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Kees de Jager Jefferson Lab NUCLAT April 21 - 22, 2008

Nucleon Electro-Weak Form Factors. g. Z 0. General Introduction Electromagnetic Form Factors Formalism Neutron Proton Parity Violation Formalism Strange Form Factors Summary. Kees de Jager Jefferson Lab NUCLAT April 21 - 22, 2008. Thomas Jefferson National Accelerator Facility.

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Kees de Jager Jefferson Lab NUCLAT April 21 - 22, 2008

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  1. Nucleon Electro-Weak Form Factors g Z0 • General Introduction • Electromagnetic Form Factors • Formalism • Neutron • Proton • Parity Violation • Formalism • Strange Form Factors • Summary Kees de Jager Jefferson Lab NUCLAT April 21 - 22, 2008 Thomas Jefferson National Accelerator Facility

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

  3. Kinematics • Q2 > 0 space-like region, studied through elastic electron scattering • Q2 < 0 time-like region, studied through creation or annihilation • e+ + e- -> N + N or N + N -> e+ + e- _ _

  4. Fundamental ingredients in “Classical” nuclear theory • A testing ground for theories constructing nucleons from quarks and gluons • Provides insight in spatial distribution of charge and magnetization • Wavelength of probe can be tuned by selecting momentum transfer Q: • < 0.1 GeV2 integral quantities (charge radius,…) • 0.1-10 GeV2 internal structure of nucleon > 20 GeV2 pQCD scaling • Caveat: If Q is several times the nucleon mass (~Compton wavelength), dynamical effects due to relativistic boosts are introduced, making physical interpretation more difficult Nucleon Electro-Magnetic Form Factors

  5. Formalism g Dirac (non-spin-flip) F1 and Pauli (spin-flip) F2 Form Factors with E (E’) incoming (outgoing) energy,  scattering angle,  anomalous magnetic moment and  = Q2/4M2 Alternatively, Sachs Form Factors GEand GM can be used In the Breit (centre-of mass) frame the Sachs FF can be written as the Fourier transforms of the charge and magnetization radial density distributions

  6. The Pre-JLab Era • Stern (1932) measured the proton magnetic moment µp ~ 2.5 µDirac • indicating that the proton was not a point-like particle • Hofstadter (1950’s) provided the first measurement of the proton’s radius through elastic electron scattering • Subsequent data (≤ 1993) were based on: • Rosenbluth separation for proton, • severely limiting the accuracy for GEpat Q2 > 1 GeV2 • Early interpretation based on Vector-Meson Dominance • Good description with phenomenological dipole form factor: corresponding to  (770 MeV) and (782 MeV) meson resonances in timelike region and to exponential distribution in coordinate space

  7. Global Analysis (1995) P. Bosted et al. PRC 51, 409 (1995) Three form factors very similar GEn zero within errors -> accurate data on GEn early goal of JLab

  8. Modern Era • Akhiezer et al., Sov. Phys. JETP 6, 588 (1958) and • Arnold, Carlson and Gross, PR C 23, 363 (1981) • showed that: • accuracy of form-factor measurements can be significantly improved by measuring an interference term GEGM through the beam-helicity asymmetry with a polarized target or with recoil polarimetry • Had to wait over 30 years for development of • Polarized beam with • high intensity (~100 µA) and high polarization (>70 %) • (strained or superlattice GaAs, high-power diode/Ti-Sapphire lasers) • Beam polarimeters with 1-3 % absolute accuracy • Polarized targets with a high polarization or • Ejectile polarimeters with large analyzing powers

  9. Double Polarization Experiments to Measure GnE • Study the (e,e’n) reaction from a polarized ND3 target • limitations: low current (~80 nA) on target • deuteron polarization (~25 %) • Study the (e,e’n) reaction from a LD2 target and • measure the neutron polarization with a polarimeter limitations: Figure of Merit of polarimeter • Study the (e,e’n) reaction from a polarized 3He target • limitations: current on target (12 µA) • target polarization (40 %) • nuclear medium corrections

  10. GnE Experiment with Neutron Polarimeter • Use dipole to precess neutron spin • Up-down asymmetry  proportional to neutron sideways polarization • GE/GM depends on phase shift w.r.t. precession angle 

  11. Galster: a parametrization fitted to old (<1971) data set of very limited quality Neutron Electric Form Factor GEn Schiavilla and Sick analyzed data on deuteron elastic quadrupole form factor Most recent results (Mainz, JLab) are in excellent agreement, even though all three different techniques were used For Q2 > 1 GeV2 data hint that GEn has similar Q2-behaviour as GEp

  12. Exclusive QE scattering: 3He(e,e′n) 7 Iron/scintillator sandwich planes Q2 = 1.3, 1.7, 2.5, 3.5 GeV2 n Target polarization ~50% Beam polarization 84% 2 veto planes e e′

  13. First physics result from Hall A GEn • 1.7 GeV2 datum is well above Galster • Nuclear corrections include neutron polarization and FSI estimate (5%) • Present error (∼20%) dominated by preliminary “neutron dilution factor”, and is expected to be ∼7% stat. and 8% syst. with further analysis • 3.4 GeV2 datum, however, is on top of Galster

  14. Old method: quasi-elastic scattering from 2H large systematic errors due to subtraction of proton contribution Measuring GnM • Measure (en)/(ep) ratio • Luminosities cancel • Determine neutron detector efficiency • On-line through e+p->e’+π+(+n) reaction (CLAS) • Off-line with neutron beam (Mainz) • Measure inclusive quasi-elastic scattering off polarized 3He RT’ directly sensitive to (GMn)2

  15. Measurement of GnM at low Q2

  16. Preliminary CLAS results for GMn A systematic difference of several % between results ( ) in Q2 range 0.4 - 0.8 GeV2. A final analysis and paper from CLAS is coming soon. Reminder that at least two independent experiments are always needed.

  17. Early Measurements of GEp • relied on Rosenbluth separation • measure d/d at constant Q2 • GEp inversely weighted with Q2, increasing the systematic error above Q2 ~ 1 GeV2 At 6 GeV2R changes by only 8% from =0 to =1 if GEp=GMp/µp Hence, measurement of GEp with 10% accuracy requires 1.6% cross-section measurement

  18. Spin Transfer Reaction 1H(e,e’p) • No error contributions from • analyzing power • beam polarimetry

  19. Recoil Polarization Measurement Focal-Plane Polarimeter Observed angular distribution

  20. JLab Polarization Transfer Data • E93-027 PRL 84, 1398 (2000) Used both HRS in Hall A with FPP • E99-007 PRL 88, 092301 (2002) used Pb-glass calorimeter for electron detection to match proton HRS acceptance • Reanalysis of E93-027 (Punjabi, nucl-ex/0501018) Using corrected HRS properties • No dependence of polarization transfer on any of the kinematic variables

  21. Super-Rosenbluth (E01-001) • I. Qattan et al. (PRL 94, 142301 (2005)) • Detect recoil protons in HRS-L to diminish sensitivity to: • Particle momentum • Particle angle • Rate • Use HRS-R as luminosity monitor • Very careful survey Rosenbluth Pol Trans MC simulations

  22. Rosenbluth Compared to Polarization Transfer • John Arrington performed detailed reanalysis of SLAC data • Hall C Rosenbluth data (PRC 70, 015206 (2004)) in agreement with SLAC data • No reason to doubt quality of either Rosenbluth or polarization transfer data • Investigate possible theoretical sources for discrepancy

  23. Two-Photon Exchange • Proton form factor measurements • Comparison of precise Rosenbluth and polarization measurements of GEp/GMp show clear discrepancy at high Q2 • Two-photon exchange corrections believed to explain the discrepancy P.A.M.Guichon and M.Vanderhaeghen, PRL 91, 142303 (2003) • Compatible with e+/e- ? • Yes: previous data limited to low Q2 or small scattering angle • Still lack direct evidence of effect on cross section • Transverse single spin asymmetry is the only observable in elastic e-p where TPE observed Chen et al., PRL 93, 122301 (2004)

  24. Two-Photon Exchange Measurements • Comparisons of e+-p and e--p scattering [VEPP-III,JLab-Hall B, BLAST@DORIS] • ε dependence of polarization transfer and unpolarized σe-p [JLab-Hall C] • More quantitative measure of the discrepancy • Test against models of TPE at both low and high Q2 • TPE effects in Born-forbidden observables [JLab-Hall A, Hall C, Mainz] • Target single spin asymmetry Ayin e-n scattering • Induced polarization pyin e-p scattering • Vector analyzing power AN in e-p scattering Evidence (3s level) for TPE in existing data J. Arrington, PRC 69, 032201(R) (2004) World’s data Novosibirsk JLab – Hall B

  25. Two-Photon Exchange Calculations Before TPE After TPE (Blunden, et al) • Significant progress in theoretical understanding • Hadronic calculations appear sufficient up to 2-3 GeV2 • GPD-based calculations used at higher Q2 • Experimental program will quantify TPE for several e-p observables • Precise test of calculations • Tests against different observables • Want calculations well tested for elastic e-p, reliable enough to be used for other reactions

  26. Reanalysis of SLAC data on GMp E. Brash et al. (PRC 65, 051001 (2002)) have reanalyzed SLAC data with JLab GEp/GMp results as constraint, using a similar fit function as Bosted Reanalysis results in 1.5-3% increase of GMp data

  27. Charge and Magnetization Radii Experimental values <rE2>p1/2= 0.895+0.018 fm <rM2>p1/2= 0.855+0.035 fm <rE2>n= -0.119+0.003 fm2 <rM2>n1/2= 0.87+0.01 fm Even at low Q2-values Coulomb distortion effects have to be taken into account The three real radii are identical within the experimental accuracy • Foldy term = -0.126 fm2 canceled by relativistic corrections (Isgur) • implying neutron charge distribution is determined by GEn

  28. Low Q2 Systematics All EMFF show minimum (maximum for GEn) at Q ≈ 0.5 GeV

  29. Pion Cloud • Kelly has performed simultaneous fit to all four EMFF in coordinate space using Laguerre-Gaussian expansion and first-order approximation for Lorentz contraction of local Breit frame • Friedrich and Walcher have performed a similar analysis using a sum of dipole FF for valence quarks but neglecting the Lorentz contraction • Both observe a structure in the proton and neutron densities at ~0.9 fm which they assign to a pion cloud _ • Hammer et al. have extracted the pion cloud assigned to the NN2π component which they find to peak at ~ 0.4 fm

  30. New Polarization Transfer Results for GEp PRL 99, 202002 (2007) Cross Section from C. Berger et al., Phys. Lett. B35 (1971) 87 Deviation in Ratio is due to Electric Form Factor • Parasitic to G0 • 40% Polarized Beam • Approx. 12 hours/point

  31. Approved Experiment E04-007 One Day of Beam Time per Point! Will run in May/June 2008 Extensive program of accurate cross-section measurements at low Q2 ongoing at MAMI

  32. High-Q2 behaviour • Basic pQCD (Bjørken) scaling predicts F11/Q4 ; F21/Q6 • F2/F11/Q2 (Brodsky & Farrar) • Data clearly do not follow this trend • Schlumpf (1994), Miller (1996) and • Ralston (2002) agree that by • freeing the pT=0 pQCD condition • applying a (Melosh) transformation to a relativistic (light-front) system • an orbital angular momentum component is introduced in the proton wf (giving up helicity conservation) and one obtains • F2/F11/Q • and equivalently a linear drop off of GE/GM with Q2 • Brodsky argues that in pQCD limit non-zero OAM contributes to both F1 and F2

  33. High-Q2 Behaviour Belitsky et al. have included logarithmic corrections in pQCD limit They warn that the observed scaling could very well be precocious

  34. Theory • Relativistic Constituent Quark Models • Variety of q-q potentials (harmonic oscillator, hypercentral, linear) • Non-relativistic treatment of quark dynamics, relativistic EM currents • Miller: extension of cloudy bag model, light-front kinematics • wave function and pion cloud adjusted to static parameters • Cardarelli & Simula • Isgur-Capstick oge potential, light-front kinematics • constituent quark FF in agreement with DIS data • Wagenbrunn & Plessas • point-form spectator approximation • linear confinement potential, Goldstone-boson exchange • Giannini et al. • gluon-gluon interaction in hypercentral model • boost to Breit frame • Metsch et al. • solve Bethe-Salpeter equation, linear confinement potential

  35. Relativistic Constituent Quark charge magnetization proton neutron

  36. Time-Like Region _ • Can be probed through e+e- -> NN or inverse reaction • Data quality insufficient to separate charge and magnetization contributions • No scaling observed with dipole form factor • Iachello only model in reasonable agreement with data • Large new accurate data set from BaBar/ CLEO /DAFNE

  37. Valence and Sea Quarks in the Nucleon However, ss pairs are continuously created and annihilated and are known to contribute to a variety of nucleon properties, such as mass (0-30%), momentum (2-4%) and spin (0-20%). Just as pions can cause the zero-charge neutron to have a non-zero charge distribution, the strange sea is expected to contribute to the charge and magnetic moment distribution of nucleons. In the simple valence-quark model a nucleon consists of u and d quarks. but how much?

  38. Elastic Electroweak Scattering Backward angle Forward angle APV for elastic e-p scattering: Kaplan & Manohar (1988) McKeown (1989) Z0 GEs(Q2), GMs(Q2) Helium: unique GE sensitivity Deuterium: enhanced GA sensitivity

  39. Flavor Separation of Nucleon Form Factors • If we can measure with by assuming charge symmetry then we can write dropping the p superscripts on the left

  40. Instrumentation for PVES • Need • Highest possible luminosity • High rate capability • High beam polarization • Large -Acceptance Detectors (G0, A4) • Large kinematic range • Poor background suppression • Spectrometer (HAPPEx) • Good background rejection • Scatter from magnetized iron Detectors Integrating (HAPPEx) vs. Counting (G0, A4) • Cumulative Beam Asymmetry • Helicity-correlated asymmetry • Dx~10 nm, DI/I~1 ppm, DE/E~100 ppb • Helicity flips • Pockels cell • half-wave plate flips

  41. Overview of Experiments A4 open geometry fast-counting calorimeter for background rejection GEs + 0.23 GMs at Q2 = 0.23 GeV2 GEs + 0.10 GMs at Q2 = 0.1 GeV2 GMs, GAe at Q2 = 0.1, 0.23, 0.5 GeV2 HAPPEx GEs + 0.39 GMs at Q2 = 0.48 GeV2 GEs + 0.08 GMs at Q2 = 0.1 GeV2 GEs at Q2 = 0.1 GeV2 (4He) G0 open geometry fast-counting with magnetic spectrometer + TOF for background rejection GEs + hGMs over Q2 = [0.12,1.0] GeV2 GMs, GAe at Q2 = 0.23, 0.62 GeV2 SAMPLE open geometry, integrating GMs, (GA) at Q2 = 0.1 GeV2

  42. Experimental Technique PMT Polarimeters Cherenkov cones Elastic Rate: 100 x 600 mm 1H: 120 MHz Compton 1.5-3% syst Continuous Møller 2-3% syst 4He: 12 MHz PMT 12 m dispersion sweeps away inelastic events Target 400 W transverse flow 20 cm, LH2 20 cm, 200 psi 4He High Resolution Spectrometer S+QQDQ 5 mstr over 4o-8o

  43. New HAPPEx Results Hydrogen Helicity Window Pair Asymmetry Asymmetry (ppm) Hydrogen Araw correction ~11 ppb Slug Helium Hydrogen Systematic control ~ 10-8 APV = -1.58  0.12 (stat)  0.04 (syst) ppm Asymmetry (ppm) A(Gs=0) = -1.66 ppm 0.05 ppm Helium Normalization control ~ 2% normalization error ~ 2.5% APV = +6.40  0.23 (stat)  0.12 (syst) ppm A(Gs=0) = +6.37 ppm Slug

  44. World Data near Q2 ~0.1 GeV2 GMs = 0.28 ± 0.20 GEs = -0.006 ± 0.016 ~3% ± 2.3% of proton magnetic moment ~0.2 ± 0.5% of Electric distribution HAPPEX only fit suggests something even smaller: GMs = 0.12 ± 0.24 GEs = -0.002 ± 0.017 Caution: the combined fit is approximate. Correlated errors and assumptions not taken into account PRL 98, 032301 (2007)

  45. New data confront theoretical predictions 16. Skyrme Model - N.W. Park and H. Weigel, Nucl. Phys. A 451, 453 (1992). 17. Dispersion Relation - H.W. Hammer, U.G. Meissner, D. Drechsel, Phys. Lett. B 367, 323 (1996). 18. Dispersion Relation - H.-W. Hammer and Ramsey-Musolf, Phys. Rev. C 60, 045204 (1999). 19. Chiral Quark Soliton Model - A. Sliva et al., Phys. Rev. D 65, 014015 (2001). 20. Perturbative Chiral Quark Model - V. Lyubovitskij et al., Phys. Rev. C 66, 055204 (2002). 21. Lattice - R. Lewis et al., Phys. Rev. D 67, 013003 (2003). 22. Lattice + charge symmetry -Leinweber et al, Phys. Rev. Lett. 94, 212001 (2005) & hep-lat/0601025

  46. Summary and Outlook G0 backward HAPPEX-III GEs 0.6 GeV2 GMs • Suggested large values at Q2~0.1 GeV2 • Ruled out • Large possible cancellation at Q2~0.2 GeV2 • Very unlikely given constraint at 0.1 GeV2 • G0 back angle at low Q2 (error bar~1.5% of mp) maintains sensitivity to discover GMS • Possible large values at Q2=0.6 GeV2 • G0 back angle, data being analyzed • HAPPEX-III - 2009

  47. Outstanding Precision for Strange Form Factors Q2=0.1 GeV2 This has recently been shown to enable a dramatic improvement in precision in testing the Standard Model Ciq denote the V/A electron-quark coupling constants

  48. Summary • Very active experimental program on nucleon electro-weak form factors thanks todevelopment of polarized beam (> 100 µA, > 75 %) with extremely small helicity-correlated properties, polarized targets and polarimeters with large analyzing powers • Electromagnetic Form Factors • GEpdiscrepancy between Rosenbluth and polarization transfer not an experimental problem, but highly likely caused by TPE effects • GEn precise data up to Q2 = 3.5 GeV2 • GMn precise data up to Q2 = 5 GeV2, closely following dipole behaviour, but with experimental discrepancies at ~ 1 GeV2 • Further accurate data will continue to become available as benchmark for Lattice QCD calculations • Parity-violating asymmetries have provided highly accurate data on strange form factors at ~ 0.1 GeV2 with further data in the near future • Significant advances in measurement of transverse SSAs • Sensitive test of TPE calculations

  49. Extensions with JLab 12 GeV Upgrade • BLUE = CDR or PAC30 approved, GREEN = new ideas under development ~10 GeV2

  50. Acknowledgements • Many thanks to the colleagues who willingly provided me with figures/slides/discussions: • John Arrington • Roger Carlini • Doug Higinbotham • Michael Kohl • Paul Souder • Bogdan Wojtsekhowski

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