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