NUCLAT, April 21-22, 2008, 1 Kees de Jager Jefferson Lab NUCLAT April , 2008 Nucleon Electro-Weak Form Factors General Introduction Electromagnetic Form Factors Formalism Neutron Proton Parity Violation Formalism Strange Form Factors Summary Thomas Jefferson National Accelerator Facility Z0Z0

NUCLAT, April 21-22, 2008, 2 (Hadronic) Structure and (EW) Interaction Structure Interaction Probe Object |Form factor| 2 = Electroweak probe Interaction Structure (structured object) (pointlike object) Hadronic object Interference! Factorization! Lepton scattering Utilize spin dependence of electroweak interaction to achieve high precision Inelastic Elastic Born Approximation

NUCLAT, April 21-22, 2008, 3 Kinematics Q 2 > 0 space-like region, studied through elastic electron scattering Q 2 < 0 time-like region, studied through creation or annihilation e + + e - -> N + N or N + N -> e + + e - __

NUCLAT, April 21-22, 2008, 4 Nucleon Electro-Magnetic Form Factors ÙFundamental 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 GeV 2 integral quantities (charge radius,…) GeV 2 internal structure of nucleon > 20 GeV 2 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

NUCLAT, April 21-22, 2008, 5 Formalism Dirac (non-spin-flip) F 1 and Pauli (spin-flip) F 2 Form Factors with E (E) incoming (outgoing) energy, scattering angle, anomalous magnetic moment and = Q 2 /4M 2 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 Alternatively, Sachs Form Factors G E and G M can be used

NUCLAT, April 21-22, 2008, 6 The Pre-JLab Era Stern (1932) measured the proton magnetic moment µ p ~ 2.5 µ Dirac indicating that the proton was not a point-like particle Hofstadter (1950s) provided the first measurement of the protons radius through elastic electron scattering Subsequent data ( 1993) were based on: Rosenbluth separation for proton, severely limiting the accuracy for G E p at Q 2 > 1 GeV 2 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

NUCLAT, April 21-22, 2008, 7 Global Analysis (1995) P. Bosted et al. PRC 51, 409 (1995) Three form factors very similar G E n zero within errors -> accurate data on G E n early goal of JLab

NUCLAT, April 21-22, 2008, 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 G E G M 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

NUCLAT, April 21-22, 2008, 9 Double Polarization Experiments to Measure G n E Study the (e,en) reaction from a polarized ND 3 target limitations: low current (~80 nA) on target deuteron polarization (~25 %) Study the (e,en) reaction from a LD 2 target and measure the neutron polarization with a polarimeter limitations: Figure of Merit of polarimeter Study the (e,en) reaction from a polarized 3 He target limitations:current on target (12 µA) target polarization (40 %) nuclear medium corrections

NUCLAT, April 21-22, 2008, 10 G n E Experiment with Neutron Polarimeter Use dipole to precess neutron spin Up-down asymmetry proportional to neutron sideways polarization G E /G M depends on phase shift w.r.t. precession angle

NUCLAT, April 21-22, 2008, 11 Neutron Electric Form Factor G E n Galster: a parametrization fitted to old (<1971) data set of very limited quality For Q 2 > 1 GeV 2 data hint that G E n has similar Q 2 - behaviour as G E p Most recent results (Mainz, JLab) are in excellent agreement, even though all three different techniques were used Schiavilla and Sick analyzed data on deuteron elastic quadrupole form factor

NUCLAT, April 21-22, 2008, 12 Exclusive QE scattering: 3 He(e,en) e n 2 veto planes 7 Iron/scintillator sandwich planes e Beam polarization 84% Target polarization ~50% Q 2 = 1.3, 1.7, 2.5, 3.5 GeV 2

NUCLAT, April 21-22, 2008, 13 First physics result from Hall A G E n 1.7 GeV 2 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 GeV 2 datum, however, is on top of Galster

NUCLAT, April 21-22, 2008, 14 Measuring G n M 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) Old method: quasi-elastic scattering from 2 H large systematic errors due to subtraction of proton contribution R T directly sensitive to (G M n ) 2 Measure inclusive quasi-elastic scattering off polarized 3 He

NUCLAT, April 21-22, 2008, 15 Measurement of G n M at low Q 2

NUCLAT, April 21-22, 2008, 16 Preliminary CLAS results for G M n A systematic difference of several % between results ( ) in Q 2 range GeV 2. A final analysis and paper from CLAS is coming soon. Reminder that at least two independent experiments are always needed.

NUCLAT, April 21-22, 2008, 17 Early Measurements of G E p relied on Rosenbluth separation measure d /d at constant Q 2 G E p inversely weighted with Q 2, increasing the systematic error above Q 2 ~ 1 GeV 2 At 6 GeV 2 R changes by only 8% from =0 to =1 if G E p =G M p /µ p Hence, measurement of G E p with 10% accuracy requires 1.6% cross-section measurement

NUCLAT, April 21-22, 2008, 18 Spin Transfer Reaction 1 H(e,ep) No error contributions from analyzing power beam polarimetry

NUCLAT, April 21-22, 2008, 19 Recoil Polarization Measurement Observed angular distribution Focal-Plane Polarimeter

NUCLAT, April 21-22, 2008, 20 JLab Polarization Transfer Data E PRL 84, 1398 (2000) Used both HRS in Hall A with FPP E PRL 88, (2002) used Pb-glass calorimeter for electron detection to match proton HRS acceptance Reanalysis of E (Punjabi, nucl-ex/ ) Using corrected HRS properties No dependence of polarization transfer on any of the kinematic variables

NUCLAT, April 21-22, 2008, 21 Super-Rosenbluth (E01-001) I. Qattan et al. (PRL 94, (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

NUCLAT, April 21-22, 2008, 22 Rosenbluth Compared to Polarization Transfer John Arrington performed detailed reanalysis of SLAC data Hall C Rosenbluth data (PRC 70, (2004)) in agreement with SLAC data No reason to doubt quality of either Rosenbluth or polarization transfer data Investigate possible theoretical sources for discrepancy

NUCLAT, April 21-22, 2008, 23 Two-Photon Exchange Proton form factor measurements Comparison of precise Rosenbluth and polarization measurements of G Ep /G Mp show clear discrepancy at high Q 2 Two-photon exchange corrections believed to explain the discrepancy Compatible with e+/e- ? Yes: previous data limited to low Q 2 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 P.A.M.Guichon and M.Vanderhaeghen, PRL 91, (2003) Chen et al., PRL 93, (2004)

NUCLAT, April 21-22, 2008, Two-Photon Exchange Measurements Comparisons of e + -p and e - -p scattering [ VEPP-III, JLab-Hall B, ] ε dependence of polarization transfer and unpolarized σ e-p [JLab-Hall C] More quantitative measure of the discrepancy Test against models of TPE at both low and high Q 2 TPE effects in Born-forbidden observables [JLab-Hall A, Hall C, Mainz] Target single spin asymmetry A y in e-n scattering Induced polarization p y in e-p scattering Vector analyzing power A N in e-p scattering Worlds data Novosibirsk JLab – Hall B Evidence (3 level) for TPE in existing data J. Arrington, PRC 69, (R) (2004)

NUCLAT, April 21-22, 2008, 25 Two-Photon Exchange Calculations Significant progress in theoretical understanding Hadronic calculations appear sufficient up to 2-3 GeV 2 GPD-based calculations used at higher Q 2 Experimental program will quantify TPE for several e-p obser vables Before TPE After TPE (Blunden, et al) Precise test of calculations Tests against different observables Want calculations well tested for elastic e-p, reliable enough to be used for other reactions

NUCLAT, April 21-22, 2008, 26 Reanalysis of SLAC data on G M p E. Brash et al. (PRC 65, (2002)) have reanalyzed SLAC data with JLab G E p /G M p results as constraint, using a similar fit function as Bosted Reanalysis results in 1.5-3% increase of G M p data

NUCLAT, April 21-22, 2008, 27 Charge and Magnetization Radii Experimental values p 1/2 = fm p 1/2 = fm n = fm 2 n 1/2 = fm Foldy term = fm 2 canceled by relativistic corrections (Isgur) implying neutron charge distribution is determined by G E n Even at low Q 2 -values Coulomb distortion effects have to be taken into account The three real radii are identical within the experimental accuracy

NUCLAT, April 21-22, 2008, 28 Low Q 2 Systematics All EMFF show minimum (maximum for G E n ) at Q 0.5 GeV

NUCLAT, April 21-22, 2008, 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 NN2 π component which they find to peak at ~ 0.4 fm _

NUCLAT, April 21-22, 2008, 30 New Polarization Transfer Results for G E p Parasitic to G 0 40% Polarized Beam Approx. 12 hours/point Cross Section from C. Berger et al., Phys. Lett. B35 (1971) 87 Deviation in Ratio is due to Electric Form Factor PRL 99, (2007)

NUCLAT, April 21-22, 2008, 31 Approved Experiment E One Day of Beam Time per Point! Will run in May/June 2008 Extensive program of accurate cross-section measurements at low Q 2 ongoing at MAMI

NUCLAT, April 21-22, 2008, 32 High-Q 2 behaviour Basic pQCD (Bjørken) scaling predicts F 1 1/Q 4 ; F 2 1/Q 6 F 2 /F 1 1/Q 2 (Brodsky & Farrar) Data clearly do not follow this trend Schlumpf (1994), Miller (1996) and Ralston (2002) agree that by freeing the p T =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 F 2 /F 1 1/Q and equivalently a linear drop off of G E /G M with Q 2 Brodsky argues that in pQCD limit non- zero OAM contributes to both F 1 and F 2

NUCLAT, April 21-22, 2008, 33 High-Q 2 Behaviour Belitsky et al. have included logarithmic corrections in pQCD limit They warn that the observed scaling could very well be precocious

NUCLAT, April 21-22, 2008, 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

NUCLAT, April 21-22, 2008, 35 Relativistic Constituent Quark chargemagnetization proton neutron

NUCLAT, April 21-22, 2008, 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 /DA NE

NUCLAT, April 21-22, 2008, 37 In the simple valence-quark model a nucleon consists of u and d quarks. 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. but how much?

NUCLAT, April 21-22, 2008, 38 Elastic Electroweak Scattering G E s (Q 2 ), G M s (Q 2 ) A PV for elastic e-p scattering: Forward angle Backward angle Helium: unique G E sensitivity Deuterium: enhanced G A sensitivity Z0Z0 Kaplan & Manohar (1988) McKeown (1989)

NUCLAT, April 21-22, 2008, 39 Flavor Separation of Nucleon Form Factors If we can measure with dropping the p superscripts on the left then we can write by assuming charge symmetry

NUCLAT, April 21-22, 2008, 40 Instrumentation for PVES Large -Acceptance Detectors (G 0, A4) Large kinematic range Poor background suppression Spectrometer (HAPPEx) Good background rejection Scatter from magnetized iron Cumulative Beam Asymmetry Helicity-correlated asymmetry x~10 nm, I/I~1 ppm, E/E~100 ppb Helicity flips Pockels cell half-wave plate flips Need Highest possible luminosity High rate capability High beam polarization DetectorsIntegrating (HAPPEx) vs. Counting (G 0, A4)

NUCLAT, April 21-22, 2008, 41 Overview of Experiments G M s, (G A ) at Q 2 = 0.1 GeV 2 SAMPLE HAPPEx G E s G M s at Q 2 = 0.48 GeV 2 G E s G M s at Q 2 = 0.1 GeV 2 G E s at Q 2 = 0.1 GeV 2 ( 4 He) open geometry, integrating A4 G E s G M s at Q 2 = 0.23 GeV 2 G E s G M s at Q 2 = 0.1 GeV 2 G M s, G A e at Q 2 = 0.1, 0.23, 0.5 GeV 2 open geometry fast-counting calorimeter for background rejection G0G0 G E s + G M s over Q 2 = [0.12,1.0] GeV 2 G M s, G A e at Q 2 = 0.23, 0.62 GeV 2 open geometry fast-counting with magnetic spectrometer + TOF for background rejection

NUCLAT, April 21-22, 2008, 42 Experimental Technique Compton 1.5-3% syst Continuous Møller 2-3% syst Polarimeters High Resolution Spectrometer S+QQDQ 5 mstr over 4 o -8 o Target 400 W transverse flow 20 cm, LH2 20 cm, 200 psi 4 He Cherenkov cones PMT Elastic Rate: 1 H: 120 MHz 4 He: 12 MHz 100 x 600 mm 12 m dispersion sweeps away inelastic events

NUCLAT, April 21-22, 2008, 43 New HAPPEx Results Asymmetry (ppm) Slug Hydrogen A raw correction ~11 ppb Slug Asymmetry (ppm) Helium normalization error ~ 2.5% A PV = (stat) 0.04 (syst) ppm A(G s =0) = ppm 0.05 ppm Hydrogen Systematic control ~ A PV = (stat) 0.12 (syst) ppm A(G s =0) = ppm Helium Normalization control ~ 2% Helicity Window Pair Asymmetry Hydrogen

NUCLAT, April 21-22, 2008, 44 World Data near Q 2 ~0.1 GeV 2 Caution: the combined fit is approximate. Correlated errors and assumptions not taken into account G M s = 0.28 ± 0.20 G E s = ± ~3% ± 2.3% of proton magnetic moment ~0.2 ± 0.5% of Electric distribution HAPPEX only fit suggests something even smaller: G M s = 0.12 ± 0.24 G E s = ± PRL 98, (2007)

NUCLAT, April 21-22, 2008, 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, (1999). 19. Chiral Quark Soliton Model - A. Sliva et al., Phys. Rev. D 65, (2001). 20. Perturbative Chiral Quark Model - V. Lyubovitskij et al., Phys. Rev. C 66, (2002). 21. Lattice - R. Lewis et al., Phys. Rev. D 67, (2003). 22. Lattice + charge symmetry - Leinweber et al, Phys. Rev. Lett. 94, (2005) & hep-lat/

NUCLAT, April 21-22, 2008, 46 Summary and Outlook Suggested large values at Q 2 ~0.1 GeV 2 Ruled out Possible large values at Q 2 =0.6 GeV 2 G 0 back angle, data being analyzed HAPPEX-III Large possible cancellation at Q 2 ~0.2 GeV 2 Very unlikely given constraint at 0.1 GeV 2 G 0 back angle at low Q 2 (error bar~1.5% of p ) maintains sensitivity to discover G M S 0.6 GeV 2 G0 backward HAPPEX-III GMsGMs GEsGEs

NUCLAT, April 21-22, 2008, 47 Outstanding Precision for Strange Form Factors This has recently been shown to enable a dramatic improvement in precision in testing the Standard Model Q 2 =0.1 GeV 2 C iq denote the V/A electron- quark coupling constants

NUCLAT, April 21-22, 2008, 48 Summary Very active experimental program on nucleon electro-weak form factors thanks to development of polarized beam (> 100 µA, > 75 %) with extremely small helicity-correlated properties, polarized targets and polarimeters with large analyzing powers Electromagnetic Form Factors G E p discrepancy between Rosenbluth and polarization transfer not an experimental problem, but highly likely caused by TPE effects G E n precise data up to Q 2 = 3.5 GeV 2 G M n precise data up to Q 2 = 5 GeV 2, closely following dipole behaviour, but with experimental discrepancies at ~ 1 GeV 2 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 GeV 2 with further data in the near future Significant advances in measurement of transverse SSAs Sensitive test of TPE calculations

NUCLAT, April 21-22, 2008, 49 Extensions with JLab 12 GeV Upgrade. BLUE = CDR or PAC30 approved, GREEN = new ideas under development ~10 GeV 2

NUCLAT, April 21-22, 2008, 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