Recent Progress in the MAID Partial Wave Analysis Lothar Tiator Johannes Gutenberg Universität Mainz Compton scattering off Protons and Light Nuclei, ECT*, Trento, July 29 - August 2, 2013

a dispersive view of Compton scattering Born pole terms single-meson production double-meson production

current MAID projects

precise knowledge of meson photoproduction amplitudes is important for: designing of proposals, setting up experiments and data analysis comparison with EFT, near threshold and near resonances dispersion theoretical applications, as Compton scattering,  processes, various sum rules many applications by Barbara Pasquini (RCS,VCS,SSA,FFR) baryon resonance analysis, besides  is the most important source comparisons with quark models and lattice QCD, especially for N* physics our motivation

PWA groups, also doing  SAIDmodel indep. single ch. PWA   BnGamultichannel partial wave analysis,   MAIDunitary isobar model, single ch.   DMTdynamical model with few coupled channels,   Jülichdynamical model with coupled ch.,   Gießencoupled ch. unitary Lagrangian model,   Kent StateK matrix coupled channels,   ANL-Osakadynamical model with coupled ch.,  

nucleon response to real and virtual photons Threshold Region Resonance Region

D. Drechsel and L. Tiator, Ann. Rev. Nucl. Part. Sci. 2004, 54: helicity difference    –   for the proton

forward Spin polarizability and GDH sumrule forward spin polarizability GDH Coll. (MAMI & ELSA) Ahrens et al., PRL87 (2001) Dutz et al. PRL91 (2003) GDH Coll. (MAMI & ELSA, ) + MAID + Regge GDH sum rule

M A I DM A I DM A I DM A I D

2013 status of  resonances red : 4-star blue : new, upgraded or renamed mainly from kaon photoproduction from BES-III J    

2013 status of  resonances but many uncertain states with less than 3-stars no changes no new states

4 (6) invariant amplitudes (e.g. from EFT and Lagrangian models): virt 4 (6) CGLN amplitudes in cm frame (e.g. from isobar models): spin degrees of freedom: 4 for real, 6 for virtual photons 4 (6) * L max partial wave amplitudes (multipoles) in cm frame:

16 (36) observables (cross sections and polarization observables): observables for real and virtual photons 2 (4) total (inclusive) cross sections: various sum rules for real and virtual photons: : Baldin : GDH : FSP

SE and ED partial wave analysis t a (w) SE : single-energy analysis ED : energy-dependent analysis intelligent parametrization using symmetries, thresholds, branch points, poles, unitarity, dispersion relations,... closer to the exp. data, no constraints in ideal case problem: multiple solutions very likely in practise: often losely bound to ED solutions, e.g. usual chisquared penalty term and do not have the same statistics as the underlying real data

most observables that were fitted are in good agreement with MAID2007 result of single-energy and energy-dependent fitting but with higher energies the analysis becomes more difficult and less accurate reduced   from Maid07 fits to  data in different energy regions single-energy (SE) fits energy-dependent (ED) fits

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, (2006)

comparison between MAID and SAID

Roper P 11 (1710)

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

16 spin observables in photoproduction linear and circular polarized beams longitudinal and transverse polarized targets recoil polarization, in particular for  and  8 observ.12 observ.

from M. Ostrick, NSTAR2013 (Mainz data):  p  p  

MAID SAID BnGa new prel. Mainz data with transversely polarized target preliminary MAMI data: T : target asymmetry F : lin. pol. photon beam – transv. target pol.

new Bonn data with transversely polarized target

new Bonn data with longitudinally polarized target

how can we improve MAID ? main question: are the discrepancies due to background or resonance contributions? for background: we could add polynominal functions for resonance: we could add more Breit-Wigner terms PDG lists 50 resonances, MAID uses only 13 **** resonances our new strategy: obtain fits of partial waves to SE analysis then go back to observables perform a new SE-fit starting from new solution obtain a new fit of partial waves to new SE-fit continue this iteration until it converges

The singularities that strongly influence the partial wave amplitudes in the physical region are the thresholds (branch-points) on the real axis and the poles in the closest (2nd) Riemann sheet: Nucleon Resonance Analysis with Pietarinen expansion in collaboration with: Svarc (Zagreb), Osmanovic et al (Tuzla), Workman (GWU), arXiv: [hep-ph] poles and branch points (regions) in the Jülich coupled channels model: Im E CM [MeV]               

The singularities that strongly influence the partial wave amplitudes in the physical region are the thresholds (branch-points) on the real axis and the poles in the closest (2nd) Riemann sheet: Nucleon Resonance Analysis with Pietarinen expansion in collaboration with: Svarc (Zagreb), Osmanovic et al (Tuzla), Workman (GWU), arXiv: [hep-ph] poles and real and complex branch points in the Jülich coupled channels model: pole complex branch point real branch point

The L+P (Laurent+Pietarinen) expansion method is defined as: Nucleon Resonance Analysis with Pietarinen expansion in collaboration with Svarc (Zagreb), Osmanovic et al (Tuzla), Workman (GWU), arXiv: [hep-ph] 1 Pietarinen series for each branch point we have typically 3 Pietarinens 1 in unphysical region E<thresh 2 in physical region, e.g.  thresholds the Pietarinen expansion is a conformal mapping of the  plane onto the interior of the unit circle of the  plane E. Pietarinen, Nuovo Cim. Soc. Ital. Fis. 12A, 522 (1972) (successfully applied in the Karlsruhe  partial wave analysis)

Pietarinen expansion for the DMT  PWA all poles, which are not too deep in the complex region are very well recovered. here we perform an L+P fit to the energy dependent DMT solution (arbitrary error band of ~5% assigned) pole positions and residues DMT model compared to the fit

Pietarinen expansion for GWU/SAID SE(  N ) PWA the L+P expansion can discover resonance poles in the SE analysis, that did not exist in the ED solution the L+P expansion resembles very much the old Höhler analysis KH80 resonance poles found in the L+P expansion: P1 = i 89.5 P2 = i 49.5 P3 = i 71.5

Pietarinen expansion for the MAID  PWA MAID energy-dependent solution (ED) MAID single-energy solution (SE) for ED solutions, L+P expansion gives a numerical approximation ~ for SE solutions, L+P expansion gives the best-fit with a statistically significant  2 ~ 1

Pietarinen expansion for the MAID  PWA P 11 (1710) is not included in MAID but it is found in the L+P expansion of the MAID single-energy analysis MAID energy-dependent solution (ED)

  compared for MAID2007 and new L+P expansion MAID2007new L+P expansion method some improvement is visible, but the new solution fails for some observables, which are not fitted this method has less predictive power than the original unitary isobar model, however, it is perhaps a good method to solve the Complete Experiment the work is in progress

SAID-SN11 MAID2007 new L+P fit new L+P fit to new polarization data from Mainz and Bonn for E < 900 MeV the fit looks reasonable, with G observable we are not yet satisfied

new L+P fit to new polarization data from Mainz and Bonn SAID-SN11 MAID2007 new L+P fit for higher energies, E > 900 MeV the fits are not so good

summary and conclusion MAID has been very successfull over the last 15 years it has been used for many experimental proposals and also as a Partial Wave Analysis for photo- and electroproduction now, new polarization data show large discrepancies, which are due to   and  resonances, which are not yet included and nontrivial background beyond Born terms and vector mesons both can be parametrized in a Laurent+Pietarinen (L+P) expansion, that will hopefully lead in a new improved MAID model this work is still in progress