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Studying  N  Δπ N with Cross Sections and Polarization Observables

Studying  N  Δπ N 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?. In simple SU(6) quark model, N and  have 3 quarks in s-state (L=0)

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Studying  N  Δπ N with Cross Sections and Polarization Observables

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  1. 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? Shalev Gilad - MIT

  2. 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N•p - vanishes for p = 0, strong for p-wave ( resonance) Relativity – Lower components of Dirac Spinors G. A. Miller, nucl-th/0304076 Why Should the Nucleon be Deformed? Shalev Gilad - MIT

  3. 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 Shalev Gilad - MIT

  4. Multipole Amplitudes . . . Shalev Gilad - MIT

  5. 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) Shalev Gilad - MIT

  6. Response functions Shalev Gilad - MIT

  7. Truncated Legendre Expansion (M1; sp) x-sections helicity ind. Im-type helicity dep. Re-type Shalev Gilad - MIT

  8. Sensitivity to Quadrupole Amplitudes Virtual photons Real photons S1+ in leading terms E1+ in second-order terms Shalev Gilad - MIT

  9. Traditional analysis - Truncated (M1, sp) Legendre Coefficients of Cross-Section Responses Shalev Gilad - MIT

  10. Two high resolution spectrometers (p/p  10-4); DW = 6 msr • High current, high polarization (80%) cw beam • 15 cm LH2 cryotarget - luminosity ≈ 1038 cm2 sec-1 • Focal-plane hadron polarimeter Shalev Gilad - MIT

  11. 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 Q2 and W Each response – a unique combination of contributing multipoles Unique access to Imaginary part of multipoles interferences – phase info Angular, Q2, W Acceptance Q2 = 1 GeV/c Shalev Gilad - MIT

  12. Angular, Q2, W acceptances pq W pq Q2 Also W=123020 Shalev Gilad - MIT

  13. Comparison to CLAS X-Section Results Shalev Gilad - MIT

  14. Maximum Likelihood Method for Responses Maximal use of data; No binning in  or fpp Shalev Gilad - MIT

  15. Extracted responses and models Real type Imaginary type * * * Previously observed * * Larger model variations Smaller model variations • Angular distributions for 14 responses + 2 Rosenbluth combinations • Available for 5X2 (W,Q2) bins; larger model variations far from WΔ Shalev Gilad - MIT

  16. Responses and models (slightly) below resonance (1.1 available) Shalev Gilad - MIT

  17. Responses and models above resonance (1.1 available) Shalev Gilad - MIT

  18. Legendre Anaysis of Responses ------ sp ____ Legendre (as needed) Need terms beyond sp truncation • fit separately R(xCM) for each (W,Q2) bin Shalev Gilad - MIT

  19. Multipole analysis • Represent each amplitude as: • Ai(W,Q2) = Ai(0)(W,Q2) + Ai(W,Q2) • Ai = real or imaginary parts of Ml± , El± , Sl± • Ai(0) =taken from a baseline model • δAi =fitted correction • Fit all σ, Rdata for a specified (W,Q2) 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 Shalev Gilad - MIT

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

  21. 1+ multipole amplitudes P(e,e’p)π Q2=0.9 (GeV/c)2 Available for Q2=1.1; small Q2 dependence (Re2-,Re2+) (Re2-) • Good agreement with models except for ImE1+ • Only ImE1+ sensitive to correlations with other multipoles • Fits NOT sensitive to choice of baseline (MAID or DMT) Shalev Gilad - MIT

  22. Non-resonant multipole amplitudes P(e,e’p)π Q2=0.9 (GeV/c)2 Available for Q2=1.1; small Q2 dependence • Large model variations for M1-; Data shows large rise towards Roper • Large slope in ReS0+ present only in SAID • Relatively strong ReM2- in Δ region; No evidence of appreciable Im 2- Shalev Gilad - MIT

  23. 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: Shalev Gilad - MIT

  24. 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 WΔ (except SAID); different above & below WΔ Shalev Gilad - MIT

  25. Quadrupole Ratios EMR, SMR • Legendre SMR smaller than CLAS • Large difference in EMR between Legendre and Multipole Shalev Gilad - MIT

  26. EMR world data • Large difference between multipole and legendre analyses! • Legendre value consistent with previous data • Approximately Const. With Q2 • Far from pQCD-based predictions of EMR = 1 !! • (helicity conservation) Shalev Gilad - MIT

  27. SMR world data • Larger than EMR • Difference between Legendre and multipole analyses • Legendre value smaller tha CLAS (M1+ donimance?) • Significant slope with Q2 • Far from pQCD-based predictions that RSM = const. Shalev Gilad - MIT

  28. 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-mΔ| Summary Shalev Gilad - MIT

  29. 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 WRoper • 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 Shalev Gilad - MIT

  30. 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 Shalev Gilad - MIT

  31. 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 What is the shape of the nucleon (cont.)? Shalev Gilad - MIT

  32. Helicity-DependentLegendre Coefficients CLAS data K Joo et al., PR C68, 032201 (2003) Shalev Gilad - MIT

  33. RLT, R´LTInterference responses CLAS data K. Joo et al. PRL 88, 122001(2002); PR C68, 032201 (2003) Shalev Gilad - MIT

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

  35. Mainz Unitary Isobar Model Drechsel et al., MAID2000(3) • Resonance amplitudes parametrized to Breit Wigner form • Background includes Born terms, higher resonances • Interpolate between pseudovector coupling at low Q2and pseudoscalar πNN coupling at large Q2 • Adjust Resonance/non-Resonance relative phase in low partial waves (from SAID) to satisfy unitarity • Phenomenological fit to data Shalev Gilad - MIT

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

  37. 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) Shalev Gilad - MIT

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

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