Baryon Resonances Baryon Resonances (( N*, N*, )), MAID, MAIDand and

Complete ExperimentsComplete Experiments

Lothar Tiator

Johannes Gutenberg Universität Mainz

Mini-Workshop on Hadronic Resonances, Bled, Slovenia, 2012

CRC 1044

referencesreferences

Unitary isobar model MAID2007D. Drechsel, S. Kamalov, L. Tiator

Eur. Phys. J. A 34 (2007) 69-97

Towards a model-independent partial wave analysis for pseudoscalar meson photoproduction

L. TiatorAIP Conf. Proc. 1432 (2012) 162-167

Model dependence of single-energy fits to pion photoproduction dataR. Workman, M. Paris, W. Briscoe,

L. Tiator, S. Schumann, M. Ostrick, S. KamalovEur. Phys. J. A 47 (2011) 143-154

Electromagnetic excitation of nucleon resonancesL. Tiator, D. Drechsel, S. Kamalov, M. Vanderhaeghen

Eur. Phys. J. ST 198 (2011) 141-170

Singularity structure of the πN scattering amplitude in a meson-exchange model up to energies W<2GeV

L. Tiator, S. Kamalov, S. Ceci, G.Y. Chen, D. Drechsel, A. Svarc, S.N. YangPhys. Rev. C 82 (2010) 055203-14

- how to detect N*/ resonances ?

- how to measure quantum numbers of N*/ ?

- how to measure mass and width of N*/ ?

- how to measure branching ratios ?

- how to obtain pole postions and residues ?

baryon spectroscopy

theoretical poles and experimental bumpstheoretical poles and experimental bumps

poles in the

complex plane

bumps on the

physical axis

WW

WW

E. Klempt, ATHOS2012, Camogli, Italy:

N* and states, new in PDG2012

new

new

new

new newnew

new

new

80s Birthday of Peter Higgs at University of Edinburgh

during the week of the

Narrow Nucleon Resonances

Workshop

Edinburgh, June 10, 2009

nucleon responsenucleon response

to real and virtual photonsto real and virtual photons

detailed look on nucleon detailed look on nucleon resonancesresonances

photoabsorption (inclusive cross section)

regime of dynamical models

and ChPT

regime of dynamical models

and ChPTregime of quark models

and LQCD

regime of quark models

and LQCD

DMT DMT

HDTHDT

MAIDMAID

ChPTChPT

SAIDSAID

theoretical approaches to pion photoproductiontheoretical approaches to pion photoproduction

BnGa BnGa

GICC GICC

SAIDSAID

Isobar models and Dynamical modelsIsobar models and Dynamical models

MAIDMAIDDMT DMT

(Dubna-Mainz-Taipei)(Dubna-Mainz-Taipei)

biggest difference for background terms (e.g. near threshold) :

isobar models: only Born plus phenomenological terms

dynamical models: include additional loop terms similar to PT

isobar models vs dynamical modelsisobar models vs dynamical modelsisobar models vs dynamical modelsisobar models vs dynamical models

(DMT)

(MAID)

MM AA II DD

s-channel resonance contributionss-channel resonance contributions

unitarity is build in through coupling to other open channels:

e.g.

for S11(1535)

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 this comparison between MAID and SAID

one may conclude:

this must be right!!!

Buta closer look in the partial wave amplitudes (photoproduction multipoles)

shows large differences among the different analyses,

which use mainly the same data from the world data base CNS-DAC @ GWU

strong model dependence in the pw amplitudes

due to an incomplete data base:

mainly d/d and , some T, P, very few G, H

currently in CNS-DAC data base for pp for W< 2 GeV:

dd 9382 G 28 Ox‘ 7 Tx‘ 0

1885 H 24 Oz‘ 7 Tz‘ 0

T 353 E 0 Cx‘ 0 Lx‘ 0

P 556 F 0 Cz‘ 0 Lz' 0

mainly only d/d and which count !mainly only d/d and which count !

comparison of multipoles: MAID – SAID - BonnGatchinacomparison of multipoles: MAID – SAID - BonnGatchina

from Anisovich et al., Eur. Phys. J. A. 44, 203-220 (2010)

real parts of multipoles imaginary parts of multipoles

comparison of multipoles: MAID – SAID - BonnGatchinacomparison of multipoles: MAID – SAID - BonnGatchina

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

real parts of multipoles

newly measured observables will produce changes

here example with preliminary target polarization data from Mainz:

at Mainz and Bonn we will soon get good data for:

ddwith single (beam/target) polarization and

P, E, F, G, Hwith double (beam-target) polarization

MAID, SAID, BnGa and

new fits ( ) with extra T and F data (MAMI, preliminary)

changes with newly maesured polarization observables

MAIDSAID

BnGa

in our analysis we see large changes in E0+, E2- and M1-

with each newly measured polarization observables we can hope

to improve the partial wave analyses

there is a systematic way to go: the complete experimentthe complete experiment

The Complete Experiment

a complete experiment is

a set of polarization observables

that is sufficient to exactly determine

all other possible experimentsall other possible experiments

and allall underlying (complex) amplitudes up to 1 phaseamplitudes up to 1 phase

it does not give us a guarantee

to completely determine the baryon resonance spectrum

but it certainly will improve it a lot!

a complete experiment is

a set of polarization observables

that is sufficient to exactly determine

all other possible experimentsall other possible experiments

and allall underlying (complex) amplitudes up to 1 phaseamplitudes up to 1 phase

it does not give us a guarantee

to completely determine the baryon resonance spectrum

but it certainly will improve it a lot!

what is a complete experiment?what is a complete experiment?

• in pion alpha elastic scattering:1 complex amplitude (E,)1 observable is possible

• in pion nucleon elastic scattering:2 complex amplitudes (E,)4 observables are possible4 are needed for a complete experiment0 can be predicted

• in pion photoproduction:4 complex amplitudes (E,)16observables are possible

8are needed (at least) for a complete experiment 8can be predicted

• in pion electroproduction:6 complex amplitudes (E,)36observables are possible

12 are needed (at least) for a complete experiment24 can be predicted

complete experiments in different reactionscomplete experiments in different reactions

complete experimentscomplete experiments

for systemsfor systems

with with

1, 2 and 4 1, 2 and 4

spin degrees of freedomspin degrees of freedom

1.)

2.)

common choice

3.)

common choice

16 observables

analytical solutions with less than 9 obs. are not known

1616 observables expressed in helicity amplitudes observables expressed in helicity amplitudes

16 Polarization Observables in Pion Photoproduction16 Polarization Observables in Pion Photoproduction

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

earlier studies on the complete amplitude analysis

recent studies on PWA from complete experiments

• Workman, Paris, Briscoe, Tiator, Schumann, Ostrick, Kamalov, Eur. Phys. J. A 47 (2011) 143

• Sandorfi, Hoblit, Kamano, Lee, J. Phys. G 38 (2011) 053001

• Dey, McCracken, Ireland, Meyer, Phys. Rev. C 83 (2011) 055208

• Sarantsev, Anisovich, private comm. (2011), unpublished

• Workman, Paris, Briscoe, Tiator, Schumann, Ostrick, Kamalov, Eur. Phys. J. A 47 (2011) 143

• Sandorfi, Hoblit, Kamano, Lee, J. Phys. G 38 (2011) 053001

• Dey, McCracken, Ireland, Meyer, Phys. Rev. C 83 (2011) 055208

• Sarantsev, Anisovich, private comm. (2011), unpublished

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): (9 observables needed)

„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): (9 observables needed)

„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): (8 observables needed)

a carefully chosen set of 8 observables is sufficient.

Keaton, Workman (1996) and Chiang,Tabakin (1997): (8 observables needed)

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

set observables

single S dd T P

beam-target

BT G H E F

beam-recoil

BR Ox´ Oz´ Cx´ Cz´

target-recoil

TR Tx´ Tz´ Lx´ Lz´

choose any 8 out of 16 observableschoose any 8 out of 16 observableschoose any 8 out of 16 observableschoose any 8 out of 16 observables

this set does not work!this set does not work!

set observables

single S dd T P

beam-target

BT G H E F

beam-recoil

BR Ox´ Oz´ Cx´ Cz´

target-recoil

TR Tx´ Tz´ Lx´ Lz´

choose any 8 out of 16 observableschoose any 8 out of 16 observableschoose any 8 out of 16 observableschoose any 8 out of 16 observables

also this set does not work!also this set does not work!

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´

choose any 8 out of 16 observableschoose any 8 out of 16 observableschoose any 8 out of 16 observableschoose any 8 out of 16 observables

also this set does not work!also this set does not work!

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´

choose any 8 out of 16 observableschoose any 8 out of 16 observableschoose any 8 out of 16 observableschoose any 8 out of 16 observables

this set works!this set works!

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´

choose any 8 out of 16 observableschoose any 8 out of 16 observableschoose any 8 out of 16 observableschoose any 8 out of 16 observables

also this set works!also this set works!

most extensive study by Chiang, Tabakin, Phys. Rev. C55 (1997) 2054-2066most extensive study by Chiang, Tabakin, Phys. Rev. C55 (1997) 2054-2066

1 of 6 tables to find a complete set of 8 observables1 of 6 tables to find a complete set of 8 observables

checking complete experimentschecking complete experiments

with a trickMathematica can at least check exact solutions:with a trickMathematica can at least check exact solutions:

Mathematica cannot find the exact analytical solution with 4 amplitudes,

but it can find exact solutions for integer-valued amplitudes

pseudo datapseudo data

• we have generated about 108 Monte-Carlo events

with the MAID, SAID and BnGa models

in steps of

and angular bins of

GeVMeVE lab 5.1160

10cm

MeVE lab 10

we used:

• beam pol.: PT=60% (linear polarization)

• Pc=70% (circular polarization)

• target pol.: P =80% (long. and trans., frozen spin

butanol)

• recoil pol.: A =20% (analyzing power, p-scatt on 12C)

a sample of MAID pseudo data a sample of MAID pseudo data based on 10based on 1088 Monte-Carlo events Monte-Carlo events

for at 320-340 MeV and comparison with real datafor at 320-340 MeV and comparison with real data

)(G

)(

)(T

d

d MAIDMAID

pseudo datapseudo data

real datareal data

incomplete amplitude analysis with 8 observables incomplete amplitude analysis with 8 observables

results for an incompleteincomplete set of 8 observables

with high precision (numbers directly from MAID)

results for an incompleteincomplete set of 8 observables

with high precision (numbers directly from MAID)

dσ/dΩ, Σ, T, P, G, H, E, F

ChaosChaosChaosChaos

W=1217 MeV p()p

complete amplitude analysis with 8 observables complete amplitude analysis with 8 observables

results for a completecomplete set of 8 observables

with high precision (numbers directly from MAID)

results for a completecomplete set of 8 observables

with high precision (numbers directly from MAID)

dσ/dΩ, Σ, T, P, G, E, Ox, Cx

W=1217 MeV p()p

perfect solutionperfect solutionperfect solutionperfect solution

complete amplitude analysis with 8 observables complete amplitude analysis with 8 observables

results for a completecomplete set of 8 observables

with MAID pseudo data of realistic statistics

results for a completecomplete set of 8 observables

with MAID pseudo data of realistic statisticsdσ/dΩ, Σ, T, P, G, E, Ox, Cx

MAIDMAID

overcomplete amplitude analysis with 10 observables overcomplete amplitude analysis with 10 observables

results for an overcompleteovercomplete set of 10 observables

with MAID pseudo data of realistic statistics

results for an overcompleteovercomplete set of 10 observables

with MAID pseudo data of realistic statistics

dσ/dΩ, Σ, T, P, G, H, E, F, Ox, Cx

MAIDMAID

problem with the overall phase

in this kind of analysis we are left with an unknown overall phase which cannot be determined from this experiment,

and we also cannot calculate it e.g. by unitarity

therefore we cannot calculate partial wave amplitudes:

in principle a determination of the overall phase were possible, but impractical:

- Goldberger (1963) : Hanbury-Brown-Twiss experiment

as in radio astronomy

- Ivanov (2012) : Vortex beams (twisted photons)

as in optics and atomic physics

Complete AnalysisComplete AnalysisComplete AnalysisComplete Analysis

we must distinguish between 2 kinds of complete analyses:

1) the amplitude analysis that leads to 4 amplitudes: Fi(W,) (but no partial waves)

2) the truncated partial wave analysis that leads

for Lmax = 1 to 4 multipoles: Mi(W) i.e. E0+, E1+, M1+, M1-

for Lmax = 2 to 8 multipoles

for Lmax = 3 to 12 multipoles

we must distinguish between 2 kinds of complete analyses:

1) the amplitude analysis that leads to 4 amplitudes: Fi(W,) (but no partial waves)

2) the truncated partial wave analysis that leads

for Lmax = 1 to 4 multipoles: Mi(W) i.e. E0+, E1+, M1+, M1-

for Lmax = 2 to 8 multipoles

for Lmax = 3 to 12 multipoles

function of energy and angleand angle function of energy and angleand angle

function of energy only function of energy only

for this second kind of analysis we have much more than 16 observables:

each of the 16 spin observables can be expanded in a cos() or Legendre series for energy-angle separation:

e.g.:

complete analysis of 2. kind

group 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´

Omelaenko (1981)

for a truncated partial wave analysis with Lmax waves

only 5 observables are necessary, e.g. the 4 from group Sand 1 additional from any other group

Omelaenko (1981)

for a truncated partial wave analysis with Lmax waves

only 5 observables are necessary, e.g. the 4 from group Sand 1 additional from any other group

Grushin (1989)

applied it for a PWA in the (1232) region with only S+P waves (Lmax= 1Grushin (1989)

applied it for a PWA in the (1232) region with only S+P waves (Lmax= 1

requirements for the requirements for the 2. kind2. kind of a complete experiment of a complete experimentrequirements for the requirements for the 2. kind2. kind of a complete experiment of a complete experiment

group 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´

Omelaenko (1981)

for a truncated partial wave analysis with Lmax waves

only 5 observables are necessary, e.g. the 4 from group Sand 1 additional from any other group

Omelaenko (1981)

for a truncated partial wave analysis with Lmax waves

only 5 observables are necessary, e.g. the 4 from group Sand 1 additional from any other group

Grushin (1989)

applied it for a PWA in the (1232) region with only S+P waves (Lmax= 1Grushin (1989)

applied it for a PWA in the (1232) region with only S+P waves (Lmax= 1

one possible solution for the one possible solution for the 2. kind2. kind is: is:one possible solution for the one possible solution for the 2. kind2. kind is: is:

results of a

truncated partial wave analysis with Lmax=3

of the MAID pseudo data

performed in collaboration with SAID group

S11 (E0+) multipole: predicted vs. input

P11 (M1-) multipole: predicted vs. input

Summary and ConclusionSummary and Conclusion

• The Complete Experiment of 1. kind

requires 8 well selected observables8 well selected observables but it can not give us information on N* physics because it does not give us partial waves

due to an unknown angle-dependent overall phase W

• The Complete Experiment of 2. kind aims directly on partial waves and requires only 5 well selected observables5 well selected observablesthese can be: d, , T, P, For: d, , T, F, G

or: d, , Ox‘, Oz‘, Cz‘ and others

• The real challenge will come with real world datasuffering from: exp. uncertainties

limited detector acceptances

• The Complete Experiment of 1. kind

requires 8 well selected observables8 well selected observables but it can not give us information on N* physics because it does not give us partial waves

due to an unknown angle-dependent overall phase W

• The Complete Experiment of 2. kind aims directly on partial waves and requires only 5 well selected observables5 well selected observablesthese can be: d, , T, P, For: d, , T, F, G

or: d, , Ox‘, Oz‘, Cz‘ and others

• The real challenge will come with real world datasuffering from: exp. uncertainties

limited detector acceptances