Recent Progress Recent Progress in the in the

MAID Partial Wave AnalysisMAID Partial Wave Analysis

Recent Progress Recent Progress in the in the

MAID Partial Wave AnalysisMAID Partial Wave Analysis

Lothar TiatorJohannes 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 projectscurrent 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 rulesmany 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

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 rulesmany 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 motivationour motivation

PWA groups, also doing PWA groups, also doing

SAID model indep. single ch. PWA http://gwdac.phys.gwu.edu/

BnGa multichannel partial wave analysis, http://pwa.hiskp.uni-bonn.de/

MAID unitary isobar model, single ch. http://www.kph.uni-mainz.de/MAID/

DMT dynamical model with few coupled channels, http://www.kph.uni-mainz.de/MAID/

Jülich dynamical model with coupled ch.,

Gießen coupled ch. unitary Lagrangian model,

Kent State K matrix coupled channels,

ANL-Osaka dynamical model with coupled ch.,

nucleon response to real and virtual photonsnucleon response to real and virtual photons

Threshold Region Resonance Region

D. Drechsel and L. Tiator, Ann. Rev. Nucl. Part. Sci. 2004, 54:69-114

helicity difference helicity difference –– for the proton for the proton

forward Spin polarizability and GDH sumruleforward 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, 200-2005) + MAID + Regge

GDH sum rule

MM AA II DD

2013 status of 2013 status of resonances resonances

red : 4-star

blue : new, upgraded or renamed

mainly from kaon photoproduction

from BES-IIIJ

J

2013 status of 2013 status of resonances resonances

but many uncertain stateswith 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 photonsspin degrees of freedom: 4 for real, 6 for virtual photons

4 (6) * Lmax partial wave amplitudes (multipoles) in cm frame:

16 (36) observables (cross sections and polarization observables):

observables for real and virtual photonsobservables 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 ta(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 caseproblem: 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 thresholdunitarity cusp at eta threshold

unpolarizedtotal cross section

polarizedtotal cross section(helicity asymmetry)

helicity separated

cross sections

J. Ahrens et al., (GDH and A-2 Collaboration), Phys. Rev. C 74, 045204 (2006)

comparison between MAID and SAIDcomparison between MAID and SAID

comparison between MAID and SAID

RoperP11(1710)

from Anisovich et al., Eur. Phys. J. A. 44, 203-220

no problems for

Re Re

ReRe

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 - BNGAcomparison 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):

pp

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 The singularities that strongly influence the partial wave amplitudes in amplitudes in the physical region are the thresholds (branch-points) on the the physical region are the thresholds (branch-points) on the real axis real axis and the poles in the closest (2nd) Riemann sheet:and the poles in the closest (2nd) Riemann sheet:

Nucleon Resonance Analysis with Pietarinen expansionNucleon Resonance Analysis with Pietarinen expansionin collaboration with:

Svarc (Zagreb), Osmanovic et al (Tuzla), Workman (GWU), arXiv:1307.4613 [hep-ph]

poles and branch points (regions) in the Jülich coupled channels model:

Im ECM [MeV]

The singularities that strongly influence the partial wave The singularities that strongly influence the partial wave amplitudes in amplitudes in the physical region are the thresholds (branch-points) on the the physical region are the thresholds (branch-points) on the real axis real axis and the poles in the closest (2nd) Riemann sheet:and the poles in the closest (2nd) Riemann sheet:

Nucleon Resonance Analysis with Pietarinen expansionNucleon Resonance Analysis with Pietarinen expansion

in collaboration with: Svarc (Zagreb), Osmanovic et al (Tuzla), Workman (GWU), arXiv:1307.4613

[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 The L+P (Laurent+Pietarinen) expansion method is defined as:as:

Nucleon Resonance Analysis with Pietarinen expansionNucleon Resonance Analysis with Pietarinen expansion

in collaboration with Svarc (Zagreb), Osmanovic et al (Tuzla), Workman (GWU),arXiv:1307.4613 [hep-ph]

1 Pietarinen series for each branch point

we have typically 3 Pietarinens1 in unphysical region E<thresh2 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 Pietarinen expansion for the DMT PWA PWA

all poles, which are not too deep in the complex regionare very well recovered.

here we perform an L+P fitto the energy dependent DMT solution

(arbitrary error band of ~5% assigned)

pole positions and residuesDMT model compared to the fit

Pietarinen expansion for GWU/SAID Pietarinen expansion for GWU/SAID SE(SE(NN ) ) PWA 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 = 1362 - i 89.5

P2 = 1716 - i 49.5

P3 = 1999 - i 71.5

Pietarinen expansion for the Pietarinen expansion for the MAID MAID PWA PWA

MAID energy-dependent solution (ED)

MAID single-energy solution (SE)

for ED solutions, L+P expansiongives a numerical approximation ~ 10-3

for SE solutions, L+P expansiongives the best-fit with a statistically significant 2 ~ 1

Pietarinen expansion for the Pietarinen expansion for the MAID MAID PWA PWA

P11(1710) is not included in MAIDbut it is found in the L+P expansion ofthe MAID single-energy analysis

MAID energy-dependent solution (ED)

compared for MAID2007 and new L+P expansion

MAID2007 new L+P expansion method

some improvement is visible, but the new solution fails for some observables, which are not fittedthis 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 Bonnnew 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 Bonnnew 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 conclusionsummary and conclusion

• MAID has been very successfull over the last 15 yearsit has been used for many experimental proposalsand 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

• MAID has been very successfull over the last 15 yearsit has been used for many experimental proposalsand 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 modelthis work is still in progress