Baryon resonances n d maid and complete experiments
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Lothar Tiator Johannes Gutenberg Universität Mainz. Baryon Resonances ( N*, D ) , MAID and Complete Experiments. CRC 1044. Mini-Workshop on Hadronic Resonances, Bled, Slovenia, 2012. references. Singularity structure of the πN scattering amplitude

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Baryon Resonances ( N*, D ) , MAID and Complete Experiments

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Lothar Tiator

Johannes Gutenberg Universität Mainz

Baryon Resonances (N*, D), MAIDand Complete Experiments

CRC 1044

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


references

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. Yang

Phys. Rev. C 82 (2010) 055203-14

Electromagnetic excitation of nucleon resonances

L. Tiator, D. Drechsel, S. Kamalov, M. Vanderhaeghen

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

Unitary isobar model MAID2007

D. Drechsel, S. Kamalov, L. Tiator

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

Model dependence of single-energy fits to pion photoproduction data

R. Workman, M. Paris, W. Briscoe,

L. Tiator, S. Schumann, M. Ostrick, S. Kamalov

Eur. Phys. J. A 47 (2011) 143-154

Towards a model-independent partial wave analysis

for pseudoscalar meson photoproduction

L. Tiator

AIP Conf. Proc. 1432 (2012) 162-167


baryon spectroscopy

  • how to detectN*/D resonances ?

  • how to measure quantum numbers of N*/D ?

  • how to measure mass and width of N*/D ?

  • how to measure branching ratios ?

  • how to obtain pole postions and residues ?


theoretical poles and experimental bumps

poles in the

complex plane

W

bumps on the

physical axis

W


N* and D states, new in PDG2012

E. Klempt, ATHOS2012, Camogli, Italy:

new

new

new

new

new

new

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 response

to real and virtual photons


detailed look on nucleon resonances

photoabsorption (inclusive cross section)


regime of dynamical models

and ChPT

regime of quark models

and LQCD


theoretical approaches to pion photoproduction

ChPT

DMT

MAID

BnGa

HDT

GICC

SAID


SAID


Isobar models and Dynamical models

DMT

(Dubna-Mainz-Taipei)

MAID

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

isobar models: only Born plus phenomenological terms

dynamical models: include additional pN loop terms similar to cPT


isobar models vs dynamical models

(MAID)

(DMT)


MAID


e.g.

for S11(1535)

s-channel resonance contributions

unitarity is build in through coupling to other open channels:


unitarity cusp at eta threshold

J. Ahrens et al., (GDH and A-2 Collaboration), Phys. Rev. C 74, 045204 (2006)

helicity separated

cross sections

polarized

total cross section

(helicity asymmetry)

unpolarized

total cross section


comparison between MAID and SAID


comparison between MAID and SAID

Roper

P11(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 ds/dW and S, some T, P,very few G, H


currently in CNS-DAC data base for g + p -> p0 + p for W< 2 GeV:

ds/dW9382G28Ox‘7Tx‘0

S1885H24Oz‘7Tz‘0

T 353 E 0 Cx‘0 Lx‘0

P 556 F 0 Cz‘0 Lz'0

mainly only ds/dWand S which count!


comparison of multipoles: MAID – SAID - BonnGatchina

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

imaginary parts of g,p0 multipoles

real parts of g,p0 multipoles


comparison of multipoles: MAID – SAID - BonnGatchina

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


newly measured observables will produce changes

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

ds/dW, S, T with single (beam/target) polarization and

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

here example with preliminary target polarization data from Mainz:


changes with newly maesured polarization observables

MAID, SAID, BnGa and

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

E0+

E2-

BnGa

MAID

SAID

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


The Complete Experiment

with each newly measured polarization observables we can hope

to improve the partial wave analyses

there is a systematic way to go: the complete experiment


what is a complete experiment?

a complete experiment is

a set of polarization observables

that is sufficient to exactly determine

all other possible experiments

and all underlying (complex) amplitudes 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!


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

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

in pion photoproduction:4 complex amplitudes (E,q)16observables are possible8are needed (at least) for a complete experiment 8can be predicted

in pion electroproduction:6 complex amplitudes (E,q)36observables are possible12 are needed (at least) for a complete experiment24 can be predicted

complete experiments in different reactions


complete experimentsfor systemswith 1, 2 and 4 spin degrees of freedom


1.)


2.)

common choice


3.)

common choice

16 observables

analytical solutions with less than 9 obs. are not known


16 observables expressed in helicity amplitudes


16 Polarization Observables in Pion Photoproduction


studies on the complete experiment

earlier studies on the complete amplitude analysis

  • 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

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


requirements for a complete experiment in photoproduction

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.


choose any 8 out of 16 observables

this set does not work!


choose any 8 out of 16 observables

also this set does not work!


choose any 8 out of 16 observables

also this set does not work!


choose any 8 out of 16 observables

this set works!


choose any 8 out of 16 observables

also this set works!


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


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


checking complete experiments

with a trick, Mathematicacan 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 data

we have generated about 108 Monte-Carlo events with the MAID, SAID and BnGa models in steps ofand angular bins of

  • 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 based on 108 Monte-Carlo events

for g,p0 at 320-340 MeV and comparison with real data

MAID

pseudo data

real data


incomplete amplitude analysis with 8 observables

results for an incomplete set of 8 observables

with high precision (numbers directly from MAID)

dσ/dΩ, Σ, T, P, G, H, E, F

W=1217 MeV p(g,p0)p

Chaos


complete amplitude analysis with 8 observables

results for a complete set of 8 observables

with high precision (numbers directly from MAID)

dσ/dΩ, Σ, T, P, G, E, Ox, Cx

W=1217 MeV p(g,p0)p

perfect solution


complete amplitude analysis with 8 observables

results for a complete set of 8 observables

with MAID pseudo data of realistic statistics

dσ/dΩ, Σ, T, P, G, E, Ox, Cx

MAID


overcomplete amplitude analysis with 10 observables

results for an overcomplete set of 10 observables

with MAID pseudo data of realistic statistics

dσ/dΩ, Σ, T, P, G, H, E, F, Ox, Cx

MAID


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 Analysis

  • we must distinguish between 2 kinds of complete analyses:

  • the amplitude analysis that leads to4 amplitudes:Fi(W,q)(but no partial waves)

  • 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 angle

function of energy only


complete analysis of 2. kind

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(q) or Legendre series for energy-angle separation:

e.g.:


requirements for the 2. kind of a complete experiment

Omelaenko (1981)

for a truncated partial wave analysis with Lmax wavesonly 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 D(1232) region with only S+P waves (Lmax= 1)


one possible solution for the 2. kind is:

Omelaenko (1981)

for a truncated partial wave analysis with Lmax wavesonly 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 D(1232) region with only S+P waves (Lmax= 1)


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 Conclusion

  • The Complete Experiment of 1. kind requires 8 well selected observables but it can not give us information on N* physics because it does not give us partial wavesdue to an unknown angle-dependent overall phase f(W,q)

  • The Complete Experiment of 2. kind aims directly on partial waves and requires only 5 well selected observablesthese can be: ds, S, T, P, For: ds, S, T, F, Gor: ds, S, Ox‘, Oz‘, Cz‘ and others

  • The real challenge will come with real world datasuffering from: exp. uncertaintieslimited detector acceptances


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