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

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

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

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

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]], parallel sess I-B-1&4 Dey, McCracken, Ireland, Meyer, [arXiv:1010.4978 [hep-ph]], parallel sess I-B-3 Workman, Paris, Briscoe, Tiator, Schumann, Ostrick, Kamalov, [arXiv:1102.4897 [nucl-th]], parallel sess I-B-4 Sarantsev, Anisovich, parallel sess I-B-2 5

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 ......

4 helicity amplitudes

4 helicity amplitudes

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.

checking complete experiments Mathematica can find exact solutions:

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

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

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

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.

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

from Andy Sandorfi table for conversion

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

frames used for recoil polarization

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

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

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

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)

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

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

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

Complete Analysis next I will demonstrate our analysis (MAID/SAID/CB@MAMI) 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

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

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

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)

a sample of MAID pseudo data for g,p0 at 320-340 MeV and comparison with real data MAID pseudo data real data

a sample of MAID pseudo data

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

2. attempt of 10 obs. MAID

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

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

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

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

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)

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

Multipole: predicted vs input E0+

Multipole: predicted vs input M1-

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