Hadron Form Factors:G
En
Bodo ReitzJefferson Lab
Jefferson LabUser's Workshop and Annual Meeting
“ The Next Seven Years ”June 16-18, 2004
Outline
The Past:World Data on the Electric Form Factor of the Neutron
The Present:E02-013: Towards Higher Momentum Transfers
The Future:Possibilities with 12 GeV
Some Old News About the Neutron
Proton:“ Discovered” ~1920Mass 938.3 MeV/c2, charge 1e, spin 1/2
Substructure:Magnetic moment 2.8 µ
N
(Stern-Gerlach 1933)Charge radius 0.8 fm(Hofstadter, 1955) Quark substructure: 2up + 1down quark (Gell-Mann, Zweig, 1964)and gluons, and sea-quarks
Neutron:Discovered 1932 (Chadwick)Mass 939.6 MeV/c2, neutral, spin ½Free neutron is unstable
Substructure:Magnetic moment -1.9 µ
N
Mean-square charge radius -0.12 fm2 Quark substructure: 1up + 2 down ...
Matter: >99.9% of mass is in the nucleusprotons and neutrons are the basic building blocks of nucleineutrons account for ½ of the mass of matter
How are charge, current, spin, mass distributed inside the nucleon?➔ Electromagnetic form factors (EMFF)
Electron - Nucleon Elastic Scattering
Nucleon vertex:
Sachs form factors:
Breit-frame: Sachs form factors are Fourier transforms of charge and magnetization densities of the nucleon
Cross Section:
Electric Form Factor of the Neutron
No free neutron target available
Instead use of D or 3He
Nuclear effects, model dependencies
Net charge of neutron is 0
GE
n is small at low Q2
Cross section dominated by GM
n
Platchkov et al.: elastic scattering off the deuteron
Data on GE
n at High Q2
Data obtained from quasi elastic e-d scattering
Contributions from the proton
Contributions from the magnetic form factor
Nuclear effects, FSI, MEC, ...
Extraction of GE
n from cross section measurements is difficult
Results on GE
n from A(Q2) and T20
R.Schiavilla and I.Sick, Phys.Rev.C64 (2001) 041002method is also limited to Q2 below 2 (GeV/c)2
Short Excursion:Constraints on G
En from the Inverse Reaction
Scattering of thermal neutrons on atomic electrons
Kinematically limited to very low momentum transfers
Gives charge radius of the neutron
<r2ch,n
> = -0.1148(23) fm2
Charge radius is related to the slope of GE
n at Q2=0
See e.g.: S. Kopecky et al., Phys. Rev. C56 (1997) 2229
Double Polarization Approaches to Measure GE
n
with polarized beam and polarized ND3 target (NIKHEF, JLab Hall C)
limitations: low current (~80 nA), deuteron polarization (25%)
from LD2 target and utilizing recoil polarimeter (Bates, Mainz, JLab Hall C)
limitations: Figure of Merit of polarimeter with polarized beam and polarized 3He target (Bates, NIKHEF, Mainz, JLab E02-013)limitations: current on target (15 µA), target polarization (40%), nuclear medium corrections
Asymmetry measurement
Interference enhances the small amplitude contribution
Avoids Rosenbluth separation
Detection of neutron: avoids subtraction of large proton contribution
For all three types:
E93-038: GE
n in Hall C via 2H(e,e'n)p
quasielastic kinematics: low sensitivity to nuclear potential and MEC / IC
measures transferred polarizationsP
l and P
t at target;
the ratio Pt /P
l is independent of
analyzing power and beam polarization
Charybdis magnet for spin procession(since polarimeters can only measure sideways polarizations)
data taking 2000/2001
momentum transfer: Q2=0.45, 1.13 and 1.45 (GeV/c)2
similar experiments at MIT-Bates and at MAMI A1 and A3 covering: Q2= 0.15 – 0.8 (GeV/c)2
JLab E93-026 (Hall C): D(e,e'n)pmeasuring AV
ed : σ(h,P) = σ
0 (1 + hP AV
ed )
in quasielastic kinematics:low sensitivity to potential, and to MEC and IC
sensitive to GE
n
Data on GE
n from Double Polarization Experiments
Knowledge of GE
n presently limited to Q2 = 1.5 (GeV/c)2
Theory
Vector Meson Dominance (VMD)(Iachello, Gari-Kruempelmann; Lomon, nucl-th/0203081; PRC 66, 045501 (2002))
Photon couples to ρ, ω, φ, ρ', ω' ( involving form factors)
Extrapolation towards pQCD (scaling)
Up to 14 parameters
Combined Models
Isovector ππ channel, dispersion relations(Hoehler, Mergell)
Chiral pertubation theory (Fuchs)(limited to small Q2)
Relativistic Chiral Soliton Model (Holzwarth et al., hep/0201138)
Includes ρ and ω5 parameters
SU(3) Nambu-Jona-Lasinio model(Goeke et al., PRD 53:4013 (1996))
Chiral quark-soliton model
Fewer parameters
Limited Q2 range
Light-Cone Diquark Model(Ma, PRC 65 035205 (2002))
Quark and diquark spectator
5 parameters
Relativistic Constituent Quark Models
pQCD predictions
Asymptotic behaviour (very high Q2)
Lattice QCD (Ashley, Schierholz, QCDSF)
Ab initio calculation
Presently: large error bars in quenched approximation
Theory: RCQM
(Relativistic) Constituent Quark Models (RCQM)
3 constituent quarks (quasi particle)
Sea (gluons, quark/antiquarks) hidden in effective mass
Usually better at high Q2, pion cloud or finite size constituents for low-Q2
Non-relativistic quark dynamics, relativistic EM current matrix elements
Light-front Cloudy Bag Model(G.A. Miller, PRC 66, 032201 (2002)
Predicts QF2/F
1 scaling as observed
includes pion cloud
Light-front form of CQ(Simula, nucl-th/0105024)
CQ form factors fitted to low Q2 data
Goldstone-Boson-Exchange Quark Model(Wagenbrunn et al., PL B511 33 (2001))
Point-form spectator approximation (PFSA)
Parameters of GBE determined by spectroscopy
Pointlike constituent quarks
Hypercentral CQ (Giannini, PRC 62:025208 (2008))
3-quark interaction
Relativistic CQ (Metsch, EPJ A)
relativistic treatment of quark dynamics solving a Bethe-Salpeter equation
EMFF: High-Q2 Behaviour
Basic pQCD scaling (Bjorken) predicts
Schlumpf (1994), Miller (1996), Ralston (2002)
Removing PT=0 pQCD condition
Orbital momentum component of the proton wf (= giving up helicity conservation)
Relativistic (Melosh) transformations
Linear drop off of GE/G
M with Q2
Belitsky, Ji: logarithmic terms
The Next Step: JLab Hall A Experiment E02-013or
How to Go to Higher Q2
At higher Q2 the measurement of the beam target asymmetry in the reaction becomes much more attractive.
For E02-013 the FOM at high Q2 is two orders of magnitude higher than for E93-026
lower cross sections (at fixed scattering angle and increased beam energy)lower value of G
En, lower asymmetry
polarized 3He target has higher luminosity and polarization than ND3
polarized 3He target allows the use of open detectors with larger acceptance (as compared to unpolarized cryo-targets)
higher neutron momentumneutron detector with better neutron detection efficiency and good shielding against low energy stuff possibleanalyzing power of polarimeter goes down
less sensitivity to nuclear correctionsless sensitivity to MEC/IC
BigBite Spectrometer
Non focusing, large acceptance, open geometry
∆p/p = 1 - 1.5% (@ 1.2 T) ; energy resolution 50 MeV
Angular resolution 1.5 mrad, extended target resolution 6 mm
Large solid angle 76 msr
Detector package: MWDCs, segmented trigger, lead-glass shower
Neutron Detector Array
Neutron detector
241 neutron bars in 7 (5) layers
Iron converters
High neutron detection efficiency
High thresholds: (50-150 MeVee)
Large solid angle: active area 160 cm x 470 cm
Position resolution: 5-7 cm
Timing resolution: <0.5 ns
σ(pm,perp
) = 30 MeV σ(pm,par
)= 250 MeV
Veto detector
Efficiency: 99% protons, 12% neutrons
Combined
Efficiency: ~40% neutrons
Neutron Arm: An Artists View
DetectorModules
Base Assm.
Slider Bearings
ElectronicsMezzanine
Shielding(Fe, Pb)
Detector Cage Assembly
Floor Assembly
The Hall A Polarized Helium-3 Target
Principle: spin exchange between optically pumped alkali-metal vapor and 3He
High pressure cell (10 atm), cell length 40 cm
Target polarization 40%
Beam current: up to 15µA
Luminosity 1.0*1036 e-neutron/s/cm2
Projected Data for E02-013
Statistical error for δ(GE/G
M) on the
level of 0.02 with 32 days of beam, systematical uncertainty will be comparable
Status of E02-013:
approved in 2002
detectors and target are under construction
will be ready to be put on floor 2nd half of 2005
Challenges: high rates in two open detectors
Limits: maximum momentum of electron in BigBite, statistics
Proposal to PAC 26:Boosting the Recoil Polarization Method to
Higher Momentum Transfers
utilizing successful approachof E93-038utilizing the available beam energies at JLab of 6 GeVincreasing the acceptance of the polarimeter:
larger neutron arraytapering of the poles of Charybdis magnet
increasing the efficiency of the neutron polarimeter:
more neutron detectorssteel converters
proposes to measure GE
n
at Q2 = 4.3 (GeV/c)2 with δG
En = 0.002 in 25 days
this is probably the highest Q 2 value possible before the 12 GeV upgrade
with JLab@12GeV Q2 values up to 8.1 (GeV/c)2 are feasible (using HMS in Hall C)
R. Madey et al.
Possible Boosts for GE
n Experiments with the
Polarized 3He Target Target Improvements:
Increase in usable beam current and in polarization desirable
New laser technology is becoming available, allowing to combine light of several Lasers in a compact setup
Modifications of cell design with larger, eventually cylindrical pumping cells, and improved gas flow
coating of glass, modifications of end caps to decrease depolarization and increase durability
Use of Rb/K mixture instead of Rb
Spectrometers for Higher Momentum TransfersTo achieve Q2 = 5 (GeV/c)2
Using MAD in JLab Hall A(max. momentum 7 GeV/c, solid angle up to 28 msr)
Beam energy 8.65 GeV
Scattering angle 18o
Sufficiently large neutron detector
With target improvements:
to achieve a 20% measurement
beyond:
Building a Super-BigBite for JLab Hall A
Superconducting dipole magnet with 4.5 Tm, 35cm field gap, solid angle 75msr, max. mometum of 6 GeV/c
30 Days
present: BigBite or HRS
BigBite has large solid angle (76msr), but electron momenta a limited to 1.5 GeV/c
to achieve high momentum transfers one needs to stay at backward angles
HRS would allow larger electron momenta (4 GeV/c), but solid angle is significantly smaller (6msr)