1. Baryon Resonances ( N*,   ), MAID and Complete Experiments Lothar Tiator Johannes Gutenberg Universität Mainz Mini-Workshop on Hadronic Resonances, Bled, Slovenia, 2012 CRC 1044

2. references Unitary isobar model MAID2007 D. Drechsel, S. Kamalov, L. Tiator Eur. Phys. J. A 34 (2007) 69-97 Towards a model-independent partial wave analysis for pseudoscalar meson photoproduction L. Tiator AIP Conf. Proc. 1432 (2012) 162-167 Model dependence of single-energy fits to pion photoproduction data R. Workman, M. Paris, W. Briscoe, L. Tiator, S. Schumann, M. Ostrick, S. Kamalov Eur. Phys. J. A 47 (2011) 143-154 Electromagnetic excitation of nucleon resonances L. Tiator, D. Drechsel, S. Kamalov, M. Vanderhaeghen Eur. Phys. J. ST 198 (2011) 141-170 Singularity structure of the πN scattering amplitude in a meson-exchange model up to energies W<2GeV L. Tiator, S. Kamalov, S. Ceci, G.Y. Chen, D. Drechsel, A. Svarc, S.N. Yang Phys. Rev. C 82 (2010) 055203-14

3. - how to detect N*/  resonances ? - how to measure quantum numbers of N*/  ? - how to measure mass and width of N*/  ? - how to measure branching ratios ? - how to obtain pole postions and residues ? baryon spectroscopy

4. theoretical poles and experimental bumps poles in the complex plane bumps on the physical axis W W

5. E. Klempt, ATHOS2012, Camogli, Italy: N* and  states, new in PDG2012 new

6. 80s Birthday of Peter Higgs at University of Edinburgh during the week of the Narrow Nucleon Resonances Workshop Edinburgh, June 10, 2009

7. nucleon response to real and virtual photons

8. detailed look on nucleon resonances photoabsorption (inclusive cross section)

9. regime of dynamical models and ChPT regime of quark models and LQCD

10. DMT HDT MAID ChPT SAID theoretical approaches to pion photoproduction BnGa GICC GICC

11. SAID

12. Isobar models and Dynamical models MAID DMT (Dubna-Mainz-Taipei) (Dubna-Mainz-Taipei) biggest difference for background terms (e.g. near threshold) : isobar models: only Born plus phenomenological terms dynamical models: include additional  loop terms similar to  PT

13. isobar models vs dynamical models (DMT) (MAID)

15. M A I DM A I DM A I DM A I D

16. s-channel resonance contributions unitarity is build in through coupling to other open channels: e.g. for S 11 (1535)

17. unitarity cusp at eta threshold unpolarized total cross section polarized total cross section (helicity asymmetry) helicity separated cross sections J. Ahrens et al., (GDH and A-2 Collaboration), Phys. Rev. C 74, 045204 (2006)

18. comparison between MAID and SAID

19. Roper P 11 (1710)

20. from this comparison between MAID and SAID one may conclude: this must be right!!!

21. 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 CNS-DAC @ GWU strong model dependence in the pw amplitudes due to an incomplete data base: mainly d  /d  and , some T, P, very few G, H

22. currently in CNS-DAC data base for  p    p for W< 2 GeV: d  d  9382 G28 Ox‘7 Tx‘0  1885 H24 Oz‘7 Tz‘0 T 353 E 0 Cx‘0 Lx‘0 P 556 F 0 Cz‘0 Lz'0 mainly only d  /d  and  which count !

23. comparison of multipoles: MAID – SAID - BonnGatchina from Anisovich et al., Eur. Phys. J. A. 44, 203-220 (2010) real parts of   multipoles imaginary parts of   multipoles

24. comparison of multipoles: MAID – SAID - BonnGatchina from Anisovich et al., Eur. Phys. J. A. 44, 203-220  no problems for   Re surprisingly large differences, even though the world data is equally well described real parts of   multipoles

25. newly measured observables will produce changes here example with preliminary target polarization data from Mainz: at Mainz and Bonn we will soon get good data for: d  d  with single (beam/target) polarization and P, E, F, G, H  with double (beam-target) polarization

26. MAID, SAID, BnGa and new fits ( ) with extra T and F data (MAMI, preliminary) changes with newly maesured polarization observables MAID SAID BnGa     in our analysis we see large changes in E0+, E2- and M1-

27. with each newly measured polarization observables we can hope to improve the partial wave analyses the complete experiment there is a systematic way to go: the complete experiment The Complete Experiment

28. a complete experiment is a set of polarization observables that is sufficient to exactly determine all other possible experiments allamplitudes up to 1 phase and all underlying (complex) amplitudes up to 1 phase it does not give us a guarantee to completely determine the baryon resonance spectrum but it certainly will improve it a lot! what is a complete experiment?

29. in pion alpha elastic scattering: 1 complex amplitude (E,  ) 1 observable is possible in pion nucleon elastic scattering: 2 complex amplitudes (E,  ) 4 observables are possible 4 are needed for a complete experiment 0 can be predicted in pion photoproduction: 4 complex amplitudes (E,  ) 16observables are possible 8are needed (at least) for a complete experiment 8can be predicted in pion electroproduction: 6 complex amplitudes (E,  ) 36observables are possible 12 are needed (at least) for a complete experiment 24 can be predicted complete experiments in different reactions

30. complete experiments for systems with 1, 2 and 4 spin degrees of freedom

31. 1.)

32. 2.) common choice

33. 3.) common choice 16 observables analytical solutions with less than 9 obs. are not known

34. 16 observables expressed in helicity amplitudes

36. 16 Polarization Observables in Pion Photoproduction

37. 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 earlier studies on the complete amplitude analysis recent studies on PWA from complete experiments Workman, Paris, Briscoe, Tiator, Schumann, Ostrick, Kamalov, Eur. Phys. J. A 47 (2011) 143 Sandorfi, Hoblit, Kamano, Lee, J. Phys. G 38 (2011) 053001 Dey, McCracken, Ireland, Meyer, Phys. Rev. C 83 (2011) 055208 Sarantsev, Anisovich, private comm. (2011), unpublished

38. 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): (9 observables needed) „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): (8 observables needed) a carefully chosen set of 8 observables is sufficient. requirements for a complete experiment in photoproduction

39. setobservables single S d  d  TP beam- target BT GHEF beam- recoil BR Ox´Oz´Cx´Cz´ target -recoil TR Tx´Tz´Lx´Lz´ choose any 8 out of 16 observables this set does not work!

40. setobservables single S d  d  TP beam- target BT GHEF beam- recoil BR Ox´Oz´Cx´Cz´ target -recoil TR Tx´Tz´Lx´Lz´ choose any 8 out of 16 observables also this set does not work!

41. setobservables single S d  /d  TP beam- target BT GHEF beam- recoil BR Ox´Oz´Cx´Cz´ target -recoil TR Tx´Tz´Lx´Lz´ choose any 8 out of 16 observables also this set does not work!

42. setobservables single S d  /d  TP beam- target BT GHEF beam- recoil BR Ox´Oz´Cx´Cz´ target -recoil TR Tx´Tz´Lx´Lz´ choose any 8 out of 16 observables this set works!

43. setobservables single S d  /d  TP beam- target BT GHEF beam- recoil BR Ox´Oz´Cx´Cz´ target -recoil TR Tx´Tz´Lx´Lz´ choose any 8 out of 16 observables also this set works!

44. most extensive study by Chiang, Tabakin, Phys. Rev. C55 (1997) 2054-2066

45. 1 of 6 tables to find a complete set of 8 observables

46. checking complete experiments with a trick  Mathematica can at least check exact solutions: Mathematica cannot find the exact analytical solution with 4 amplitudes, but it can find exact solutions for integer-valued amplitudes

47. pseudo data we have generated about 10 8 Monte-Carlo events with the MAID, SAID and BnGa models in steps of and angular bins of we used: beam pol.: P T =60% (linear polarization) P c =70% (circular polarization) target pol.: P =80% (long. and trans., frozen spin butanol) recoil pol.: A =20% (analyzing power, p-scatt on 12 C)

48. a sample of MAID pseudo data based on 10 8 Monte-Carlo events for   at 320-340 MeV and comparison with real data MAID pseudo data real data

49. incomplete amplitude analysis with 8 observables incomplete results for an incomplete set of 8 observables with high precision (numbers directly from MAID) dσ/dΩ, Σ, T, P, G, H, E, F Chaos W=1217 MeV p(   )p

50. complete amplitude analysis with 8 observables complete results for a complete set of 8 observables with high precision (numbers directly from MAID) dσ/dΩ, Σ, T, P, G, E, Ox, Cx W=1217 MeV p(   )p perfect solution

51. complete amplitude analysis with 8 observables complete results for a complete set of 8 observables with MAID pseudo data of realistic statistics dσ/dΩ, Σ, T, P, G, E, Ox, Cx MAID

52. overcomplete amplitude analysis with 10 observables overcomplete results for an overcomplete set of 10 observables with MAID pseudo data of realistic statistics dσ/dΩ, Σ, T, P, G, H, E, F, Ox, Cx MAID

53. problem with the overall phase in this kind of analysis we are left with an unknown overall phase which cannot be determined from this experiment, and we also cannot calculate it e.g. by unitarity therefore we cannot calculate partial wave amplitudes: in principle a determination of the overall phase were possible, but impractical: - Goldberger (1963) : Hanbury-Brown-Twiss experiment as in radio astronomy - Ivanov (2012) :Vortex beams (twisted photons) as in optics and atomic physics

54. Complete Analysis we must distinguish between 2 kinds of complete analyses: 1)the amplitude analysis that leads to 4 amplitudes: F i (W,  ) (but no partial waves) 2)the truncated partial wave analysis that leads for Lmax = 1 to 4 multipoles: M i (W) i.e. E 0+, E 1+, M 1+, M 1- for Lmax = 2 to 8 multipoles for Lmax = 3 to 12 multipoles and angle function of energy and angle function of energy only

55. for this second kind of analysis we have much more than 16 observables: each of the 16 spin observables can be expanded in a cos(  ) or Legendre series for energy-angle separation: e.g.: complete analysis of 2. kind

56. groupobservables single S d  /d  TP beam- target BT GHEF beam- recoil BR Ox´Oz´Cx´Cz´ target -recoil TR Tx´Tz´Lx´Lz´ Omelaenko (1981) for a truncated partial wave analysis with L max 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  (1232) region with only S+P waves ( L max = 1  requirements for the 2. kind of a complete experiment

57. groupobservables single S d  /d  TP beam- target BT GHEF beam- recoil BR Ox´Oz´Cx´Cz´ target -recoil TR Tx´Tz´Lx´Lz´ Omelaenko (1981) for a truncated partial wave analysis with L max 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  (1232) region with only S+P waves ( L max = 1  one possible solution for the 2. kind is:

58. results of a truncated partial wave analysis with Lmax=3 of the MAID pseudo data performed in collaboration with SAID group

59. S 11 ( E 0+ ) multipole: predicted vs. input

60. P 11 ( M 1- ) multipole: predicted vs. input

61. Summary and Conclusion 8 well selected observables The Complete Experiment of 1. kind 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  W  5 well selected observables The Complete Experiment of 2. kind aims directly on partial waves and requires only 5 well selected observables these can be: d , , T, P, F or: d , , T, F, G or: d , , O x‘, O z‘, C z‘ and others The real challenge will come with real world data suffering from: exp. uncertainties limited detector acceptances