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Elastic Form Factors of the Proton, Neutron and Deuteron

INPC2007, Tokyo, June 3-8, 2007. Elastic Form Factors of the Proton, Neutron and Deuteron. Michael Kohl. MIT-Bates, Middleton, MA 01949 USA. Outline. Introduction, motivation and formalism Traditional and new techniques Overview of experimental data Theoretical calculations Proton

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Elastic Form Factors of the Proton, Neutron and Deuteron

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  1. INPC2007, Tokyo, June 3-8, 2007 Elastic Form Factors of the Proton, Neutron and Deuteron Michael Kohl MIT-Bates, Middleton, MA 01949 USA

  2. Outline • Introduction, motivation and formalism • Traditional and new techniques • Overview of experimental data • Theoretical calculations • Proton • Low Q2: Pion cloud effect • High Q2: Proton form factor ratio and two-photon exchange Neutron • Electric and magnetic form factors Deuteron • Unpolarized structure functions A and B • Separation of charge and quadrupole form factor Nucleon Deuteron

  3. Elastic Electromagnetic Form Factors … • Fundamental quantities • Describe internal structure of the nucleons and the deuteron • Related to spatial distribution of charge and magnetism • Rigorous tests of nucleon and deuteron models • Ultimately calculable by Lattice-QCD • Input for nuclear structure and parity violation experiments • 50 years of ever increasing activity • Tremendous progress in experiment and theory over last decade • New techniques / polarization experiments • Unexpected results

  4. (Hadronic) Structure and (EW) Interaction Factorization! Structure Interaction s(structured object) |Form factor|2 = s(pointlike object) → Interference! Probe Object →Utilize spin dependence of electromagnetic interaction to achieve high precision Born Approximation Inelastic Elastic Structure Hadronic object Electroweak probe Interaction Lepton scattering

  5. The Beginnings R. HofstadterNobel prize 1961 ep-elastic Finite size of the proton ed-elastic Finite size + nuclear structure

  6. Nucleon Elastic Form Factors • General definition of the nucleon form factor • Sachs Form Factors • In One-photon exchange approximation above form factors are observables of elastic electron-nucleon scattering

  7. Rosenbluth Separation GE2 tGM2 θ=180o θ=0o

  8. GpE and GpM from Unpolarized Data • charge and magnetization density • Dipole form factor within 5% for Q2 < 10 (GeV/c)2

  9. Nucleon Form Factors and Polarization • Double polarization in elastic/quasielastic ep or en scattering:Recoil polarization or (vector) polarized target • Polarized cross section • Double spin asymmetry = spin correlation • Asymmetry ratio (“Super ratio”)independent of polarization or analyzing power 1,2H(e,e’p), 1,2H(e,e’p), 2H(e,e’n), 2H(e,e’n)

  10. Recoil Polarization Technique • Pioneered at MIT-Bates • Pursued at Hall A and MAMI A1 • In preparation for Hall C V. Punjabi et al., Phys. Rev. C71 (2005) 05520 Focal-plane polarimeter Secondary scattering of polarizedproton from unpolarized analyzer Spin transfer formalism to account for spin precession through spectrometer

  11. Proton Form Factor Ratio Jefferson Lab Dramatic discrepancy! • All Rosenbluth data from SLAC and Jlab in agreement • Dramatic discrepancy between Rosenbluth and recoil polarization technique • Multi-photon exchange considered best candidate

  12. Proton Form Factor Ratio Iachello 1973: Drop of the ratio alreadysuggested by VMD F. Iachello et al., PLB43 (1973) 191F. Iachello, nucl-th/0312074 1 mpGpE/GpM 0 0 2 4 6 8 10 Q2/(GeV/c)2 A.V. Belitsky et al., PRL91 (2003) 092003 G. Miller and M. Frank, PRC65 (2002) 065205 S. Brodsky et al., PRD69 (2004) 076001 Quark angular momentum Helicity non-conservation  Q F2/F1 = const. (contradicting pQCD)

  13. Two-Photon Exchange Two-photon exchange theoretically suggested • P.G. Blunden, W. Melnitchouk, and J.A. Tjon, PRC72 (2005) 034612, PRL91 (2003) 142304 • P.A.M. Guichon and M. Vanderhaeghen, PRL91, 142303 (2003) • M.P. Rekalo and E. Tomasi-Gustafsson,EPJA22 (2004) 331 • Y.C. Chen et al., PRL93 (2004) 122301 • A.V. Afanasev and N.P. Merenkov, PRD70 (2004) 073002 Experiment proposals to verify hypothesis: e+/e-: CLAS/PR04-116 Novosibirsk/VEPP-3 BLAST@DORIS/DESY SSA: PR05-15 e-dep.: PR04-119 (pol.), PR05-017 (unp.)

  14. New Measurements at high Q2 • Extension proposed at Jefferson Lab • Hall C PR01-109/PR04-108 recoil polarization to run in fall 2007 • Hall C PR05-017 Super-Rosenbluth Q2 = 0.9 - 6.6 (GeV/c)2 now running M.K. Jones et al., PRC74 (2006) 035201 Polarized Target: Independent verification crucial Polarized internal target / low Q2: BLAST

  15. BLAST at MIT-Bates Bates Large Acceptance Spectrometer Toroid • Symmetric, large acceptance, general purpose detectorDetection of e±, p±, p, d, n • Longitudinally polarized electrons in SHR850 MeV, 200 mA, Pe = 65% • Highly polarized internal gas target of pure H and D (Atomic Beam Source)6 x 1013 atoms/cm2, L = 6 x 1031/(cm2s), PH/D = 80%

  16. Separately prepare mI = +½, -½ (hydrogen) and mI = +1, 0, -1 (deuterium)with sextupoles and RF transitions • Switch between states every 5 minutes ABS polarized target Hydrogen Deuterium

  17. * Proton Form-Factor Ratio mpGpE/GpM C.B. Crawford et al., PRL98 (2007) 052301 • Impact of BLAST data combined with cross sections on separation of GpE and GpM • Errors factor ~2 smaller • Reduced correlation • Deviation from dipole at low Q2! *Ph.D. work of C. Crawford (MIT) and A. Sindile (UNH)

  18. New Measurements on Proton at low Q2 Hall A PR07-004 Recoil polarization LEDEX PR05-004, to be published soon Mainz A1 Rosenbluth

  19. Neutron Electric Form Factor GnE BLASTMC (e,e’n) (e,e’p) • GnE small, hard to measure,least known only to 10-20% • Amplification by interference with GnM • No free neutron target → quasi-elastic scattering 2H(e,e’n) • GnE(0) = Z = 0distribution of net-zero charge→ role of pion cloud • Input for interpretation of parity violation electron scattering

  20. * Neutron Electric Form Factor GnE • GnE world data fromunpolarized ed-elastic • GnE world data fromdouble pol. Experimentsincluding BLAST 2007 • BLAST fit<r2n> = -0.115 fm2→ Pion cloud effect? • Theoretical models • Dispersion theory+ error band PRELIMINARY *Ph.D. work of V. Ziskin (MIT) and E. Geis (ASU)

  21. Transverse radiusfrom GPD G. Miller, nucl-th/0705.2409 Neutron Electric Form Factor GnE Charge form factor ↔ Charge distribution PRELIMINARY Breit frame PRELIMINARY Forbidden interpretation asrest charge distribution r (fm)

  22. Future Measurements of GnE xMAMI 3He(e,e’n) GEn x

  23. d(e,e’n) d(e,e’p) Neutron Magnetic Form Factor GnM • Pre-polarization era • GnM world data fromunpolarized experiments • Cross section ratioquasielastic • Polarization era • GnM world data + 3He • + CLAS preliminary • VMD/Dispersion Theory + BLAST preliminary

  24. Nucleon Elastic Form Factors Before JLab and recent non-JLab Data

  25. Nucleon Elastic Form Factors Today, with Available JLab Data Data taken; analysis underway

  26. Nucleon Elastic Form Factors Today, with Available JLab Data and Planned GEp Extension

  27. Nucleon Elastic Form Factors EM form factors provide a testing ground for theories constructing nucleons from quarks and glue

  28. Deuteron

  29. Deuteron Degrees of Freedom e’ Nucleon-nucleon potential: from one-pion exchange to short-range repulsion p e’ e n p Beyond nucleons and mesons: Isobar configurations, 6-quarks cluster (hidden color)? p,r,w e’ e n Isoscalar meson-exchange currents e e’ e Asymptotic regime: perturbative QCD Low Q Intermediate Q High Q

  30. NN Interaction Potential Ms=0 Ms= 1 Structure ↔ Interaction • Phenomenological NN potentials: OPE + 2-body + … PD=4-6% ↔ tensor force • Bound state (structure) generatedby interaction potential minimum • Repulsive core • Qd problem / pNN coupling Tensor force generates bound deuteron state

  31. * * Elastic Electron-Deuteron Scattering • Spin 1 ↔ three elastic form factors GdC, GdQ, GdM • Quadrupole momentM2dQd = GdQ(0) = 25.83 • GdQ↔ Tensor force, D-wave • Unpolarized elastic cross section • Polarized cross section

  32. A and B

  33. Deuteron Structure Function A(Q2) Gilman and Gross, JoPG28 (2002) R37 High Q2: Hall A / C results compatible but shifted by ~10% Hall A Hall C Low Q2: Mainz/Saclay discrepancy: 8% in A, 100% in GnE Jlab Hall A / PR05-004: Data 2006, analysis in progress Simon 1981 LEDEX Platchkov 1990

  34. Deuteron Structure Function B(Q2) • High-Q: First minimum unconfirmed • Location of node and of second maximumquite uncertain Measurements on B to be extended up to ~12 fm-1 (Petratas, PAC 2008) Low-Q: Same Mainz data consistent

  35. Deuteron Polarization Experiments The deuteron cross section depends on the deuteron alignment Polarized target (T20) Recoil polarization (t20) d d e e e’ e’ Atomic gas in storage ring Novosibirsk NIKHEF Bates/BLAST Cryogenic solid target in extracted beam Bonn Bates/Argonne3He(d,p) Bates/AHEADH(d,p) JLab/POLDER H(d,pp) External calibration required Polarimeter analysis challenging Target polarization measurement challenging Data analysis “straightforward”

  36. Tensor-pol. Elastic ed Scattering • Tensor asymmetry and tensor analyzing powers • T20dominant, T21 significant, T22small • Global fit analysis to determine GdC, GdQand GdMfrom world data + BLAST

  37. * Tensor Analyzing Power T20 PRELIMINARY *Ph.D. work of C. Zhang (MIT)

  38. * Tensor Analyzing Powers T20 and T21 PRELIMINARY PRELIMINARY *Ph.D. work of C. Zhang (MIT)

  39. GQ(Q) GC and GQ PRELIMINARY GC(Q)

  40. Node of GC PRELIMINARY GC(Q)

  41. Node of GC GC(Q) Node of GC discovered 1994 at MIT-Bates Location confirmed with Jlab, VEPP-3, and BLAST 4.19 ± 0.05 fm-1 PRELIMINARY

  42. Vector-pol. Elastic ed Scattering Unpolarized cross section Polarized cross section Polarization observables Can extract GM independently of back angles measurements (B) GC GQ GM Spin 1

  43. Vector-pol. Elastic ed Scattering • Beam-target vector asymmetry and vector spin correlation parameters • Te10small, Te11 dominant • Determine GdM at low Q2 from Te11,T20 and world data on A(Q2)

  44. * Vector observables Te10, Te11, and GdM PRELIMINARY PRELIMINARY *Ph.D. work of P. Karpius (UNH)

  45. Nonrelativistic potential models From the impulse approximation (NRIA) to the inclusion of meson-exchange currents

  46. Relativistic calculation framework Quantum Field Theory (explicitly covariant) Quantum Mechanics (equation of motion from different representations of Poincaré group) Bethe-Salpeter (4D) 3D-reductions Light-front dynamics Light-front form Point form Instant form Chung…, Strikman… Lev, Pace, Salme Spectator nucleon on-shell Integration over relative energy (ET) Allen, Klink, Polyzou… Gross, Van Orden … Devine, Phillips, Wallace Carbonell, Karmanov... Cooke, Miller… Forest, Schiavilla 2 nucleons equally off mass shell Hummel, Tjon…

  47. Chiral Effective Field Theory The Qd problem D. Phillips, J. Phys. G 34, 365 (2007) BLAST (preliminary)

  48. Summary • Nucleonand Deuteron electromagnetic elastic form factors • Tremendous progress during last decade High precision, low systematics through polarization experimentsWorldwide activity at its peak • Nucleon: • Deuteron: • High-Q2 surprise in GpE/GpM; strong impact on theoretical pictureEvidence for two-photon exchange effects • New precise picture of GnE for Q2<1.5 (GeV/c)2, GnM <5 (GeV/c)2 • Evidence for structure beyond GDipole at low Q2in all form factors • Precision measurement of T20allows to separate GCand GQ • First measurement of Te11 allows to determine GM at low Q2 • Some problems in data unresolved • Progress in theory: Relativistic calculations, Chiral EFT

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