are needed for a complete experiment 0 can be predicted in pion photoproduction: 16observables are possible 8are needed (at least) for a complete experiment 8can be predicted in pion electroproduction: 36observables are possible 12 are needed (at least) for a complete experiment 24 can be predicted

8. spin amplitudes vs. partial wave amplitudes

9. setobservables single S d  /d  TP beam- target BTGHEF beam- recoil BROx´Oz´Cx´Cz´ target -recoil TRTx´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. requirements for a complete experiment in photoproduction

10. definitions from Barker, Donnachie, Storrow, 1975 BT: polarized photons and polarized target BT: polarized photons and polarized target BR: polarized photons and recoil polarization BR: polarized photons and recoil polarization TR: polarized target and recoil polarization TR: polarized target and recoil polarization

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

12. comparison between different groups now we have 2 options: 1)we go on as before and use these tables for translations 2)we try to find agreement on a common convention that everybody should use

13. 16 Polarization Observables in Pion Photoproduction

14. for  and  one can only measure the transverse recoil polarization in the lab frame and transformation into the cm frame is not possible for  one gets it for free from the weak hyperon decays

15. frames used for recoil polarization

16. J.J. Kelly et al., Phys. Rev. C 75, 025201 (2007) and arXiv:nucl-ex/0509004 also used by Dey et al. for their „longitudinal basis“ most common „helicity basis“ however oriented along the pion don‘t miss the preprint „classical“ recoil polarization bases

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

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

19. pseudo data we have generated about 10 8 Monte-Carlo events with the MAID, SAID and BoGa models in steps of and angular bins of we assume: beam pol.: P   (linear polarization) P c  (circular polarization) target pol.: P  (long. and trans., frozen spin butanol) recoil pol.:  (analyzing power, rescattering on 12 C) the pseudo data have not yet been folded with a particular detector acceptance (will be our next step)

20. a sample of MAID pseudo data for   at 320-340 MeV and comparison with real data MAID pseudo data real data

21. amplitude analysis with a minimal complete set of 8 observables MAID

22. of 10 obs. MAID

23. predicted target-recoil observables not simulated in the pseudo data MAID of 10 obs. predictive power of the complete experiment

24. from Andrej Sarantsev, on the overall phase problem even in the  region, no symmetry or theorem can tell us this phase  W 

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

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

27. second approach: truncated partial wave analysis TPWA truncated partial wave analysis (TPWA) in practice all PWA are truncated to a certain L max for   it means L = 0,... L max being analyzed L > L max taken from Born terms

28. 1) amplitude analysis: 4 complex amplitudes, e.g. F 1, F 2, F 3, F 4 (W,  ) 16 observables, d  /d , ,... T z´ (W,  ) 2) truncated p.w. analysis up to ℓ=L max : 4 L max complex multipoles E 0+, E 1+, M 1+, M 1 , E 2+, E 2  (W),... 32 L max +8 measurable quantities A i k (W) from 16 observables O i (W,  ) expanded in powers of cos  amplitude analysis vs. TPWA

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

30. constrained fits beyond the Watson region step 1:energy dependent (ED) fit to all available observables for a large energy range using the SAID ansatz (we use 4/8/12 obs. S,BT,BR for 160MeV < E < 1.5GeV) provides an energy dependent phase for each multipole step 2:energy independent or single-energy (SE) fits to data typically in intervals of  E  10MeV with determination of all moduli of all multipoles with fixed phases from ED fits step 3: finally we can relax some critical phases and search for an unconstrained solution alternatively we can acquire or develop new search algorithms, that can deal with multiple   minima step 1:energy dependent (ED) fit to all available observables for a large energy range using the SAID ansatz (we use 4/8/12 obs. S,BT,BR for 160MeV < E < 1.5GeV) provides an energy dependent phase for each multipole step 2:energy independent or single-energy (SE) fits to data typically in intervals of  E  10MeV with determination of all moduli of all multipoles with fixed phases from ED fits step 3: finally we can relax some critical phases and search for an unconstrained solution alternatively we can acquire or develop new search algorithms, that can deal with multiple   minima

31. first in the Watson region at E = 340 MeV ED and SE fits are indistinguishable also BT and TR obs are described very well Maid pseudo data Maid pseudo data single energy fit to 4 obs dσ/dΩ, Σ, T, P p    p

32. beam-target double pol. obs. at E = 340 MeV Maid pseudo data Maid pseudo data energy dependent fit to 4 obs single energy fit to 4 obs  F  G  p    p predictions

33. Prediction compared to a fit of double-polarization observable dσ/dΩ, P, Σ, T = 4 + E, F, G, H = 8+ O x, O z, C x, C z = 12 Ox´ double pol. obs. at E = 600 MeV p    p 6-8 observables are enough

34. Multipole: predicted vs input E0+ (S11)

35. Multipole: predicted vs input M1- (P11)

36. Summary   We have studied the possibilities to obtain a model independent PWA for   from a Complete Experiment, which requires at least 8 different polarization observables, using beam, target and recoil polarization Such experiments are currently starting at Mainz, Bonn and JLab. We used pseudo data from Monte-Carlo event simulations using MAID a true model independent amplitude analysis From this experiment we can get a true model independent amplitude analysis but these amplitudes do not give us the desired partial waves because of the missing overall phase  Therefore we do a truncated partial wave analysis directly from the data

37. Conclusions 1.in the Watson region, W 1 can be taken from Born terms all unitary phases are fixed to  N by Watson‘s theorem such an analysis requires only 2 observables d  d   and  (R. Beck@MAMI 1997) 2.above the Watson region 1.3 GeV < W < 1.8 GeV, S,P,D and F waves needed, (+ G waves for W = 2 GeV) with an overcomplete set of 12 observables everything works very well, already with sets of 6-8 observables without recoil polarization we get very good results 3.this looks very encouraging for an unconstrained model independent PWA with real experimental data - coming soon

38. PWA Workshop, Trento, June 2009