E01-01
Precision measurement of the proton electric to
magnetic form factor ratio with BLAST
Spokespersons: H. Gao, J.R. Calarco, H. Kolster
BLAST weekly meeting
November 8, 2001
Ben Clasie
Outline
1. Introduction and Motivation
2. Existing Measurements
3. The Proposed Experiment
a. Overview
b. Formalism
c. Requirements
4. Conclusions
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1. Introduction and Motivation
 The electromagnetic form factors are fundamental
quantities related to the distribution of charge and
magnetization within a nucleon.
 The electromagnetic form factor ratio is also important,
as any Q2 dependence will suggest different charge and
magnetization spatial distributions inside the nucleon.
o High Q2 (beginning at 0.5 (GeV/c)2 ) results from
JLAB show a downward trend in this ratio for the
proton.
o More recent higher Q2 data from JLAB show a
continuing downward trend up to Q2 =5.6 (GeV/c)2.
o Low Q2 data from 0 to 1 (GeV/c)2 is the focus of
this experiment, which is required to determine the
turning point in the Q2 dependence of the ratio.
2
 The precision form factor ratio data will provide
constraints on theoretical models of the nucleon.
o Q2 data from 0 to 1 (GeV/c)2 is crucial for the
developing QCD lattice calculations, expected to be
available in the near future for low Q2.
o Models with explicit meson degrees of freedom:
 Vector Meson Dominance (VMD), Höhler
1976. Photons couple to hadrons only via
intermediate vector bosons.
 VMD and Perturbative QCD (pQCD) Mergell
et al. 1996.
 Soliton Model, Holzworth 1996. This treats
the Baryon as an extended object with
coupling to vector mesons.
o QCD based Quark models:
 Constituent quarks, Frank et al. 1996. This
model constructs valence quark wavefunctions
and does not include the pion cloud or gluons.
 Cloudy bag, Lu et al. 1998. Photons couple
with a valence quark core and meson fields.
3
4
2. Existing Measurements
 Rosenbluth separation
unpol
P2
P2



G E GM
 d 
1
2  e

P2
  Mott f recoil 
 2 GM tan 


2 

1


 d 


2
o Plot d d vs. tan 2  and the slope gives GMP ,
2
2
and, the intercept GEP .
 
o For Q 2  1 GeV 2 , GEP is difficult to measure due to
kinematic factors.
o At low Q 2 , G MP becomes difficult to extract.
 
 Polarization transfer measurements p (e , ep ) using a
Focal Plane Polarimeter (FPP).
Pt E  E    e 
GEP


tan 
P
GM
Pl 2M P
2
Pt and Pl of the scattered proton were measured
simultaneously within the FPP using scattering from 12 C .
 
o Milbrath et al. (BATES), 1999. Also the d (e , ep)n
reaction was used with similar results.
o Jones et al. (JLAB), 2000.
o Dieterich et al. (MAMI, Mainz), 2001.
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Unpolarized Scattering and Polarization Transfer Data
Polarization Transfer Data
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3. The Proposed Experiments
3a. Overview
 
 This experiment will use the reaction p(e , ep) to
measure  p GEP GMP from Q2 = 0.07 to 0.9 (GeV/c) 2 to
unprecedented precision using two beam energies,
440MeV and 880MeV.
 At the 28th meeting of the BATES program advisory
committee, this experiment was approved with the
highest scientific priority.
 These measurements will fit nicely between the
experiments at JLAB at higher beam energy and the
future data from the RPEX experiment (BATES) at
lower energy and will together provide high precision
data on  p GEP GMP from Q2 = 0.02 to 6 (GeV/c) 2.
 The proposed experiment employs a completely different
experimental technique, that is, a polarized H target
instead of a recoil proton polarimeter.
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3b. Formalism
 A longitudinally polarized electron scatters from a
polarized proton in the lab frame.
 The proton may be polarized in any direction described

by  * and  * with respect to q .
 The cross section for polarized scattering
d
   h
d
where h is the helicity of the electron beam,  is the
unpolarized cross section and  is the spin dependent
part.
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 Theoretical asymmetry
*
*
* P
P
P2
2

v
cos


GM  2 2 (1   )vTL sin  cos  GM GE
T
A 
2
2

(1   )vL GEP  2vT GMP
 The experimental asymmetry depends on the beam
and target polarizations
N  N
Aexp  Pb Pt A  
N  N
where the arrows indicate a change in either beam or
target polarization and N is the number of scattering
events in a given bin.
 The asymmetry will be measured in both the left and
right sectors of BLAST simultaneously as the target

polarization angles  * and  * with respect to q are
different in each sector.
 AL and AR are measured at the same Q 2 .
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 Super ratio definition
AL 2vT  cos L*  2 2 (1   )vTL sin  L* cos  L* GEP GMP
Rexp 

AR 2vT  cos R*  2 2 (1   )vTL sin  R* cos  R* GEP GMP
 We are therefore able to extract the form factor ratio
independent of the beam and target polarizations to
first order.
The asymmetry Super Ratio assuming Höhler
form factors
(Left Asymmetry)/(Right Asymmetry)
15
10
5
0
-5
-10
440 MeV
880 MeV
-15
25
45
65
85
105
Theta (degrees)
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3c. Requirements
 This experiment will employ the polarized stored
electron beam of the South Hall ring at Bates, the ABS
polarized hydrogen source and BLAST.
 The beam is required to have a polarization of 60% or
higher and an average beam current of 80 mA.
 The target is anticipated to have a polarization of up to
80% with a total target density of
5.5 1013 atoms / cm2 .
 Elastically scattered electrons and protons will be
detected using BLAST.
E(MeV)
440(c)
880(c)
880(s)
880(c)*
 e min(deg)  e max(deg)  p min(deg)  p max(deg)
33.5
26.5
82.5
82.5
103.0
113.0
37.8
30.5
18.9
18.9
66.2
65.5
30.5
22.3
(c) coincidence
(s) proton singles
(c)* coincidence with extra detectors
 The proton singles measurement will be attempted
where the electrons are outside of the BLAST
acceptance. Momentum determination allows the
identification of elastically scattered protons.
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 The pion background may be a problem with a singles
measurement (max pion momentum = 826 GeV/c in
this bin, greater than 6% difference to protons).
 An independent scintillator and calorimeter system
may be necessary to detect the large angle electrons in
coincidence.
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4. Conclusions
 This experiment will be the first determination of the
 
proton form factor ratio using the p(e , ep) reaction.
 The proton form factor ratio will be measured from
Q2 = 0.07 to 0.9 (GeV/c) 2 to unprecedented precision
and dominated by statistical error.
 This experiment is well suited for BLAST.
 In the future a 1.1GeV beam may be used with the same
technique with BLAST to determine the proton form
factor ratio to Q2 = 1.2 (GeV/c) 2.
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References
Proposal to the MIT-Bates PAC “Precision measurement of
the proton electric to magnetic form factor ratio with BLAST”.
M. Jones et al., Phys. Rev. Lett. 84, 1398 (2000).
B. Milbrath et al., Phys. Rev. Lett. 80, 452 (1998), Phys.
Rev. Lett. 82, 221 (E) (1999).
S. Dieterich et al., Phys. Lett. B500, 47 (2001).
T. W. Donnelly et al., Ann. Phys. 169, 247 (1986).
G. Höhler et al., Nucl. Phys. B114, 505 (1976).
P. Mergell et al., Nucl. Phys. A596, 367 (1996).
G. Holzworth, Z. Phys. A356, 339 (1996).
M. R. Frank et al., Phys. Rev. C54, 920 (1996).
D. H. Lu et al., Phys. Rev. C57, 2628 (1998).
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