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Model-independent partial-wave analysis for pion photoproduction

Model-independent partial-wave analysis for pion photoproduction. Lothar Tiator. Motivation Complete Experiments Pseudo Data from Monte-Carlo events Complete Amplitude Analysis Complete Truncated P artial W ave A nalysis Summary and Conclusion. in collaboration with.

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Model-independent partial-wave analysis for pion photoproduction

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  1. Model-independent partial-wave analysisfor 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

  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 S11 SAID, Arndt et al. 2006 Dubna-Mainz-Taipei, Chen et al. 2007 Regensburg, Bonn, Bruns et al. 2010

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

  6. studies on the complete experiment earlier studies on the complete amplitude analysis • 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 recent studies on PWA from complete experiments • 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

  7. What is a complete experiment? a set of polarization observables which allow usto exactly predict all other possible experiments (if experimental errors are neglected) in pion nucleon scattering:4 observables are possible4 are needed for a complete experiment 0 can be predicted in pion photoproduction:16 observables are possible8 are needed (at least) for a complete experiment 8 can be predicted in pion electroproduction:36 observables are possible12 are needed (at least) for a complete experiment 24 can be predicted

  8. spin amplitudes vs. partial wave amplitudes

  9. requirements for a complete experiment in photoproduction 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. definitions from Barker, Donnachie, Storrow, 1975 • BT: polarized photons and polarized target • BR: polarized photons and recoil polarization • TR: polarized target and recoil polarization

  11. 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.

  12. comparison between different groups • now we have 2 options: • we go on as before and use these tablesfor translations • we try to findagreement on a common conventionthat everybodyshould use

  13. 16 Polarization Observables in Pion Photoproduction

  14. 16 Polarization Observables in Pion Photoproduction • for g,p and g,h one can only measure the transverse • recoil polarization in the lab frame • and transformation into the cm frame is not possible • for g,K one gets it for free from the weak hyperon decays

  15. frames used for recoil polarization

  16. „classical“ 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, 025201 (2007) and arXiv:nucl-ex/0509004

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

  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 108 Monte-Carlo events with the MAID, SAID and BoGa models in steps ofand angular bins of • we assume: • 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, rescattering on 12C) • the pseudo data have not yet been folded with a particulardetector acceptance (will be our next step)

  20. a sample of MAID pseudo data for g,p0 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. predictive power of the complete experiment predicted target-recoil observables not simulated in the pseudo data of 10 obs. MAID

  24. 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)

  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 Lmax forg,p it means L = 0, ... Lmax being analyzed L > Lmaxtaken from Born terms

  28. amplitude analysis vs. TPWA 1) amplitude analysis: 4 complex amplitudes, e.g. F1, F2, F3, F4(W,q) 16 observables, ds/dW, S,... Tz´(W,q) 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 Aik(W) from 16 observables Oi(W,q) expanded in powers of cosq

  29. second approach: truncated partial wave analysis TPWA truncated partial wave analysis (TPWA) in practice all PWA are truncated to a certain Lmax forg,p it means L = 0, ... Lmax being analyzed L > Lmaxtaken 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 with a small model dependence for p0 (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 DE = 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 solutionalternatively we can acquire or develop new search algorithms, that can deal with multiple c2 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 single energy fit to 4 obs dσ/dΩ, Σ, T, P Maid pseudo data p(g,p0)p

  32. 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)

  33. Ox´ double pol. obs. at E = 600 MeV + E, F, G, H = 8 + Ox , Oz , Cx , Cz = 12 dσ/dΩ, P, Σ, T = 4 p(g,p0)p Prediction compared to a fit of double-polarization observable 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 g + N -> p + Nfrom 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 • 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 f(E,q) • Therefore we do a truncated partial wave analysis directly from the data

  37. Conclusions • in the Watson region, W < 1.3 GeV only S and P waves must be analyzedhigher pw L > 1 can be taken from Born termsall unitary phases are fixed to pN by Watson‘s theoremsuch an analysis requires only 2 observables ds/dWand S(q)(R. Beck@MAMI 1997) • 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 • this looks very encouraging for an unconstrained model independent PWAwith real experimental data - coming soon

  38. PWA Workshop, Trento, June 2009

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