The shape of the Nucleon from Out of Plane

Transcription

1 The shape of the Nucleon from Out of Plane Some History On sizes and Shapes On out of Plane Some recent data.. Interpreting the data, connecting to theory Past, future and the Bates Legacy C. N. Papanicolas Dep. of Physics, Univ. of Athens Institute of Accelerating Systems and Applications (IASA) MIT, Sept 28,

2 Some History Associated with Bates form 1975 to 2005! Have seen it all! All the eras Rotators Lead Few body FPP Parity OOPS Blast 2

3 How is it done? Thoroughly! Identify the physics, the question Push the instrumentation Get the data Define new ways of analysis Extract the physics, answer the question 3

4 How is it done? Thoroughly! Case Study I: Heavy Nuclei Identify the physics: Nuclear Mean Field and Correlations Push the instrumentation High Resolution (ELSSY!), Energy Loss Define new ways of analysis MIA methods Extract the physics Limits of the mean filed description 4

5 How is it done? Thoroughly! Case Study II: The Shape of the Nucleon Identify the physics: QCD at low energies, nucleon structure Push the instrumentation Out of plane spectrometry (OOPS) Define new ways of analysis Multipole extraction, in search of MIA methods Extract the physics Not there yet! 5

6 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 6

7 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 only protons. 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. 7

8 The signal for deformation in the N Δ transition p(qqq) γ* Μ1, Ε2, C2 Δ(qqq) 1 2 I = J = 1 2 u u d u u d 3 2 I = J = MeV Μ 1+, Ε 1+, S 1+ π o 1232 MeV Spherical M1 Deformed M1, E2, C2 Deformation signal 8

9 Proposal #

10 What do measure? e / γ * e / γ * π + π 0 e M1, E2, C2 e E0+,S0+,M1-,S1- E1+,S1+,M1+, Short Range Physics? Gluon exchange D-state admixtures Long Range Physics? Excite qq pairs from vacuum Shape of pion cloud 10

11 Using the precision of the electromagnetic probe 11

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13 Proposal #

14 Methodology p Η(e,e p)π o π 0 ) alignment precision: 1 mm, 1 mrad Out of plane capability: ~ 65 o 14

15 First Out of Plane Measurement! 15

16 Extract the Information from the Interference Responses Primarily: Sensitive to C2 Primarily: Sensitive to E2 16

17 Dynamical Model of Sato-Lee e.g. PRC 63, (2001) Quark core and pion-cloud contributions Dynamical scattering equation using effective Lagrangian; accounts for off-shell pion interactions effects Need to explore momentum transfer dependence Effect of quark core Effect of quark core + meson cloud 17

18 Electroproduction Results from second generation experiments are now released, they are getting published All 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, 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 (?) 18

19 Results: Q 2 = (GeV/c) 2 Latest compilation of Bates data and comparison with Mainz data 19

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21 Results: Q 2 = 0.20 (GeV/c) 2 Preliminary MAMI: N. Sparveris et al JLab: C. Smith et al } Consistent! 21

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23 VCS on the Delta 23

24 CMR Bates 24

25 Chiral extrapolation NLO chiral extrapolation on the ratios using m π /Μ~δ 2, Δ/Μ~δ. G M1 itself not given. V. Pascalutsa and M. Vanderhaeghen, hep-ph/

26 EMR Bates 26

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28 Getting the physics out n n n n Models without pions fail badly Models without deformation fail badly Models which include the pionic degrees of freedom appear to describe the data adequately well 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! 28

29 Deformed Deformed Spherical Spherical CMR & EMR ± 0.32 stat+sys ± 0.10 mod ± 0.40 stat+sys ± 0.27 mod 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. CNP Eur. Phys. J. Α18, 141 (2003) 29 N. Sparveris et al PRL 94, (2005)

30 Model Errors (Theory & Experiment) Experiment: 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! 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! n Lattice: Statistical uncertainties. Model and systematic? n n EFT: Estimation of next order terms.. Models: Model assumptions, model parameters, fitted experimental values. 30

31 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 ) 31

32 Multipole Extraction: A novel method of Analysis S. Styliaris and cnp Work also by: A.Bernstein, S.Stave and I. Nakawa 32

33 Model Errors 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 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! 33

34 Model Independent Extraction of Multipoles from Nucleon Resonance data n n n Method relies on Satatistical concepts Makes very few assumptions Makes no model assumptions n n Assume that any value for a given multipole is allowed if it is consistent with the principles of physics Le the data constrain the allowed values 34

35 PaStyl Flowchart L = 0 50 Total = (36-5) complex Multipoles Experimental Data Random Variation of ALL Amplitudes Ai (uniformly ±1σ, ± 2σ, ) Unitarization Calculation of Cross Sections Calculation of χ2 Will of course result in solutions with varying χ2 35

36 χ 2 -Distribution Variation of ALL Amplitudes Wider range in the variation yields different ensembles of solutions χ2 After a sufficiently wide range in the variation a CONVERGENCE in χ 2 is reached σ --- 3σ --- 4σ --- 5σ χ2 36

37 Applying χ 2 Cut on SENSITIVE Amplitude A i A i Distribution PROJECTION ALL VALUES χ 2 < 200 χ 2 < 120 χ 2 < 80 χ 2 < 40 37

38 Central value remains stable Uncertainty depends on the χ 2 cut 38

39 Applying χ 2 Cut on NON SENSITIVE Amplitude A i A i Distribution PROJECTION ALL VALUES χ 2 < 200 χ 2 < 120 χ 2 < 80 χ 2 < 40 39

40 Rigorous and elegant method: Do not apply χ2 cuts; weigh the significance of each solution by its likelihood to be correct L1+ Multipole 40

41 Correlations Amplitude Correlations are automatically included through randomization in the ensemble and can be easily investigated. L0 + vs L1 + L0 E2 + vs E2 L2 + 41

42 Bates-Mainz Data (Q 2 =0.127 (GeV/c) 2, W=1232 MeV) Apply the Model Independent Analysis for Multipole Extraction Lcut = 5 42

43 Bates-Mainz Data (Q 2 =0.127 (GeV/c) 2, W=1232 MeV) Total 31 Data Points MAID2003 N. Sparveris et al. 43

44 Non Sensitive Multipole E3+ 44

45 Bates-Mainz Data Q 2 =0.127 (GeV/c) 2 W=1232 MeV L = 0 L = 1 L = 2 L = 3 L = 4 L = 5 45

46 Fitted Value Relative Error MAID-2003 M ± % L ± % L ± % E ± % E ± % L1-4.6 ± % M1-2.5 ± % E ± % E ± % L ± %

47 Bates-Mainz Data (Q 2 =0.127 (GeV/c) 2, W=1232 MeV) σ LT σ E2 1σ Error Band Spherical E1 + =0 L1 + =0 σ TT σ E0 σ LT 47

48 Conclusions The new method is a model independent analysis for identifying sensitivities and extracting Multipole values from experimental data on Nucleon Resonances. The method has been examined extensively with pseudodata and with limited set of experimental data. It is stable and robust. Remaining Issues (work in progress) Self adapting randomization width Additional variation of phases with respect to unitarization Extend the method to handle W dependence 48

49 How is it done? Case Study II: The Shape of the Nucleon Identify the physics: QCD at low energies, nucleon structure Push the instrumentation Out of plane spectrometry (OOPS) Define new ways of analysis Multipole extraction, in search of MIA methods Extract the physics Not there yet! Watch the rest of the world finish the program! 49

50 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 50