Recent Progress in the MAID Partial Wave Analysis
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Transcript of Recent Progress in the MAID Partial Wave Analysis
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