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The shape of the Nucleon The shape of the Nucleon from Out of Planefrom Out of Plane

Some HistoryOn sizes and ShapesOn out of PlaneSome recent data..Interpreting the data, connecting to theoryPast, future and the Bates Legacy

C. N. Papanicolas

Dep. of Physics, Univ. of Athens

Institute of Accelerating Systems and Applications (IASA)

MIT, Sept 28, 2006

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Some History

“Rotators”…LeadFew body…FPPParityOOPSBlast

Associated with Bates form 1975 to 2005! Have seen it all! All the eras

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How is it done?

Identify the physics, the questionPush the instrumentationGet the dataDefine new ways of analysisExtract the physics, answer the question

Thoroughly!

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How is it done?

Identify the physics:Nuclear Mean Field and Correlations

Push the instrumentationHigh Resolution (ELSSY!), Energy Loss

Define new ways of analysisMIA methods

Extract the physicsLimits of the mean filed description

Thoroughly!Case Study I: Heavy Nuclei

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How is it done?

Identify the physics:QCD at low energies, nucleon structure

Push the instrumentationOut of plane spectrometry (OOPS)

Define new ways of analysisMultipole extraction, in search of MIA methods

Extract the physicsNot there yet!

Thoroughly!Case Study II: The Shape of the Nucleon

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Measuring shapes in the microcosmos:

•MISCONCEPTIONS•The shape is not a well defined quantity in Q.M.

•Deformation can be measured only for objects having J≥1

•Shape can be measured only for objects having J≥1

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Where do we measure hadron deformation?The only stable hadron is the proton.

Theoretically, mesons and unstable baryons can be studied.

Experimental investigation in the near future will involve onlyprotons. A J= ½ system, with a very complicated excitation spectrum.

The shape of unstable hadrons, the issue of the shape (even size) of hadrons within the nuclear medium, are NOT within reach of experimental investigation.

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u du

u d

u

γ* Μ1 , Ε2 , C2

Μ1+ , Ε1+ , S1+ πo

p(qqq)

I = J =

938 MeV

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Δ(qqq)

I = J =

1232 MeV

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Spherical ⇒ M1

Deformed ⇒ M1 , E2 , C2Deformation signal

The signal for deformation in the N ⇒ Δ transition

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Proposal #87-05

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e

e /γ *

π +What do measure?π 0

Short Range Physics?

•Gluon exchange → D-state admixtures

Long Range Physics?

•Excite qq pairs from vacuum

• Shape of pion cloud

e

e /γ *

M1, E2, C2

E0+,S0+,M1-,S1-E1+,S1+,M1+,…

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Using the precision of the electromagnetic probe

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Proposal #87-05

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p

π0

)

alignment precision: 1 mm , 1 alignment precision: 1 mm , 1 mradmrad

Out of plane capability: ~ 65Out of plane capability: ~ 65oo

ΗΗ((e,e’pe,e’p))ππoo

Methodology Methodology

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First Out of Plane Measurement!

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Extract the Information from the Interference Responses

Primarily: Sensitive to C2

Primarily: Sensitive to E2

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Dynamical Model of Sato-Leee.g. PRC 63, 055201 (2001)

• Quark core and pion-cloud contributions

• Dynamical scattering equation using effective Lagrangian; accounts for off-shell pioninteractions effects

• Need to explore momentum transfer dependence

Effect of quark core

Effect of quark core + meson cloud

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Electroproduction

Results from second generation experiments are now released, they are getting publishedAll possible reaction channels are being explored. Two general trends:

Measure with high precision (high luminosity, high resolution) crititically important points to isolate the important amplitude (Bates/OOPS, Mainz, FPP@Hall-A….)

Measure «everything» (maximum angular and invariant mass coverage). Get a global picture of the picture. (Bonn, Hall B, Hall C..)

Consistent picture has emerged (?)

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Results: Q2 = 0.127 (GeV/c)2

Latest compilation of Bates data and comparison with Mainz data

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Results: QResults: Q22 = 0.20 (GeV/c)= 0.20 (GeV/c)22Preliminary

MAMI: N. Sparveris et alJLab: C. Smith et al } Consistent!

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VCS on the Delta

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CMR Bates

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Chiral extrapolation

NLO chiral extrapolation on the ratios using mπ/Μ~δ2 , Δ/Μ~δ. GM1 itself not given.

V. Pascalutsa and M. Vanderhaeghen, hep-ph/0508060

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EMRBates

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Getting the physics outn Models without pions fail badlyn Models without deformation fail badlyn Models which include the pionic degrees of freedom

appear to describe the data adequately welln Lattice QCD and EFTs appear to be within reach of

accurate description of the data

Caution: Model uncertainties both in theory and experiment are not under control!

Comparison is therefore only qualitative!

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Experiment:Extract multipoles by assuming that “not known” multipoles are fixed by a model. The spread of solutions resulting from credible models provides a “measure” of model error.Ad hoc. Not quantitative, theory dependent.

-2.00 ± 0.40stat+sys ± 0.27mod-6.27 ± 0.32stat+sys ± 0.10modCMR & EMR

CNP Eur. Phys. J. Α18, 141 (2003)N. Sparveris et al PRL 94, 022003 (2005)

Deformed

Spherical

Deformed

Spherical

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Model Errors (Theory & Experiment)

n Lattice: Statistical uncertainties. Model and systematic?n EFT: Estimation of next order terms..n Models: Model assumptions, model parameters, fitted

experimental values.

Theory:Theory: Calculated amplitudes and their ratios are characterized by model error and model parameters uncertainty. So far we have only seen very little discussion at best!

ExperimentExperiment: Extracted amplitudes and their ratios (EMR,CMR) are characterized by statistical, systematic and model error. Model error often dominates. So far we have only guestimates for it, at best!

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Getting the physics out (II)n A situation reminiscent of the 70s in single arm

electron scattering:

n Very precise and consistent data, but could not get the physics out because of simplistic model interpretation.

Resolution: Introduction of Model independent techniques in the reconstruction of charge and magnetization densities (Friar, Negele,.. J. Heisenberg…)

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Multipole Extraction: Multipole Extraction: A novel method of AnalysisA novel method of Analysis

S. Styliaris and cnp

Work also by: A.Bernstein, S.Stave and I. Nakawa

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Model Errors

n Extracted amplitudes and their ratios (EMR, CMR) are characterized by statistical, systematic and model error.

n Model error often dominates.

n So far we have only guestimates, at best!

Usual procedure followed:Extract multipoles by assuming that “not known” multipoles(typically only 3 to 4, “dominant”) are fixed by a model.

Estimate model error by extracting these multipoles using all available “reasonable” models. Spread in values is taken to be indicative of model error

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Model Independent Extraction of Multipoles from Nucleon Resonance data

n Method relies on Satatistical conceptsn Makes very few assumptionsn Makes no model assumptions

n Assume that any value for a given multipole is allowed if it is consistent with the principles of physics

n Le the data constrain the allowed values

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Random VariationRandom Variationof of ALLALL AAmplitudes Aimplitudes Ai

(uniformly (uniformly ±±11σσ, , ±± 22σσ, , ……))UnitarizationUnitarization

L = 0L = 0……55Total = (36Total = (36--5) complex 5) complex

MultipolesMultipoles

Calculation ofCross Sections

Experimental Data

Will of course Will of course result in solutions result in solutions with varying with varying χ2

PaStyl Flowchart

Calculation of χ2

36χχ22

------ 2σ2σ------ 3σ3σ------ 4σ4σ------ 5σ5σ

χχ22

χ2 -Distribution

Variation Variation ofof

ALL AmplitudesALL Amplitudes

Wider range Wider range in the in the variation yields different variation yields different ensembles of solutionsensembles of solutions

After a sufficiently After a sufficiently wide range in the wide range in the variation variation a a CONVERGENCECONVERGENCE in in χχ22 is reached.is reached.

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PROJECTIONPROJECTION

ALL VALUESALL VALUES

χχ22 < 200< 200

Applying Applying χχ22 Cut on Cut on SENSITIVESENSITIVEAmplitude AAmplitude Aii

χχ22 < < 8800

χχ22 < < 112020

χχ22 < < 4400

AAii DistributionDistribution

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Uncertainty depends on Uncertainty depends on thethe χχ22 cutcut

Central value remains stableCentral value remains stable

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PROJECTIONPROJECTION

Applying Applying χχ22 Cut on Cut on NON SENSITIVENON SENSITIVE

Amplitude AAmplitude Aii

ALL VALUESALL VALUES

χχ22 < 200< 200

χχ22 < < 8800

χχ22 < < 112020

χχ22 < < 4400

AAii DistributionDistribution

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L1+ L1+ MultipoleMultipole

Rigorous and elegant method:Do not apply χχ22 cuts; weigh the significance of each solution by its likelihood to be correct

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L0L0++ vsvs E2E2++L0L0++ vsvs L1L1++ E2E2++ vsvs L2L2++

CorrelationsAmplitude Correlations are automatically included through randomization in the ensemble and can be easily investigated.

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BatesBates--Mainz Data Mainz Data (Q(Q22=0.127 (GeV/c)=0.127 (GeV/c)22 , W=1232 MeV), W=1232 MeV)

Apply the Model Independent Analysis for Multipole ExtractionApply the Model Independent Analysis for Multipole Extraction

Lcut = 5Lcut = 5

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BatesBates--Mainz Data (QMainz Data (Q22=0.127 (GeV/c)=0.127 (GeV/c)22 , W=1232 MeV), W=1232 MeV)

Total 31 Data PointsTotal 31 Data Points

MAID2003MAID2003 N. N. SparverisSparveris et al.et al.

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Non Sensitive MultipoleE3+

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L = 0L = 0

L = 5L = 5L = 4L = 4

L = 3L = 3L = 2L = 2

L = 1L = 1

Bates-Mainz Data

Q2=0.127 (GeV/c)2

W=1232 MeV

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0.186185 %0.07 ± 0.13L2+L2+

2.525136 %1.10 ± 1.50E2E2--

0.426100 %0.32 ± 0.32E2+E2+

4.23788 %2.5 ± 2.2M1M1--

3.14350 %4.6 ± 2.3L1L1--

13.8025 %12.0 ± 3.0E0+E0+

1.36515 %1.12 ± 0.17E1+E1+

7.17014 %4.10 ± 0.56L0+L0+

1.4258 %1.24 ± 0.10L1+L1+

40.7900.6 %40.96 ± 0.23M1+M1+

MAIDMAID--20032003Relative ErrorRelative ErrorFitted ValueFitted Value

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BatesBates--Mainz Data (QMainz Data (Q22=0.127 (GeV/c)=0.127 (GeV/c)22 , W=1232 MeV), W=1232 MeV)

σσLTLT

σσTTTT σσE0E0

σσE2E2

σσLTLT’’

11σ σ Error BandError Band

SphericalSphericalE1E1++=0=0L1L1++=0 =0

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ConclusionsConclusions•• The new method is a The new method is a model independentmodel independent analysis for analysis for identifying sensitivities and extracting Multipole values identifying sensitivities and extracting Multipole values from experimental data on Nucleon Resonances.from experimental data on Nucleon Resonances.

•• The method has been examined extensively with The method has been examined extensively with pseudodatapseudodata and with limited set of experimental data. and with limited set of experimental data. It is It is stable and robust.stable and robust.

Remaining Issues (work in progress)Remaining Issues (work in progress)

• Self adapting randomization width

• Additional variation of phases with respect to unitarization

• Extend the method to handle W dependence

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How is it done?

Identify the physics:QCD at low energies, nucleon structure

Push the instrumentationOut of plane spectrometry (OOPS)

Define new ways of analysisMultipole extraction, in search of MIA methods

Extract the physicsNot there yet!

Watch the rest of the world finish the program!

Case Study II: The Shape of the Nucleon

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The MIT/Bates way!Thoroughly, thoughtfully and with joy!

We have reached the end of the road. Bates will no longer be. We have arrived at the end. At Ithaca.

Ithaca bestowed upon you the marvelous journey: If not for her you would never have set out.But she has nothing left to impart you.

If you find Ithaca wanting, it’s not that she’s deceived you.That you have gained so much wisdom and experience will have told you everything of what such Ithacas mean.

Costa Cavafy