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
our motivation
precise knowledge of meson photoproduction amplitudes
is important for:
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designing of proposals, setting up experiments and data analysis
comparison with EFT, near threshold and near resonances
dispersion theoretical applications,
as Compton scattering, 2g processes, various sum rules
many applications by Barbara Pasquini (RCS,VCS,SSA,FFR)
baryon resonance analysis,
besides pN -> pN, gN->pN is the most important source
comparisons with quark models and lattice QCD,
especially for N* physics
PWA groups, also doing g,N
SAID
2006/2012
model indep. single ch. PWA pN->pN, pN->hN, gN->pN, gN->hN
http://gwdac.phys.gwu.edu/
BnGa
2012
multichannel partial wave analysis, pN, hN, ppN, KL, KS, gN
http://pwa.hiskp.uni-bonn.de/
MAID
2007
unitary isobar model, single ch. gN->pN, gN->hN, gN->KL(S)
http://www.kph.uni-mainz.de/MAID/
DMT
2007
dynamical model with few coupled channels, pN, hN, ppN, gN
http://www.kph.uni-mainz.de/MAID/
Jülich
2012
dynamical model with coupled ch., pN, hN, ppN, KL, KS, ..., gN
Gießen
2012
coupled ch. unitary Lagrangian model, pN, hN, ppN, KL, KS, gN
Kent State
2013
K matrix coupled channels, pN, hN, ppN, KL, KS, gN
ANL-Osaka
2013
dynamical model with coupled ch., pN, hN, ppN, KL, KS, ..., gN
nucleon response to real and virtual photons
Threshold Region
Resonance Region
helicity difference Ds = s3/2 – s1/2 for the proton
D. Drechsel and L. Tiator, Ann. Rev. Nucl. Part. Sci. 2004, 54:69-114
forward Spin polarizability and GDH sumrule
forward spin polarizability
GDH Coll. (MAMI & ELSA)
Ahrens et al., PRL87 (2001)
Dutz et al. PRL91 (2003)
GDH sum rule
GDH Coll. (MAMI & ELSA, 200-2005) + MAID + Regge
MAID
2013 status of 28 N resonances
red : 4-star
blue : new, upgraded
or renamed
g,h
g,K
g,K
g,K
J/Y
g,K
mainly from
kaon photoproduction
g,K
J/Y
from BES-III
2013 status of 22 D resonances
no changes
no new states
but many uncertain states
with less than 3-stars
spin degrees of freedom: 4 for real, 6 for virtual photons
virt
4 (6) invariant amplitudes (e.g. from EFT and Lagrangian models):
4 (6) CGLN amplitudes in cm frame (e.g. from isobar models):
4 (6) * Lmax partial wave amplitudes (multipoles) in cm frame:
observables for real and virtual photons
16 (36) observables (cross sections and polarization observables):
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 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
result of single-energy and energy-dependent fitting
most observables that were fitted are in good agreement with MAID2007
reduced c2 from Maid07 fits to g,p data in different energy regions
single-energy (SE) fits
energy-dependent (ED) fits
but with higher energies the analysis becomes more difficult and less accurate
unitarity cusp at eta threshold
J. Ahrens et al., (GDH and A-2 Collaboration), Phys. Rev. C 74, 045204 (2006)
unpolarized
total cross section
polarized
total cross section
(helicity asymmetry)
helicity separated
cross sections
comparison between MAID and SAID
comparison between MAID and SAID
Roper
P11(1710)
comparison of multipoles: MAID – SAID - BNGA
from Anisovich et al., Eur. Phys. J. A. 44, 203-220 (2010)
real parts of g,p0 multipoles
Re
Re
Re
Re
no problems for M1+
surprisingly large differences, even though the world data is equally well described
due to an incomplete data base
16 spin observables in photoproduction
linear and circular polarized beams
longitudinal and transverse polarized targets
recoil polarization, in particular for KL and KS
8 observ.
12 observ.
from M. Ostrick, NSTAR2013 (Mainz data):
g p -> p p0
new prel. Mainz data with transversely polarized target
MAID
SAID
BnGa
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
Nucleon Resonance Analysis with Pietarinen expansion
in collaboration with:
Svarc (Zagreb), Osmanovic et al (Tuzla), Workman (GWU), arXiv:1307.4613 [hep-ph]
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:
poles and branch points (regions) in the Jülich coupled channels model:
0
-50
-100
Im ECM [MeV]
D3/2+
N3/2-
N1/2+
N1/2-
Nucleon Resonance Analysis with Pietarinen expansion
in collaboration with:
Svarc (Zagreb), Osmanovic et al (Tuzla), Workman (GWU), arXiv:1307.4613 [hep-ph]
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:
poles and real and complex branch points in the Jülich coupled channels model:
real branch point
complex branch point
pole
Nucleon Resonance Analysis with Pietarinen expansion
in collaboration with Svarc (Zagreb), Osmanovic et al (Tuzla), Workman (GWU),
arXiv:1307.4613 [hep-ph]
The L+P (Laurent+Pietarinen) expansion method is defined as:
1 Pietarinen series
for each branch point
we have typically 3 Pietarinens
1 in unphysical region E<thresh
2 in physical region,
e.g. pN, ppN, hN thresholds
the Pietarinen expansion is a conformal mapping of the w-plane
onto the interior of the unit circle of the Z-plane
E. Pietarinen, Nuovo Cim. Soc. Ital. Fis. 12A, 522 (1972)
(successfully applied in the Karlsruhe pN partial wave analysis)
Pietarinen expansion for the DMT pN PWA
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
all poles, which are not too deep in the complex region
are very well recovered.
Pietarinen expansion for GWU/SAID SE(pN ) PWA
resonance poles
found in the L+P expansion:
P1 = 1362 - i 89.5
P2 = 1716 - i 49.5
P3 = 1999 - i 71.5
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
Pietarinen expansion for the MAID g,p PWA
MAID
energy-dependent solution (ED)
for ED solutions, L+P expansion
gives a numerical approximation ~ 10-3
MAID
single-energy solution (SE)
for SE solutions, L+P expansion
gives the best-fit with a statistically significant c2 ~ 1
Pietarinen expansion for the MAID g,p PWA
MAID
energy-dependent solution (ED)
P11(1710)
is not included in MAID
but it is found in the L+P expansion of
the MAID single-energy analysis
c2 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 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
new L+P fit to new polarization data from Mainz and Bonn
new L+P fit
MAID2007
SAID-SN11
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
new L+P fit
MAID2007
SAID-SN11
for higher energies, E > 900 MeV the fits are not so good
summary and conclusion
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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 N* and D 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