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:

Spin Transfer Reaction n(e,e'n)

n

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

Beam Target Asymmetry: Formalism

Asymmetry:

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

We Really Need Data at High Q2 on the Neutron

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

Hall A: Layout for E02-013

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

Hall A E02-013: An Artists View

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

The Box: Magnet And Shielding

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)

Summary