1. MENU 2004 Beijing, ChinaShalev Gilad - MIT Studying  N  Δ  πN with Cross Sections and Polarization Observables Quadrupole Amplitudes in the  *N → Δ Transition Why do we want to measure quadrupole amplitudes? Is the nucleon spherically symmetric?

2. MENU 2004 Beijing, ChinaShalev Gilad - MIT Why Should the Nucleon be Deformed? In simple SU(6) quark model, N and  have 3 quarks in s-state (L=0)  spherically symmetric N  transition is a pure spin-flip M1+ transition Non-central (tensor) forces between quarks S.L. Glashow, Physica 96A, 27 (1979) Deformed pion cloud of N and  - coupling of  to N is g  N  Np  - vanishes for p  = 0, strong for p-wave (  resonance) Relativity – Lower components of Dirac Spinors G. A. Miller, nucl-th/0304076

3. MENU 2004 Beijing, ChinaShalev Gilad - MIT Can We Measure Nucleon Deformation? Intrinsic quadrupole moment (g.s w.f. deformation due to D-state admixture) of nucleon (J=½) cannot be measured directly  Measure quadrupole amplitudes in the N  transition: p( ,  )N or p( ,p)  reactions for E1+ p(e,e’p)  º or p(e,e’  + )n for E1+, S1+ Problems: Resonance properties vs. reaction dynamics poorly known background amplitudes large model dependence - minimize Method: Measure complex multipole amplitudes: small E1+ and S1+ amplitudes interfere with large M1+ amplitudes in x-section combinations, recoil or target polarization (response functions) in π electro-production

4. MENU 2004 Beijing, ChinaShalev Gilad - MIT Multipole Amplitudes lπlπ 2J P N*, Δ* jγjγ lγlγ multipoles 01-1- S 11, S 31 10,2E 0+, S 0+ 11+1+ P 11, P 31 11M 1- 01S 1- 13+3+ P 13, P 33 11M 1+ 21,3E 1+, S 1+ 23-3- D 13, D 33 22M 2- 10,2E 2-, S 2- 25-5- D 15, D 35 22M 2+ 32,4E 2+, S 2+......

5. MENU 2004 Beijing, ChinaShalev Gilad - MIT Origin of N  Quadrupole Amplitude configuration mixing: color hyperfine interaction gives L=2 admixtures Buchmann and Henley hep-ph/0101027 gluon or pion exchange currents with double spin flip Buchmann and Henley, hep-ph/0101027 Quark models predict M1+ 30% too small; E1+, O.O.M. too small in ( ,  )! πN final-state interactions Kamalov and Yang, PRL 83, 4494 (1999)

6. MENU 2004 Beijing, ChinaShalev Gilad - MIT Response functions

7. MENU 2004 Beijing, ChinaShalev Gilad - MIT Truncated Legendre Expansion (M1; sp)  x-sections helicity ind.  Im-type  helicity dep. Re-type

8. MENU 2004 Beijing, ChinaShalev Gilad - MIT Sensitivity to Quadrupole Amplitudes Real photonsVirtual photons S1+ in leading terms E1+ in second-order terms

9. MENU 2004 Beijing, ChinaShalev Gilad - MIT Traditional analysis - Truncated (M1, sp) Legendre Coefficients of Cross-Section Responses

10. MENU 2004 Beijing, ChinaShalev Gilad - MIT Two high resolution spectrometers (  p/p  10 -4 );  = 6 msr Two high resolution spectrometers (  p/p  10 -4 );  = 6 msr High current, high polarization (  80%) cw beam High current, high polarization (  80%) cw beam 15 cm LH 2 cryotarget - luminosity ≈ 10 38 cm 2 sec -1 15 cm LH 2 cryotarget - luminosity ≈ 10 38 cm 2 sec -1 Focal-plane hadron polarimeter Focal-plane hadron polarimeter

11. MENU 2004 Beijing, ChinaShalev Gilad - MIT Angular, Q 2, W Acceptance CM → lab boost folds angular distribution into a  = 13° cone Const. Electron kinematics; 12 proton angles around Significant Out-of-Plane coverage, especially in forward angles, facilitates extraction of several response function in addition to 6 “in-plane” responses Binning in Q 2 and W Each response – a unique combination of contributing multipoles Unique access to Imaginary part of multipoles interferences – phase info Q 2 = 1 GeV/c

12. MENU 2004 Beijing, ChinaShalev Gilad - MIT Angular, Q 2, W acceptances Q2Q2 W  pq  pq Also W=1230  20

13. MENU 2004 Beijing, ChinaShalev Gilad - MIT Comparison to CLAS X-Section Results

14. MENU 2004 Beijing, ChinaShalev Gilad - MIT Maximum Likelihood Method for Responses Maximal use of data; No binning in  or  fpp

15. MENU 2004 Beijing, ChinaShalev Gilad - MIT Extracted responses and models Real typeImaginary type * Previously observed Smaller model variations Larger model variations Angular distributions for 14 responses + 2 Rosenbluth combinations Available for 5X2 (W,Q 2 ) bins; larger model variations far from W Δ * * * *

16. MENU 2004 Beijing, ChinaShalev Gilad - MIT Responses and models (slightly) below resonance (1.1 available)

17. MENU 2004 Beijing, ChinaShalev Gilad - MIT Responses and models above resonance (1.1 available)

18. MENU 2004 Beijing, ChinaShalev Gilad - MIT Legendre Anaysis of Responses fit separately R  (x CM ) for each (W,Q 2 ) bin ------ sp ____ Legendre (as needed) Need terms beyond sp truncation

19. MENU 2004 Beijing, ChinaShalev Gilad - MIT Multipole analysis Represent each amplitude as: A i (W,Q 2 ) = A i (0) (W,Q 2 ) +  A i (W,Q 2 ) A i = real or imaginary parts of M l±, E l±, S l± A i (0) = taken from a baseline model δA i = fitted correction Fit all σ, R data for a specified (W,Q 2 ) bin simultaneously Vary appropriate subset of lower partial waves Higher multipoles from baseline model Enforces symmetries and positivity constraints that are ignored by Legendre analysis Relatively little sensitivity to choice of base model Typically fits 14 angular distributions using only 12-15 parameters

20. MENU 2004 Beijing, ChinaShalev Gilad - MIT Multipole Analysis of Responses Largest improvement in Im-type responses (s, p, Re2-, Re2+) (s, p, Re2-)

21. MENU 2004 Beijing, ChinaShalev Gilad - MIT 1+ multipole amplitudes P(e,e’p)π Q 2 =0.9 (GeV/c) 2 Available for Q 2 =1.1; small Q 2 dependence Good agreement with models except for ImE 1+ Only ImE 1+ sensitive to correlations with other multipoles Fits NOT sensitive to choice of baseline (MAID or DMT) (Re2-,Re2+) (Re2-)

22. MENU 2004 Beijing, ChinaShalev Gilad - MIT Non-resonant multipole amplitudes P(e,e’p)π Q 2 =0.9 (GeV/c) 2 Available for Q 2 =1.1; small Q 2 dependence Large model variations for M 1- ; Data shows large rise towards Roper Large slope in ReS 0+ present only in SAID Relatively strong ReM 2- in Δ region; No evidence of appreciable Im 2-

23. MENU 2004 Beijing, ChinaShalev Gilad - MIT Observations Resonance amplitudes are less well known (below and) above resonance Background amplitudes are very poorly known Below resonance – Born terms Above resonance – Born + higher resonances Need to better know multipoles for constraining model dependence Quadrupole ratios from multipoles:

24. MENU 2004 Beijing, ChinaShalev Gilad - MIT EMR, SMR Values are different for the 2 methods, especially EMR Models are different for the 2 methods – use different formulae Models are similar near W Δ (except SAID); different above & below W Δ

25. MENU 2004 Beijing, ChinaShalev Gilad - MIT Quadrupole Ratios EMR, SMR Legendre SMR smaller than CLAS Large difference in EMR between Legendre and Multipole

26. MENU 2004 Beijing, ChinaShalev Gilad - MIT EMR world data Large difference between multipole and legendre analyses! Legendre value consistent with previous data Approximately Const. With Q 2 Far from pQCD-based predictions of EMR = 1 !! (helicity conservation)

27. MENU 2004 Beijing, ChinaShalev Gilad - MIT SMR world data Larger than EMR Difference between Legendre and multipole analyses Legendre value smaller tha CLAS (M 1+ donimance?) Significant slope with Q 2 Far from pQCD-based predictions that RSM = const.

28. MENU 2004 Beijing, ChinaShalev Gilad - MIT Summary Polarization observables for electro- production of pseudo-scalar mesons are sensitive to interference of non-resonant and non-dominant resonant with dominant amplitudes This is a powerful technique!! Measured simultaneously angular distributions for 16 responses for the first time in Model variations - larger for Im-type responses - smaller for Re-type responses - Increase with |W-m Δ |

29. MENU 2004 Beijing, ChinaShalev Gilad - MIT Summary (cont.) and Outlook Nearly model-independent multipole analysis - Good agreement with models for 1+ (resonant) multipoles except ImE1+ - Many non-resonant multipoles not well known - Strong ImM2- in Δ region - Increasing ImM1- amplitude towards W Roper Deviation from M1+ dominance affects EMR, SMR Future possibilities -Separate R/T – smaller ε for Rosenbluth or for using polarizations (similar to elastic) - Higher Q2 for Δ - η production near S11, etc. - Higher W for Roper

30. MENU 2004 Beijing, ChinaShalev Gilad - MIT So, what is the shape of the nucleon? Buchman obtains similar qualitative answer from 3 models: hep-ph/0207368 proton is prolate (longer at poles) delta is oblate (flatter at poles) Quark model Deformed pion clound Bohr-Mottelson collective model

31. MENU 2004 Beijing, ChinaShalev Gilad - MIT What is the shape of the nucleon (cont.)? G. Miller – infinite numbers of non-spherical shapes: nucl-th/0304076 quark spin parallel to ptoton’s – peanut quark spin anti-parallel to proton’s – bagel Alexandrou - Lattice gauge calculations Nucl-th/0311007 slightly oblate delta

32. MENU 2004 Beijing, ChinaShalev Gilad - MIT Helicity-Dependent Legendre Coefficients CLAS data K Joo et al., PR C68, 032201 (2003)

33. MENU 2004 Beijing, ChinaShalev Gilad - MIT R LT, R´ LT Interference responses CLAS data K. Joo et al. PRL 88, 122001(2002); PR C68, 032201 (2003)

34. MENU 2004 Beijing, ChinaShalev Gilad - MIT SAID - Partial-Wave Analysis of Electroexcitation Parametrizes photo-excitation multipoles A as: t πN = t matrix fit to πN elastic scattering data that enforces Watson’s theorm below π threshold A R – parameterized as a polynomial in E π with correct threshold behavior for each partial wave A B – partial wave of pseudoscalar Born Amplitude A Q – parameterized using Legendre functions of 2 nd kind R. A. Arndt et al. SAID

35. MENU 2004 Beijing, ChinaShalev Gilad - MIT Mainz Unitary Isobar Model Resonance amplitudes parametrized to Breit Wigner form Background includes Born terms, higher resonances Interpolate between pseudovector coupling at low Q 2 and pseudoscalar πNN coupling at large Q 2 Adjust Resonance/non-Resonance relative phase in low partial waves (from SAID) to satisfy unitarity Phenomenological fit to data Drechsel et al., MAID2000(3)

36. MENU 2004 Beijing, ChinaShalev Gilad - MIT Dynamical Model - DMT Based on MAID πN re-scattering (FSI) yields unitarity decomposition into background and “bare” γ v N → Δ potentials “dressed” by FSI t πN from πN data Re-scattering important for M1+; dominant for E1+, S1+ S. S. Kamalov et al. PRC 64 032201 (2001)

37. MENU 2004 Beijing, ChinaShalev Gilad - MIT Dynamical Model of Sato-Lee Quark core and pion-cloud contributions Solves dynamical scattering equation using effective Lagrangian Accounts for off-shell pion interactions effects Main contribution to quadrupole amplitudes from pion cloud PRC 63, 055201 (2001)

38. MENU 2004 Beijing, ChinaShalev Gilad - MIT Other models Relativistic quark models (CapsticK, Warnes) Dispersion relations models (Aznauryan) Chiral quark soliton models (Silver) None works very well!!!