model-independent partial-wave analysis for pion photoproduction
DESCRIPTION
Model-independent partial-wave analysis for pion photoproduction. Lothar Tiator. Motivation Complete Experiments Pseudo Data from Monte-Carlo events Complete Amplitude Analysis Complete Truncated P artial W ave A nalysis Summary and Conclusion. in collaboration with. - PowerPoint PPT PresentationTRANSCRIPT
Model-independent partial-wave Model-independent partial-wave analysisanalysis
for pion photoproductionfor pion photoproduction
Lothar TiatorLothar Tiator
• Motivation
• Complete Experiments
• Pseudo Data from Monte-Carlo events
• Complete Amplitude Analysis
• Complete Truncated Partial Wave Analysis
• Summary and Conclusion
• Motivation
• Complete Experiments
• Pseudo Data from Monte-Carlo events
• Complete Amplitude Analysis
• Complete Truncated Partial Wave Analysis
• Summary and Conclusion
in collaboration within collaboration with
Michael Ostrick and Sven Schumann
Institut für Kernphysik, Johannes Gutenberg UniversitätMainz, Germany
Sabit Kamalov
Bogoliubov Laboratory for Theoretical Physics, JINR Dubna, Russia
Ron Workman and Mark Paris
Center for Nuclear Studies, Department of Physics, GWUWashington, DC, USA
arXiv:1102.4897arXiv:1102.4897
3 recent partial wave analyses for S3 recent partial wave analyses for S1111
SAID, Arndt et al. 2006SAID, Arndt et al. 2006
Dubna-Mainz-Taipei, Chen et al. 2007
Regensburg, Bonn, Bruns et al. 2010
Regensburg, Bonn, Bruns et al. 2010
1. resonance: S11(1535)
Re Wp -2 Im Wp |res| [°]
Said 1502 95 16 -16
DMT 1499 78 14 -45
Bruns 1506 280
2. resonance: S11(1650)
Re Wp -2 Im Wp |res| [°]
Said 1648 80 14 -69
DMT 1631 120 35 -83
Bruns 1692 92
how can this be improved ?how can this be improved ?how can this be improved ?how can this be improved ?
• more precise piN data not possible in near future
• coupled channels analysesnecessary, but database still very limited
• J/ decays very helpful if statistics can be improved
• high-precision analyses of and photoproduction
• more precise piN data not possible in near future
• coupled channels analysesnecessary, but database still very limited
• J/ decays very helpful if statistics can be improved
• high-precision analyses of and photoproduction
currently at Mainz, Bonn and JLab:
• „complete experiments“ are in preparation for • using linearly and circularly polarized photon beams
• longitudinal and transverse polarized targets
• measuring recoil polarization of outgoing nucleon
currently at Mainz, Bonn and JLab:
• „complete experiments“ are in preparation for • using linearly and circularly polarized photon beams
• longitudinal and transverse polarized targets
• measuring recoil polarization of outgoing nucleon
studies on the complete experiment
• 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
• 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
• Sandorfi, Hoblit, Kamano, Lee, J. Phys. G 38, 053001 (2011) [arXiv:1010.4555 [nucl-th]]
• Dey, McCracken, Ireland, Meyer, [arXiv:1010.4978 [hep-ph]]
• Workman, Paris, Briscoe, Tiator, Schumann, Ostrick, Kamalov,
[arXiv:1102.4897 [nucl-th]]
• Sarantsev, Anisovich
• Sandorfi, Hoblit, Kamano, Lee, J. Phys. G 38, 053001 (2011) [arXiv:1010.4555 [nucl-th]]
• Dey, McCracken, Ireland, Meyer, [arXiv:1010.4978 [hep-ph]]
• Workman, Paris, Briscoe, Tiator, Schumann, Ostrick, Kamalov,
[arXiv:1102.4897 [nucl-th]]
• Sarantsev, Anisovich
earlier studies on the complete amplitude analysis
recent studies on PWA from complete experiments
What is a complete experiment?What is a complete experiment?
a set of polarization observables which allow usto exactly predict all other possible experiments
(if experimental errors are neglected)
• in pion nucleon scattering:4 observables are possible4 are needed for a complete experiment0 can be predicted
• in pion photoproduction:16 observables are possible
8 are needed (at least) for a complete experiment 8 can be predicted
• in pion electroproduction:36 observables are possible12 are needed (at least) for a complete experiment24 can be predicted
spin amplitudes vs. partial wave amplitudes
spin amplitudes vs. partial wave amplitudes
set observables
single S d/d 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.“
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.
Keaton, Workman (1996) and Chiang,Tabakin (1997):
a carefully chosen set of 8 observables is sufficient.
requirements for a complete experiment in photoproductionrequirements for a complete experiment in photoproductionrequirements for a complete experiment in photoproductionrequirements for a complete experiment in photoproduction
definitions from Barker, Donnachie, Storrow, definitions from Barker, Donnachie, Storrow, 19751975
• BT: BT: polarized photons and polarized targetpolarized photons and polarized target• BT: BT: polarized photons and polarized targetpolarized photons and polarized target
• BR: BR: polarized photons and recoil polarizationpolarized photons and recoil polarization• BR: BR: polarized photons and recoil polarizationpolarized photons and recoil polarization
• TR: TR: polarized target and recoil polarizationpolarized target and recoil polarization• TR: TR: polarized target and recoil polarizationpolarized target and recoil polarization
definitions from Fasano, Tabakin, Saghai, definitions from Fasano, Tabakin, Saghai, 19921992
7 minus signs removed:7 minus signs removed:
asign
used here
by A. Sandorfi et al.
asign
used here
by A. Sandorfi et al.
B. Dey et al.
and
A. Sarantsev et al.
use the same sign convention
B. Dey et al.
and
A. Sarantsev et al.
use the same sign convention
comparison between different groupscomparison between different groups
now we have 2 options:
1) we go on as before and use these tablesfor translations
2) we try to findagreement on a common conventionthat everybodyshould use
now we have 2 options:
1) we go on as before and use these tablesfor translations
2) we try to findagreement on a common conventionthat everybodyshould use
16 Polarization Observables in Pion 16 Polarization Observables in Pion PhotoproductionPhotoproduction
16 Polarization Observables in Pion 16 Polarization Observables in Pion PhotoproductionPhotoproduction
• for and one can only measure the transverse
recoil polarization in the lab frame
and transformation into the cm frame is not possible
• for one gets it for free from the weak hyperon decays
• for and one can only measure the transverse
recoil polarization in the lab frame
and transformation into the cm frame is not possible
• for one gets it for free from the weak hyperon decays
frames used for recoil polarization frames used for recoil polarization frames used for recoil polarization frames used for recoil polarization
J.J. Kelly et al., Phys. Rev. C 75, 025201 (2007) and arXiv:nucl-ex/0509004J.J. Kelly et al., Phys. Rev. C 75, 025201 (2007) and arXiv:nucl-ex/0509004
also used by Dey et al.
for their
„longitudinal basis“
also used by Dey et al.
for their
„longitudinal basis“
most common
„helicity basis“
however oriented
along the pion
most common
„helicity basis“
however oriented
along the pion
don‘t miss the preprintdon‘t miss the preprint
„„classical“ recoil polarization basesclassical“ recoil polarization bases„„classical“ recoil polarization basesclassical“ recoil polarization bases
recoil polarization basesrecoil polarization basesrecoil polarization basesrecoil polarization bases
for a new convention, the better choices were 3 or 6for a new convention, the better choices were 3 or 6for a new convention, the better choices were 3 or 6for 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
pseudo datapseudo data
• we have generated about 108 Monte-Carlo events
with the MAID, SAID and BoGa models
in steps of
and angular bins of
GeVMeVE lab 5.1160
10cm
MeVE lab 10
we assume:
• beam pol.: P (linear polarization)
• Pc (circular polarization)
• target pol.:P (long. and trans., frozen spin
butanol)
• recoil pol.: (analyzing power, rescattering 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 a sample of MAID pseudo datadata
for at 320-340 MeV and comparison with real datafor at 320-340 MeV and comparison with real data
)(G
)(
)(T
dd MAIDMAID
pseudo datapseudo data
real datareal data
amplitude analysis with a minimal complete set of 8 observables
amplitude analysis with a minimal complete set of 8 observables
MAIDMAID
of 10 obs.of 10 obs.
MAIDMAID
predicted target-recoil observablesnot simulated in the pseudo data
predicted target-recoil observablesnot simulated in the pseudo data
MAIDMAID
of 10 obs.of 10 obs.
predictive power of the complete experimentpredictive power of the complete experimentpredictive power of the complete experimentpredictive power of the complete experiment
from Andrej Sarantsev,
on the overall phase problem
from Andrej Sarantsev,
on the overall phase problem
even in the region, no symmetry or theorem can tell us this phase Weven in the region, no symmetry or theorem can tell us this phase W
from Andrej Sarantsev,
on the overall phase problem
from Andrej Sarantsev,
on the overall phase problem
this is the right way to gothis is the right way to gothis is the right way to gothis is the right way to go
partial wave expansion up to Lmax = 4partial wave expansion up to Lmax = 4
from Andrej Sarantsevfrom Andrej Sarantsev
Lmax=3Lmax=4
Lmax=3Lmax=4
• second approach: truncated partial wave analysis TPWA
truncated partial wave analysis (truncated partial wave analysis (TPWATPWA))
in practice all PWA are truncated to a certain Lmaxfor it means L = 0, ... Lmax being analyzed
L > Lmax taken from Born terms
1) amplitude analysis:1) amplitude analysis:
4 complex amplitudes, e.g. F1, F2, F3, F4(W,)
16 observables, d/d, ,... Tz´(W,)
4 complex amplitudes, e.g. F1, F2, F3, F4(W,)
16 observables, d/d, ,... Tz´(W,)
2) truncated p.w. analysis up to ℓ=Lmax :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,) expanded in powers of cos
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,) expanded in powers of cos
amplitude analysis vs. TPWAamplitude analysis vs. TPWAamplitude analysis vs. TPWAamplitude analysis vs. TPWA
• second approach: truncated partial wave analysis TPWA
truncated partial wave analysis (truncated partial wave analysis (TPWATPWA))
in practice all PWA are truncated to a certain Lmaxfor it means L = 0, ... Lmax being analyzed
L > Lmax taken from Born terms
we will use Lmax = 3 (SPDF waves)we will use Lmax = 3 (SPDF waves)
-> 12 -> 12 complex multipolescomplex multipoles
-> 23-> 23 real fit parameters and 1 fixed real fit parameters and 1 fixed phasephase
from experiment we getfrom experiment we get
2424 numbers from each set S, BTnumbers from each set S, BT
28 28 numbers from each set BR, TRnumbers from each set BR, TR
104104 numbers in total from 16 numbers in total from 16 observablesobservables
we will use Lmax = 3 (SPDF waves)we will use Lmax = 3 (SPDF waves)
-> 12 -> 12 complex multipolescomplex multipoles
-> 23-> 23 real fit parameters and 1 fixed real fit parameters and 1 fixed phasephase
from experiment we getfrom experiment we get
2424 numbers from each set S, BTnumbers from each set S, BT
28 28 numbers from each set BR, TRnumbers from each set BR, TR
104104 numbers in total from 16 numbers in total from 16 observablesobservables
finally the overall phase can be obtained by the -pole term for
and with a small model dependence for (Grushin‘s method, 1988)
constrained fits beyond the Watson region
• step 1: energy dependent (ED) fit to all available observablesfor a large energy range using the SAID ansatz
(we use 4/8/12 obs. S,BT,BR for 160MeV < E < 1.5GeV)
provides an energy dependent phase for each multipole
• step 2: energy independent or single-energy (SE) fits to data typically in intervals of E10MeVwith determination of all moduli of all multipoles with fixed phases from ED fits
• step 3: finally we can relax some critical phasesand search for an unconstrained solution
alternatively we can acquire or develop new search algorithms,
that can deal with multiple minima
• step 1: energy dependent (ED) fit to all available observablesfor a large energy range using the SAID ansatz
(we use 4/8/12 obs. S,BT,BR for 160MeV < E < 1.5GeV)
provides an energy dependent phase for each multipole
• step 2: energy independent or single-energy (SE) fits to data typically in intervals of E10MeVwith determination of all moduli of all multipoles with fixed phases from ED fits
• step 3: finally we can relax some critical phasesand search for an unconstrained solution
alternatively we can acquire or develop new search algorithms,
that can deal with multiple minima
first in the Watson region at E = 340 MeV
ED and SE fits are indistinguishablealso BT and TR obs are described very well
ED and SE fits are indistinguishablealso BT and TR obs are described very well
Maid
pseudo data
Maid
pseudo data
single energy fit to 4 obs dσ/dΩ, Σ, T, P single energy fit to 4 obs dσ/dΩ, Σ, T, P
pppp
beam-target double pol. obs. at E = 340 MeV
Maid
pseudo data
Maid
pseudo data
energy dependent fit to 4 obsenergy dependent fit to 4 obs
single energy fit to 4 obssingle energy fit to 4 obs
F
G pppp
predictionspredictions
Prediction compared to a fit of double-polarization observable
dσ/dΩ, P, Σ, T = 4
+ E, F, G, H = 8
+ Ox , Oz , Cx , Cz = 12
Ox´ double pol. obs. at E = 600 MeV
pppp
6-8 observables are enough6-8 observables are enough6-8 observables are enough6-8 observables are enough
Multipole: predicted vs input E0+ (S11)
Multipole: predicted vs input M1- (P11)
SummarySummary
• We have studied the possibilities to obtain a model independent PWA for from a Complete Experiment, which requires at least 8 different polarization observables, using beam, target and recoil polarization
• Such experiments are currently starting at Mainz, Bonn and JLab.
• We used pseudo data from Monte-Carlo event simulations using MAID
• From this experiment we can get a true model independent amplitude analysisa true model independent amplitude analysis
but these amplitudes do not give us the desired partial wavesbecause of the missing overall phase
• Therefore we do a truncated partial wave analysis directly from the data
• We have studied the possibilities to obtain a model independent PWA for from a Complete Experiment, which requires at least 8 different polarization observables, using beam, target and recoil polarization
• Such experiments are currently starting at Mainz, Bonn and JLab.
• We used pseudo data from Monte-Carlo event simulations using MAID
• From this experiment we can get a true model independent amplitude analysisa true model independent amplitude analysis
but these amplitudes do not give us the desired partial wavesbecause of the missing overall phase
• Therefore we do a truncated partial wave analysis directly from the data
ConclusionsConclusions
1. in the Watson region, W < 1.3 GeV only S and P waves must be analyzedhigher pw L > 1 can be taken from Born termsall unitary phases are fixed to N by Watson‘s theorem
such an analysis requires only 2 observables ddand (R. Beck@MAMI 1997)
2. above the Watson region 1.3 GeV < W < 1.8 GeV, S,P,D and F waves needed, (+ G waves for W = 2 GeV) with an overcomplete set of 12 observables everything works very well, already with sets of 6-8 observables without recoil polarization we get very good results
3. this looks very encouraging for an unconstrained model independent PWA
with real experimental data - coming soon
PWA Workshop, Trento, June 2009