The Electromagnetic Form Factors of the Nucleon Introduction Proton Form Factors Neutron Form Factors Summary September 28, 2006 R. Alarcon @ MIT Symposium
e i k r Form factor in quantum mechanics Elastic scattering of fast electrons on atoms. e ik ' r ρ ( r ) = ψ ( r ) 2 charge density σ ( 2 q) ~ F ( q) The cross section: Atomic form factor: iqr F( q ) dr ( r = e ρ ) Fourier transform of diagonal elements of the density matrix! E.g., the hydrogen atom in the ground state: ψ ( r) = e rme π 2 2 F( q) = 1 + q 4m e 2 2 4 2 2
EM Nucleon Form Factors They are the basic observables that contain important information about the electromagnetic structure of the proton and the neutron in the non-perturbative region. Extensively studied by 40 years now, through electron scattering: SLAC, Saclay, Mainz,NIKHEF, MIT-Bates, JLab, They are required for knowledge of many other things: structure of nuclei at short distances Proton charge radius and Lamb shift precision tests of Weak interaction at low Q 2 They should give clues on how to connect QCD to the NN force
EM Nucleon Form Factors e-n elastic scattering (Rosenbluth s formula): dσ = σ dω Mott E E ε (1 + τ ) 1 2 E M [ ( ) ( )] 2 2 2 ε G Q + τ G Q G E p (0) =1 G E n (0) = 0 G M p (0) = μ P G M n (0) = μ n p G μ E P p G (Q2 ) 1 M e-n elastic scattering does not work for the neutron
Proton
World Data from Rosenbluth s separation
μ P G E p G M p (Q 2 ) const
Akhiezer+Rekalo, Sov.JPN 3 (1974) 277 Arnold,Carlson+Gross, PRC 21 (1980) 1426
Akhiezer+Rekalo, Sov.JPN 3 (1974) 277 Arnold,Carlson+Gross, PRC 21 (1980) 1426
Akhiezer+Rekalo, Sov.JPN 3 (1974) 277 Arnold,Carlson+Gross, PRC 21 (1980) 1426
Hall A at Jefferson Laboratory
ln 2+ Q 2 8 9β Q 2 Λ 2 F 2 (Q 2 ) F 1 (Q 2 ) const PRL 91 (2003) 092003
e Internal Target Physics at MIT-Bates E e 1 GeV, P e = 40-80 % I m = 200 ma, τ 10 min A e pure species thin South Hall Ring high polarization thin cell low holding field L = 10 31-10 33 atoms cm -2 s -1 Novosibirsk, AmPS, HERMES, IUCF, COSY
Polarized H/D Target
The BLAST Detector Left-right symmetric Large acceptance: 0.1 < Q 2 /(GeV/c) 2 < 0.8 20 o < θ < 80 o, -15 o < φ < 15 o COILS B max = 3.8 kg DRIFT CHAMBERS Tracking, PID (charge) δp/p=3%, δθ = 0.5 o CERENKOV COUNTERS e/π separation SCINTILLATORS Trigger, ToF, PID (π/p) NEUTRON COUNTERS Neutron tracking (ToF) COILS BEAM TARGET NEUTRON COUNTERS DRIFT CHAMBERS SCINTILLATORS CERENKOV COUNTERS BEAM
The BLAST Collaboration
Experimental Program High quality data for nucleon and deuteron structure by means of spin-dependent electron scattering Pol. H Vect-Pol. D Tens-Pol. D p (e,e') p ( e,e'p) + o + p(e,e' π )n, p(e,e'p) π, p(e,e'n) π Inclusive d ( e,e') G n M T 20 G p E/G p M d ( e,e'p) D-state d (e,e'd) d (e,e'p) D-state d ( e,e'n) G n E N- : C2/M1 d ( e,e'd) T e 11
Experimental Technique NC 1 m e- left θ* 90 o spin-perpendicular e- right θ* 0 o spin-parallel upstream 32 o downstream WC CC TOF LADS NC L20 L15
C. Crawford (submitted to PRL)
C. Crawford (submitted to PRL)
Neutron
Methods to Determine G E n
Methods to Determine G E n
Methods to Determine G E n
Methods to Determine G E n
Review of G E n world data
Review of G E n world data
Review of G E n world data
Review of G E n world data
Review of G E n world data
Review of G E n world data
Review of G E n world data
Identification of Neutron Events Very clean quasielastic 2 H(e,e n) spectra Highly efficient proton veto (drift chambers + TOF)
Extraction of G n E Quasielastic 2 H(e,e n) Full Montecarlo simulation of the BLAST experiment Deuteron electrodisintegration by H. Arenhövel Accounted for FSI,MEC,RC,IC Spin-perpendicular beam-target vector asymmetry A V ed shows high sensitivity to G n E BLASTMC Compare measured A V ed with BLASTMC, vary G n E (e,e p) (e,e n)
V. Ziskin (MIT), E. Geis (ASU)
Discussion vs. Nucleon Models
Discussion vs. Nucleon Models
Discussion vs. Nucleon Models
Discussion vs. Nucleon Models
Discussion vs. Nucleon Models
Discussion vs. Nucleon Models
Discussion vs. Nucleon Models
G M n Polarized beam + polarized target: Donnelly + Raskin, Ann. Phys. 169 (1986)247 p n 3 H e p * 2 * σ σ a( θ ) GM + b( θ ) G A = σ + σ σ 3 He( ee ') d ( e e') unpol neutron magnetic ff M G E p n d d(e,e' n) d(e,e' p)
Friedrich & Walcher Parametrization Expressed form factors as smooth part plus bump smooth bump
Friedrich & Walcher Parametrization
Extraction of G n M Quasielastic 2 H(e,e ) inclusive Full Montecarlo simulation of the BLAST experiment Deuteron electrodisintegration by H. Arenhövel Accounted for FSI,MEC,RC,IC Beam-target vector asymmetry A V ed spin-parallel + perpendicular show sensitivity to G n M PWIA: BLASTMC BLASTMC
Neutron Magnetic Form Factor G M n 1. New measurement technique. 2. Includes full deuteron structure. 3. Consistent with recent polarization and other data. 4. Provides a tighter fit to form factor in the low Q2 region.
N. Meitanis (MIT) Neutron Magnetic Form Factor G M n
Summary A lot of progress (experimental) in the last few years: Polarization techniques G Ep /G Mn biggest surprise (JLab) G En known to 5% at low Q 2 (Mainz, Bates) and better at high Q 2 (JLab) G Mn accurately known at low Q 2 and new results expected soon at high Q 2 (CLAS) Structure at low Q 2 (challenge for chiral models and lattice QCD) Significant issues: beyond Born Approximation (JLab) Bates played a significant role at low Q 2 and in the development of the polarization techniques.