The Electromagnetic Form Factors of the Nucleon · 2006. 11. 27. · EM Nucleon Form Factors •...
Transcript of The Electromagnetic Form Factors of the Nucleon · 2006. 11. 27. · EM Nucleon Form Factors •...
September 28, 2006 R. Alarcon @ MIT Symposium
The Electromagnetic Form Factors of the Nucleon
• Introduction
• Proton Form Factors
• Neutron Form Factors
• Summary
Form factor in quantum mechanics
e i k
r e i k r'
Elastic scattering of fast electrons on atoms.Elastic scattering of fast electrons on atoms.
F q dr ri q r( ) ( )= −∫ e ρ
Atomic form factor:Atomic form factor:
σ ( ) ~ ( )q F q2
Fourier transform of diagonalFourier transform of diagonalelements of the density matrix!elements of the density matrix!
The cross section:The cross section:
E.g., the hydrogen atom in the ground state:E.g., the hydrogen atom in the ground state:
F qq
m e( ) = +
⎛⎝⎜
⎞⎠⎟
−
14
2
2 4 2
2
ψπ
( )rr me
=− ⋅e
2 2
ρ ( r ) = ψ (r ) 2
charge densitycharge density
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 distancesProton charge radius and Lamb shiftprecision tests of Weak interaction at low Q2
• They should give clues on how to connect QCD to the NN force
[ ])()()1(
1 2222 QGQGEE
dd
MEMott τετε
σσ+
+′
=Ω
EM Nucleon Form Factors• e-N elastic scattering (Rosenbluth’s formula):
GEp (0) =1 GM
p (0) = μ P
GEn(0) = 0 GM
n (0) = μ n
• e-N elastic scattering does not work for the neutron μ P
GEp
GMp (Q2 ) → 1
Proton
World Data from Rosenbluth’s separation
μ P
GEp
GMp (Q 2 ) → const
Akhiezer+Rekalo, Sov.JPN 3 (1974) 277Arnold,Carlson+Gross, PRC 21 (1980) 1426
Akhiezer+Rekalo, Sov.JPN 3 (1974) 277Arnold,Carlson+Gross, PRC 21 (1980) 1426
Akhiezer+Rekalo, Sov.JPN 3 (1974) 277Arnold,Carlson+Gross, PRC 21 (1980) 1426
Hall A at Jefferson Laboratory
Q2
ln2+
89β Q2
Λ2
F2(Q2)F1(Q
2)→ const
PRL 91 (2003) 092003
A e
Internal Target Physics at MIT-Bates
Ee ≤ 1 GeV, Pe= 40-80 % Im= 200 mA, τ ≥ 10 min
e
South Hall Ring
• pure species• thin• high polarization• thin cell• low holding field
L = 1031-1033 atoms cm-2 s-1
Novosibirsk, AmPS, HERMES, IUCF, COSY
Polarized H/D Target
Left-right symmetric
Large acceptance:0.1 < Q2/(GeV/c)2 < 0.820o < θ < 80o, -15o < φ < 15o
COILS Bmax = 3.8 kG
DRIFT CHAMBERSTracking, PID (charge)δp/p=3%, δθ = 0.5o
CERENKOV COUNTERSe/π separation
SCINTILLATORSTrigger, ToF, PID (π/p)
NEUTRON COUNTERSNeutron tracking (ToF)
DRIFT CHAMBERS
CERENKOVCOUNTERS
SCINTILLATORS
NEUTRON COUNTERS
TARGETBEAM
BEAM
COILS
The BLAST Detector
The BLAST Collaboration
Experimental Program
D-stateT20
Tens-Pol. D
Te11Gn
ED-stateGnM
Vect-Pol. D
N-∆: C2/M1GpE/Gp
MInclusivePol. H
)e',e(p p (e ,e'p) +o+ n)e',e(p ,p)e',e(p n,)e',e(p πππ
d (e ,e') d (e ,e'p) d (e ,e'n) d (e ,e'd)
d (e,e'd) d (e,e'p)
High quality data for nucleon and deuteron structureby means of spin-dependent electron scattering
NC
TOFCC
WC
NC
LADS L20 L15
upstream downstream
1 m
32o
e- left θ* ≈ 90o
“spin-perpendicular”
e- right θ* ≈ 0o
“spin-parallel”
Experimental Technique
C. Crawford (submitted to PRL)
C. Crawford (submitted to PRL)
Neutron
Methods to Determine GEn
Methods to Determine GEn
Methods to Determine GEn
Methods to Determine GEn
Review of GEn world data
Review of GEn world data
Review of GEn world data
Review of GEn world data
Review of GEn world data
Review of GEn world data
Review of GEn world data
Identification of Neutron Events
Very clean quasielastic 2H(e,e’n) spectra
Highly efficient proton veto (drift chambers + TOF)
Extraction of GnE
Quasielastic 2H(e,e’n)
Full Montecarlo simulation of the BLAST experiment
Deuteron electrodisintegrationby H. Arenhövel
Accounted for FSI,MEC,RC,IC
Spin-perpendicular beam-target vector asymmetry AV
ed shows high sensitivity to Gn
E
Compare measured AVed
with BLASTMC, vary GnE
BLASTMC
(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
GMn
• Polarized beam + polarized target:
unpol
EMM GGbGaAσ
θθσσσσ )()( *2* +
∝+−
=↑↓↑↑
↑↓↑↑p p
n
d (e e')
)'(3 eeeH→ neutron magnetic ff
Donnelly + Raskin, Ann. Phys. 169 (1986)247
3H 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 GnM
Quasielastic 2H(e,e’) inclusive
Full Montecarlo simulation of the BLAST experiment
Deuteron electrodisintegrationby H. Arenhövel
Accounted for FSI,MEC,RC,IC
Beam-target vector asymmetry AV
ed spin-parallel + perpendicular show sensitivity to Gn
M
PWIA:BLASTMC
BLASTMC
Neutron Magnetic Form Factor GMn
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 GMn
Summary• A lot of progress (experimental) in the last few years:
– Polarization techniques– GE
p/GMn biggest surprise (JLab)
– GEn known to 5% at low Q2 (Mainz, Bates) and better
at high Q2 (JLab)– GM
n accurately known at low Q2 and new results expected soon at high Q2 (CLAS)
– Structure at low Q2 (challenge for chiral models and lattice QCD)
• Significant issues: beyond Born Approximation (JLab)
• Bates played a significant role at low Q2 and in the development of the polarization techniques.