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Andrei Afanasev, Lepton Scattering… HEP School, January 11-13, 2010, Valparaiso, Chile Lepton Scattering as a Probe of Hadronic Structure Andrei Afanasev Jefferson Lab/Hampton U USA Part 2

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Andrei Afanasev, Lepton Scattering… Plan of Lectures Basic formulae Scattering cross section, spin asymmetries Experimental data on nucleon form factors Overview of lepton scattering processes, experimental results and future programs

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Andrei Afanasev, Lepton Scattering… Form Factors Exercise: Calculate the charge distribution ρ(x) is the form factor is described by a dipole formula F(q 2 )=1/(1+q 2 /μ 2 ) 2

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Andrei Afanasev, Lepton Scattering… Fourier Transform Excercise Magnetic form factor of the proton follows the dipole formula up to Q 2 ~25GeV 2 : Exponential fall-off of magnetic moment distribution with radius

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Andrei Afanasev, Lepton Scattering… Mean Square Radius Defines characteristic size of the charge and magnetic moment distribution Believed to be the same for charge and magnetic moment But is it really the same? JLAB experiments proved otherwise

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Andrei Afanasev, Lepton Scattering… Elastic Nucleon Form Factors Based on one-photon exchange approximation Two techniques to measure Latter due to: Akhiezer, Rekalo; Arnold, Carlson, Gross

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Andrei Afanasev, Lepton Scattering… Deriving the Rosenbluth formula Matrix element of electron-proton scattering in the first Born approximation: For scattering ep->ep, the electromagnetic current is Hermitian and form factors F 1,2 (q 2 ) are real functions Squaring the matrix element, we obtain for the elastic contribution to the hadronic tensor:

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Andrei Afanasev, Lepton Scattering… Rosenbluth Formula (cont.) Computing the trace over spinor indices, we obtain structure functions of elastic scattering: Differential cross section in terms of structure functions (Rosenbluth formula:

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Andrei Afanasev, Lepton Scattering… Polarization formula

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Andrei Afanasev, Lepton Scattering… Polarization formula: result

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Andrei Afanasev, Lepton Scattering… 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 (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 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

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Andrei Afanasev, Lepton Scattering… Global Analysis 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 First JLab G E p proposal rated B + !

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Andrei Afanasev, Lepton Scattering… Magnetic Form Factor of the Proton at High Momentum Transfers In perturbative QCD description, G Mp ~1/Q 4 at large values of Q 2. How large? Data from SLAC, (Andivahis et al,1986) show scaling behavior

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Andrei Afanasev, Lepton Scattering… Modern Era Akhiezer et al., Sov. Phys. JETP 6 (1958) 588 and Arnold, Carlson and Gross, PR C 23 (1981) 363 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 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

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Andrei Afanasev, Lepton Scattering… Pre-Jlab Measurements of G E n Elastic e-d scattering (Platchkov, Saclay) No free neutron target available, early experiments used deuteron Large systematic errors caused by subtraction of proton contribution Yellow band represents range of G E n -values resulting from the use of different NN-potentials

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Andrei Afanasev, Lepton Scattering… Double Polarization Experiments to Measure G n E Study the (e,e’n) reaction from a polarized ND 3 target limitations: low current (~80 nA) on target deuteron polarization (~25 %) Study the (e,e’n) reaction from a LD 2 target and measure the neutron polarization with a polarimeter limitations: Figure of Merit of polarimeter Study the (e,e’n) reaction from a polarized 3 He target limitations:current on target (12 µA) target polarization (40 %) nuclear medium corrections

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Andrei Afanasev, Lepton Scattering… 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

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Andrei Afanasev, Lepton Scattering… 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) Measure inclusive quasi-elastic scattering off polarized 3 He (Hall A) 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

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Andrei Afanasev, Lepton Scattering… Measurement of G n M at low Q 2

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Andrei Afanasev, Lepton Scattering… New G n M Results from CLAS J. Lachinet et al, [CLAS Collab.] Phys. Rev. Lett. 102: , 2009

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Andrei Afanasev, Lepton Scattering… 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 measurements over a large range of electron energies

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Andrei Afanasev, Lepton Scattering… Spin Transfer Reaction 1 H(e,e’p) No error contributions from analyzing power beam polarimetry These errors cancel in the ratio of polarizations P x /P z

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Andrei Afanasev, Lepton Scattering… 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 (Pentchev) Using corrected HRS properties → Clear discrepancy between polarization transfer and Rosenbluth data → Investigate possible source, first by doing optimized Rosenbluth experiment

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Andrei Afanasev, Lepton Scattering… Charge and Magnetization Densities JLAB experiments demonstrated large differences in charge and magnetization densities of a nucleon Kelly (2002)

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Andrei Afanasev, Lepton Scattering… Super-Rosenbluth (E01-001) 1 H(e,p) J. Arrington and R. Segel Detect recoil protons in HRS-L to diminish sensitivity to: Particle momentum and angle Data rate Use HRS-R as luminosity monitor Very careful survey Careful analysis of background Rosenbluth Pol Trans MC simulations

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Andrei Afanasev, Lepton Scattering… Rosenbluth Compared to Polarization Transfer John Arrington performed detailed reanalysis of SLAC data Hall C Rosenbluth data (E94-110, Christy) in agreement with SLAC data No reason to doubt quality of either Rosenbluth or polarization transfer data → Investigate possible theoretical sources for discrepancy

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Andrei Afanasev, Lepton Scattering… Two-photon Contributions Guichon and Vanderhaeghen (PRL 91 (2003) ) estimated the size of two-photon effects (TPE) necessary to reconcile the Rosenbluth and polarization transfer data Need ~3% value for Y 2 (6% correction to - slope), independent of Q 2, which yields minor correction to polarization transfer

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Andrei Afanasev, Lepton Scattering… Two-Photon Contributions (cont.) Afanasev, Brodsky, Carlson et al, PRD 72: (2005); PRL 93: (2004) Model schematics: Hard eq-interaction GPDs describe quark emission/absorption Soft/hard separation Assume factorization Polarization transfer 1 +2 (hard) 1 +2 (hard+soft) Blunden et al. have calculated elastic contribution of TPE Resolves ~50% of discrepancy

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Andrei Afanasev, Lepton Scattering… Experimental Verification of TPE contributions Experimental verification non-linearity in -dependence (test of model calculations) transverse single-spin asymmetry (imaginary part of two-photon amplitude) ratio of e + p and e - p cross section (direct measurement of two-photon contributions) CLAS experiment PR aims at a measurement of the -dependence for Q 2 -values up to 2.0 GeV 2

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Andrei Afanasev, Lepton Scattering… Reanalysis of SLAC data on G M p E. Brash et al., PRC submitted, 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

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Andrei Afanasev, Lepton Scattering… Theory → Vector Meson Dominance Photon couples to nucleon exchanging vector meson ( Adjust high-Q 2 behaviour to pQCD scaling Include 2π-continuum in finite width of Lomon3 isoscalar, isovector poles, intrinsic core FF Iachello2 isoscalar, 1 isovector pole, intrinsic core FF Hammer4 isoscalar, 3 isovector poles, no additional FF → Relativistic chiral soliton model Holzwarthone VM in Lagrangian, boost to Breit frame GoekeNJL Lagrangian, few parameters → Lattice QCD (Schierholz, QCDSF) quenched approximation, box size of 1.6 fm, m π = 650 MeV chiral “unquenching” and extrapolation to m π = 140 MeV (Adelaide)

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Andrei Afanasev, Lepton Scattering… Vector-Meson Dominance Model chargemagnetization proton neutron

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Andrei Afanasev, Lepton Scattering… Constituent quark model predictions Relativistic Constituent Quark Models: |p>=|uud>, |n>=|udd> 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

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Andrei Afanasev, Lepton Scattering… Relativistic Constituent Quark Model chargemagnetization proton neutron

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Andrei Afanasev, Lepton Scattering… Form Factors and Generalized Parton Distributions Radyushkin, PRD58: (1998); AA, hep- ph/ ; Guidal et al, PRD 72: (2005); Diehl et al, EPJ 39, 1 (2005) Fits to the data; additional constraints from parton distributions measured in deep-inelastic scattering

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Andrei Afanasev, Lepton Scattering… High-Q 2 behaviour Basic pQCD scaling (Bjørken) predicts F 1 1/Q 4 ; F 2 1/Q 6 F 2 /F 1 1/Q 2 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 or equivalently a linear drop off of G E /G M with Q 2 Brodsky argues that in pQCD limit non- zero OAM contributes to F 1 and F 2

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Andrei Afanasev, Lepton Scattering… High-Q 2 Behaviour (cont) Belitsky et al. have included logarithmic corrections in pQCD limit Solid: proton open: neutron They warn that the observed scaling could very well be precocious

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Andrei Afanasev, Lepton Scattering… Low-Q 2 Behaviour All EMFF allow shallow minimum (max for G E n ) at Q ~ 0.5 GeV

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Andrei Afanasev, Lepton Scattering… Pion Cloud of a Nucleon 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 _

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Andrei Afanasev, Lepton Scattering… Summary Very successful experimental program at JLab on nucleon form factors thanks to development of polarized beam (> 100 µA, > 75 %), polarized targets and polarimeters with large analyzing powers G E n 3 successful experiments, precise data up to Q 2 = 1.5 GeV 2 G M n Q 2 < 1 GeV 2 data from 3 He(e,e’) in Hall A Q 2 < 5 GeV 2 data from 2 H(e,e’n)/ 2 H(e,e’p) in CLAS G E p Precise polarization-transfer data set up to Q 2 =5.6 GeV 2 New Rosenbluth data from Halls A and C confirm SLAC data The experimental discrepancy between polarization transfer and Rosenbluth data may be resolved with two-photon exchange contributions; further experimental tests coming up JLab at 12 GeV will make further extensions to even higher Q 2 possible

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Andrei Afanasev, Lepton Scattering… Coming up next Electroweak form factors and parity-violating electron scattering Form factors of mesons Excitation of baryon resonances Virtual Compton scattering on a nucleon Primakoff production of mesons Search for mesons with exotic quantum numbers

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