arXiv:1103.5784v1 [nucl-ex] 29 Mar 2011
Low Q2measurements of the proton form factor ratio µpGE/GM
G. Ron,1,2,3X. Zhan,4J. Glister,5,6B. Lee,7K. Allada,8W. Armstrong,9J. Arrington,10A. Beck,4,11
F. Benmokhtar,12B.L. Berman,13W. Boeglin,14E. Brash,15A. Camsonne,11J. Calarco,16J. P. Chen,11
Seonho Choi,7E. Chudakov,11L. Coman,17B. Craver,17F. Cusanno,18J. Dumas,19C. Dutta,8R. Feuerbach,11
A. Freyberger,11S. Frullani,18F. Garibaldi,18R. Gilman,19, 11O. Hansen,11D. W. Higinbotham,11
T. Holmstrom,20C.E. Hyde,21H. Ibrahim,21Y. Ilieva,13C. W. de Jager,11X. Jiang,19M. Jones,11A. Kelleher,20
E. Khrosinkova,22E. Kuchina,19G. Kumbartzki,19J. J. LeRose,11R. Lindgren,17P. Markowitz,14
S. May-Tal Beck,4,11E. McCullough,5M. Meziane,20Z.-E. Meziani,9R. Michaels,11B. Moffit,20B.E. Norum,17
Y. Oh,7M. Olson,23M. Paolone,24K. Paschke,17C. F. Perdrisat,20E. Piasetzky,25M. Potokar,26
R. Pomatsalyuk,27,11I. Pomerantz,25A. Puckett,4V. Punjabi,28X. Qian,29Y. Qiang,4R. Ransome,19
M. Reyhan,19J. Roche,30Y. Rousseau,19A. Saha,11A.J. Sarty,5B. Sawatzky,17,9E. Schulte,19M. Shabestari,17
A. Shahinyan,31R. Shneor,25S.ˇSirca,32,26K. Slifer,17P. Solvignon,10J. Song,7R. Sparks,11R. Subedi,22
S. Strauch,24G. M. Urciuoli,18K. Wang,17B. Wojtsekhowski,11X. Yan,7H. Yao,9and X. Zhu33
(The Jefferson Lab Hall A Collaboration)
1The Weizmann Institute of Science, Rehovot 76100, Israel
2Lawrence Berkeley National Lab, Berkeley, CA 94720, USA
3Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem, Israel 91904
4Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
5Saint Mary’s University, Halifax, Nova Scotia B3H 3C3, Canada
6Dalhousie University, Halifax, Nova Scotia B3H 3J5, Canada
7Seoul National University, Seoul 151-747, Korea
8University of Kentucky, Lexington, Kentucky 40506, USA
9Temple University, Philadelphia, Pennsylvania 19122, USA
10Argonne National Laboratory, Argonne, Illinois, 60439, USA
11Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606, USA
12University of Maryland, Baltimore, Maryland, USA
13George Washington University, Washington D.C. 20052, USA
14Florida International University, Miami, Florida 33199, USA
15Christopher Newport University, Newport News, Virginia, 2360X, USA
16University of New Hampshire, Durham, New Hampshire 03824, USA
17University of Virginia, Charlottesville, Virginia 22904, USA
18INFN, Sezione Sanit´ a and Istituto Superiore di Sanit´ a, Laboratorio di Fisica, I-00161 Rome, Italy
19Rutgers, The State University of New Jersey, Piscataway, New Jersey 08855, USA
20College of William and Mary, Williamsburg, Virginia 23187, USA
21Old Dominion University, Norfolk, Virginia 23508, USA
22Kent State University, Kent, Ohio 44242, USA
23Saint Norbert College, Greenbay, Wisconsin 54115, USA
24University of South Carolina, Columbia, South Carolina 29208, USA
25Tel Aviv University, Tel Aviv 69978, Israel
26Institute “Joˇ zef Stefan”, 1000 Ljubljana, Slovenia
27Kharkov Institue, Kharkov 310108, Ukraine
28Norfolk State University, Norfolk, Virginia 23504, USA
29Duke University, Durham, NC 27708, USA
30Ohio University, Athens, Ohio 45701, USA
31Yerevan Physics Institute, Yerevan 375036, Armenia
32Dept. of Physics, University of Ljubljana, 1000 Ljubljana, Slovenia
33Duke University, Durham, North Carolina 27708, USA
(Dated: March 31, 2011)
We present an updated extraction of the proton electromagnetic form factor ratio, µpGE/GM,
at low Q2. The form factors are sensitive to the spatial distribution of the proton, and precise
measurements can be used to constrain models of the proton. An improved selection of the elastic
events and reduced background contributions yielded a small systematic reduction in the ratio
µpGE/GM compared to the original analysis.
PACS numbers: 13.0.Gp, 13.60.Fz, 13.88.+e, 14.20.Dh
We present a detailed reanalysis of polarization trans-
fer measurements of the proton form factor ratio
µpGE/GM. This is an update of the original analysis
of this experiment , with improved selection of elas-
tic events and significantly reduced contamination from
quasielastic events in the target windows. The new re-
sults are typically lower by ∼1%, with comparable or
somewhat smaller statistical uncertainties.
The electric and magnetic form factors, GE(Q2) and
GM(Q2), are related to the spatial distribution of charge
and magnetization in the proton. The form factors can
be extracted in elastic electron–proton scattering, and
mapped out as a function of the four-momentum trans-
fer squared, Q2, to yield the momentum-space structure
of the proton. In a non-relativistic framework, these form
factors are the Fourier transforms of the spatial distribu-
tions of the rest-frame charge and magnetization distri-
butions. Relativistically, the form factors represent the
Fourier transform of the Breit frame rather than the rest
frame, and it is necessary to apply Q2-dependent boost
corrections to extract the rest-frame distributions. These
corrections are model-dependent, and there is no consen-
sus on how they should best be applied. Thus, while the
form factors are directly related to the protons spatial
distribution, these distributions cannot be extracted in a
It has been argued that the large-scale structure is not
significantly impacted by these corrections because the
boost corrections decrease at small Q2values. However,
this is not entirely correct. The boost corrections are pro-
portional to Q2at very low values of Q2, and thus there
is no correction in the limit Q2→ 0. However, while
the value of the form factor at Q2= 0 is not affected by
these boost corrections, the Q2dependence is modified,
even at Q2= 0. The proton charge radius is typically de-
fined as the slope of the form factor at Q2= 0, so while
the boost corrections are small, they still have a finite
impact on the radius extraction. Note that because the
form factor for a point particle is Q2-independent, the
information on the internal structure is contained in the
deviation of the form factor from the value at Q2= 0,
GE(0) = 1,GM(0) = µp. Thus the small boost correc-
tions at low Q2need to be compared to the small devia-
tions from the Q2= 0 value of the form factors, making
the impact of even small boost corrections larger than
one might expect. For a more detailed discussion see
Fortunately, in most instances the presence of these
model-dependent boost corrections is not an issue. While
discussion of finite-size corrections in atomic physics are
typically phrased in terms of the rest-frame charge distri-
butions, these corrections can in fact be directly related
to the measured form factors. For example, the extrac-
tion of the proton RMS charge radius from Lamb shift
measurements in hydrogen  and muonic hydrogen  is
a measure of the slope of the form factor at Q2= 0, rather
than the true RMS of the rest-frame charge density. Sim-
ilarly, corrections to the hyperfine splitting [5–7], which
are related to the charge and magnetization radii of the
proton, are extracted directly from the form factors. So
while these are discussed in terms of the proton’s size or
shape, it is not necessary to have the rest frame densities
to apply these corrections.
Recently, it has been demonstrated that the transverse
densities can be extracted in a model-independent fash-
ion  in the infinite momentum frame (IMF). This is
a natural frame in which to work for the study of gen-
eralized parton distributions, but some features of the
IMF distributions may not correspond to features in the
rest-frame distributions [9, 10]. So while the Breit-frame
distributions are not identical to the rest-frame distribu-
tions, they can provide an approximate, but somewhat
more intuitive, picture for thinking about the distribu-
tions in the rest frame of the proton .
In spite of the difficulties in extracting the rest-frame
charge and magnetization densities, the form factors still
encode a great deal of information on the structure of the
nucleon. With precision measurements of both proton
and neutron form factors over a large kinematic range,
they can provide significant constraints on models of the
nucleon. The lack of a free neutron target and the limita-
tions of the unpolarized cross section measurements led
to significant limitations in these measurements. In par-
ticular, it was difficult to precisely separate GEfrom GM
in the proton for very high or very low Q2values, and
even more difficult to separate proton and neutron contri-
butions when attempting to extract neutron form factors
from measurements on light nuclei. Polarization mea-
surements [12–15] provide a significantly improved way to
isolate the neutron form factors and to separate GEand
GM. Initial measurements for the proton focused on the
high-Q2region [16–19], which showed a significant falloff
in the ratio µpGE/GM with Q2, in contrast to previous
extractions from Rosenbluth separations . The differ-
ence is now believed to be due to the contribution of two-
photon exchange effects which significantly impact the
extractions from the unpolarized cross section measure-
ments but have significantly less impact on the measure-
ments which use polarization observables [21–23]. These
significantly improved measurements of GEled to a great
deal of theoretical work aimed at understanding this be-
havior [24–27], which showed, among other things, the
importance of quark orbital angular momentum in under-
standing the proton structure at high momentum [28–30].
These results also had a significant impact on studies of
the correlations between the spatial distribution of the
quarks and the spin or momentum they carry, showing
that the spherically symmetric proton is formed from a
rich collection of complex overlapping structures .
While initial investigations focused on extending pro-
ton measurements to higher Q2, the polarization mea-
surements can also be used to improve the precision at
lower Q2values, and in particular improve the extraction
of the magnetic form factor for very low Q2values. The
low-Q2form factors relate to the large-scale structures
in the proton’s charge and magnetization distributions.
As such, it has long been believed that the “pion cloud”
contributions, e.g. the fluctuation of a proton into a vir-
tual neutron–π+system, will be significant at low Q2, as
the mass difference means that the pion will contribute
to the large distance distribution in the bound nucleon–
pion system. Such fluctuations yield small corrections to
the charge distribution of the proton, but are more im-
portant in the neutron, where the charge form factor is
small, with Gn
case, the small contribution from the fluctuation of the
neutron into a proton–π−system yields a positive charge
density at the neutron core and a negative pion cloud at
large distance yields a significant part of the net charge
Recently it has been suggested that such structures
are present in all the nucleon form factors , reflecting
contributions from the pion cloud of the nucleon. How-
ever, the significance of the proposed structures and their
interpretation as a pion cloud effect have been much dis-
puted. This is also the region in which parity violat-
ing electron scattering measurements [33–36] are being
done, to investigate the strange-quark contributions to
the proton electromagnetic structure and to determine
the proton weak charge, as a constraint on physics be-
yond the standard model. Extracting the strange quark
contributions and weak charge both rely on precise de-
terminations of the proton form factors.
Finally, these form factors can be used to extract the
proton charge and magnetization radii [37–40].
charge radius is of particular interest at present, due to
the conflicting results between Lamb shift measurements
on muonic hydrogen  and the electron scattering re-
sults and measurements from the Lamb shift in electronic
hydrogen . While higher order corrections, which de-
pend on the values of the form factors at finite Q2, can
modify the extracted radius, these corrections appear to
be far to small to explain the discrepancy.
work  has proposed a possible mechanism to explain
a difference between electronic and muonic probes of the
proton structure, due to off-shell effects in the hadronic
intermediate state in the two-photon exchange diagrams.
However, while this is an area that has received a great
deal of attention in the recent past, the question is still
E→ 0 in the limit of small Q2. In this
Since the 1960s, measurements of the unpolarized
cross section for elastic e–p scattering have been used
to separate GE and GM.
portional to (τG2
ε = (1 + 2(1 + (Q2/4m2
fixed by varying the beam energy and scattering angle,
one can very ε, and thus perform a “Rosenbluth separa-
tion”  of the contributions from GEand GM. At high
Q2, the factor of τG2
Mdominates, as τ becomes large and
extraction of GEdifficult, as it contributes only a small,
angle-dependent correction to the primary cross section
contribution from GM. Similarly, in the limit of very
small Q2, and thus very small τ, it is difficult to isolate
The cross section is pro-
E), where τ = Q2/4m2
p))tan2θ/2)−1. By keeping Q2
E(with GM/ge = µpat Q2= 0). This makes
GM, except in the limit where ε → 0, i.e. scattering
angle → 180◦.
Polarization measurements are sensitive to the ratio
GE/GM, and thus, when combined with cross section
measurements, can cleanly separate the electric and mag-
netic form factors, no matter how small their contribu-
tion to the cross section becomes. It has been known
for some time [12–15] that measurements of polariza-
tion observables would provide a powerful alternative to
Rosenbluth separation measurements, but only in the last
decade or so have the high polarization, high intensity
electron beams been available, combined with polarized
nucleon targets or high efficiency nucleon recoil polarime-
ters [25, 26].
The first such measurements for the proton [16, 43]
showed a decrease in µpGE/GM with Q2, which dif-
fered from the existing Rosenbluth separation measure-
ments, which showed approximate form factor scaling,
i.e. µpGE/GM ≈ 1. This discrepancy appeared to be
larger than could be explained even accounting for the
scattering in the previous Rosenbluth measurements .
A measurement using a modified Rosenbluth extraction
technique  was able to extract the ratio µpGE/GM
with comparable precision to the polarization measure-
ments, and showed a clear discrepancy, well outside of the
experimental systematics for either technique. Experi-
ments extending polarization measurements to higher Q2
show a continued decrease of µpGE/GMwith Q2[17, 19].
It was suggested that the two-photon exchange (TPE)
correction may be able to explain the discrepancy be-
tween the two techniques . While these corrections
are expected to be of order αEM≈ 1%, they can have a
very similar ε dependence to the contribution from GE.
Because the contribution to GE is small at large Q2, a
TPE correction of a few percent could still be signifi-
cant to the extraction of GE. It was estimated that a
TPE contribution of ∼5%, with a linear ε dependence,
could explain the difference [21, 45], and early calcula-
tions suggested effects of a few percent, with just such
a linear ε-dependence [46, 47]. These corrections should
also modify the polarized cross section measurements,
but it should be a percent-level correction in the extrac-
tion of GE/GM, as there is is no equivalent amplifica-
tion of the effect. Including the best hadronic calcula-
tions available yields consistency between the two tech-
niques, and good separation of GE and GM up to high
Q2. Comparisons of electron–proton and positron–
proton scattering can be used to isolate TPE contribu-
tions , and a series of such measurements are currently
planned or underway [49–51].
At low Q2values, the TPE should be well described by
the hadronic calculations, and in fact the contributions
become very small for 0.3 < Q2< 0.7 GeV2. While this is
a region where high precision Rosenbluth separations are
possible, the existing measurements in this region have
relatively large uncertainties, typically larger than 3–5%,
on µpGE/GM. Measurements using polarization observ-
ables in this region can provide a significant improvement
in precision, even in this low Q2regime. The MIT-Bates
BLAST experiment made measurements of µpGE/GM
using a polarized target  for 0.1 < Q2< 0.6 GeV2,
with typical uncertainties around 2%. The updated re-
sults of this reanalysis provide an improved extraction of
µpGE/GM in this kinematic region.
III. EXPERIMENT DETAILS
This experiment was carried out in Hall A of the
Thomas Jefferson National Accelerator Facility (JLab),
in the summer and fall of 2006, as part of experiment
E05-103 . While the experiment was focused on po-
larization observables in low energy deuteron photodis-
integration , elastic electron–proton scattering mea-
surements used to calibrate the focal plane polarimeter
provided high statistics data that allowed for an improved
extraction of the proton form factor ratio µpGE/GM at
A polarized electron beam was incident on a cryogenic
liquid hydrogen target, 10 cm in length for the 362 MeV
beam energy running and 15 cm for the 687 MeV set-
tings (the target length was misstated as 15 cm for all
runs in the previous publication ). Elastic e–p scatter-
ing events were identified by detecting the struck proton
in one of the High Resolution Spectrometers (HRS) .
Data were taken with a longitudinal polarization of ap-
proximately 40% and with the beam helicity flipped
pseudo-randomly at 30Hz. For some settings, the scat-
tered electron was detected in the other HRS spectrom-
The polarization of the struck protons is measured in
a focal plane polarimeter (FPP) in the proton spectrom-
eter. Operation and analysis of events in the FPP is
described in detail in Refs. [18, 55]. Analysis of the angu-
lar distribution of rescattering in the polarimeter allows
us to extract the transverse polarization at the detector,
which can be used to reconstruct the longitudinal and
transverse (in-plane) components of the polarization of
the elastically scattered protons. In the Born approx-
imation, the ratio of these polarization components is
directly related to the ratio GE/GM,
= −E0+ E′
where Cz,x are the longitudinal and transverse compo-
nents of the proton polarization, E0is the beam energy,
and θeand E′are the scattered electron’s angle and mo-
mentum (reconstructed from the measured proton kine-
matics). Because the extraction of µpGE/GM depends
on the ratio of two polarization components, knowledge
of the absolute beam polarization and FPP analyzing
power are not necessary, although high polarization and
analyzing power improve the figure of merit of the mea-
In the experiment, we measure the polarization not at
the target, but in the spectrometer, and the asymmetry
in the rescattering is sensitive only to polarization com-
ponents perpendicular to the proton direction. If we look
at the central proton trajectory, where the spectrometer
is well represented by a simple dipole, then the transverse
component, Cx, will be unchanged, while the longitudinal
component, Cz, will be precessed in the dipole field. If we
chose a spin precession angle, χ, near 90 degrees, the lon-
gitudinal and transverse polarization components at the
target will yield ”vertical” and ”horizontal” components
in the frame of the focal plane polarimeter, allowing for
both to be extracted by a measurement of the azimuthal
distribution of rescattering in the carbon analyzer. In
the analysis, we use a detailed model of the spectrometer
to perform the full spin precession, rather than taking a
dipole approximation, as described in detail in Ref. .
TABLE I: Kinematics and FPP parameters for the measure-
netic energy, respectively. Tanalyzer is the thickness of the
FPP carbon analyzer and χ is the spin precession angle for
the central trajectory. The final column shows which kine-
matics had single-arm (S), coincidence (C), or a combination
of both (C/S).
laband Tp are the proton lab angle and proton ki-
(GeV2) (GeV) (deg) (GeV) (inches) (deg)
0.474 0.687 34.4
A follow-up experiment, JLab E08-007  was pro-
posed to make extremely high precision measurements in
this kinematic regime. The measurements was run in the
summer of 2008, and in the analysis of the E08-007 data,
it was observed that the result was somewhat sensitive to
the cuts applied to the proton kinematics when isolating
elastic e–p scattering.
In the original analysis of our results , only the pro-
ton was detected for most kinematic settings, and the
elastic scattering events were isolated using cuts on the
over-determined elastic kinematics.
surement was statistics limited, relatively loose cuts were
applied, as little cut dependence had been observed in
the two coincidence settings or in previous measurements
where electrons were detected [18, 43] or in a previ-
ous work comparing singles and coincidence measure-
ments . Most of these measurements had high res-
olution reconstruction of both the proton and electron
kinematics, and so loose cuts on the combined proton and
electron kinematics provided clean isolation of the elas-
tic peak. In addition, the previous measurements were
generally at higher Q2and so of significantly lower sta-
Because the mea-
tistical precision, typically 3–5%, so it was difficult to
make precise evaluation of the impact of tight cuts on
the proton kinematics. Because in most cases the elastic
events could be cleanly identified without tight cuts on
the proton kinematics, this was not considered to be a
In the analysis of the E08-007 data , the electron
was detected in a large acceptance spectrometer with lim-
ited momentum and angle resolution. The electron detec-
tion led to significant suppression of scattering from the
target windows, but the poor electron resolution required
that the elastic peak be identified using cuts on the pro-
ton kinematics. Because of this, and the high statistics of
the data set, it was possible to make detailed studies of
the cut dependence of the result. It was found that there
were small but noticeable changes in the extracted form
factor ratio if the proton kinematic cuts were made too
loose, even in cases where the endcap contributions were
fairly small. This may be due to events where the spin
precession was incorrectly calculated due to poor recon-
struction of the proton vertex kinematics for events that
are far out the tails of the elastic peak as defined by the
proton kinematics. Therefore, we reexamined the cuts
used to identify the proton events, and made a careful
reevaluation of the contribution from the target endcaps.
For our measurement, applying a more restrictive cut
on the elastic peak yielded small but systematic changes
in the extracted form factor ratio. However, the primary
effect was due to the reduction in the contribution from
endcap scattering. This was typically a 3–5% contribu-
tion to the cross section, much less for the two coinci-
dence settings, and it was difficult to apply the correction
precisely. For systematic checks, we took data with the
elastic peak centered on the focal plane, but also with
the spectrometer momentum approximately 2% higher
and lower, to map out the response of the FPP across
the focal plane. Data on the Aluminum dummy targets
was typically taken for only one setting, and so there
was a systematic uncertainty associated with the sta-
bility of the size of the background contamination and
the possible variation of the polarization transfer coef-
ficients measured from the dummy target. In addition,
while data was taken on both a 15 cm and a new 10 cm
cryogenic hydrogen target, the dummy foils were for the
standard cryotargets of 4 cm and 15 cm. Also, during
some of our runs, fluctuations in beam position caused
by problems with the position feedback system caused
parts of the beam to go through both sets of dummy
foils, making beam charge based corrections impossible.
Finally, when the cuts used to identify elastic scattering
were applied to the dummy target, the statistics available
for measuring the polarization coefficients for scattering
from Aluminum were very limited, and the statistical
fluctuations in the Aluminum contribution were some-
times large enough to be a significant contribution to the
total uncertainty, especially after accounting for the un-
certainty in the measurement of the endcap contribution
to the scattering.
For elastic scattering with an electron beam at a fixed
beam energy, the complete scattering kinematics can be
determined from the measurement of a single kinematic
quantity, typically the angle or energy of the final state
electron or proton. If two quantities are measured, then
the consistency of the two kinematic variables can be
used to determine if the event was associated with elastic
scattering. For this analysis, we use the proton scattering
angle and momentum to reconstruct the kinematics and
to identify elastic events. For some kinematics, the elec-
tron was also detected, which allows for almost complete
suppression of events coming from quasielastic scattering
in the Aluminum entrance and exit windows of the target.
To identify the elastic peak, we use the difference between
the measured proton momentum and the momentum cal-
culated for elastic scattering using the measured proton
angle. The specific variable we use in DpKin, which is
the momentum difference, pp− pelastic(θp), divided by
the central momentum setting of the proton spectrome-
ter. This yields a fractional momentum deviation from
the expectation for elastic scattering.
FIG. 1: Plots showing the reconstructed target position, Ytg
vs. DpKin, the deviation of the momentum from the ex-
pected elastic peak position, for the 10 cm liquid hydrogen
target and the dummy foils.
Figure 1 shows the distribution of events versus DpKin
and the reconstructed target position, Ytg, as seen by the
spectrometer. For the hydrogen target (top panel), there
is a strong peak at DpKin ≈ 0, corresponding to elastic
events. At the extreme Ytg values, there is a faint but
broad distribution corresponding to quasielastic scatter-
ing in the endcaps. We apply a cut to Ytg to remove
most of the contribution from the endcap scattering, and
use the measurements from the dummy target (bottom
panel) to subtract the residual contribution. The mea-
surements from the dummy target need to be normalized
to the endcap scattering to subtract away the contribu-
tion from quasielastic scattering. However, note that for
the spectra shown in Fig. 1, the length of the LH2 target
does not match either the inner or the outer pair of foils
from the dummy target. This means that the acceptance
as a function of DpKin will not be identical for the end-
caps and the foils in the dummy target, and this is clear
for the outer foils of the dummy target, where there is
a significant loss of events at extreme positive (negative)
values of DpKin for the upstream (downstream) dummy
Because of the difficulty in determining the normaliza-
tion of the dummy target relative to the aluminum end-
caps, the spectra are normalized to match the observed
“super-elastic” contribution (DpKin > 0) in the LH2
data, using only the inner foils for the dummy target,
as they have a DpKin acceptance which better matches
the endcaps. Figure 2 shows the spectra for the LH2 tar-
get (thick black histogram) and the dummy target (grey
histogram), after the dummy target has been normal-
ized in the region indicated by the vertical dashed lines.
After normalizing the spectra in this region, we can de-
termine the endcap contribution under the elastic peak.
The region used to define elastic events in the analysis is
indicated by the vertical dotted lines.
FIG. 2: (Color online) The DpKin distribution for the hy-
drogen target (thick black histogram) and the dummy targets
(thin red histogram). The dashed vertical lines indicate the
region used to normalize the dummy contribution to match
the contribution from the aluminum endcaps of the hydrogen
target and the vertical dotted lines indicate the part of the
elastic peak used in the analysis.
Having determined the contribution from endcap scat-
tering, we use the data from the dummy targets to de-
termine the contributions from quasielastic scattering to
the recoil polarization components Cxand Cz. If we ap-
ply the same cuts to the dummy target as we use in the
analysis of the hydrogen, there is very little data left, and
we can not make a reliable extraction of Cxand Cz. For
the quasielastic scattering, we use all four aluminum foils
and a broader cut on DpKin to determine the quasielas-
tic values for Cxand Cz, and then assume that the co-
efficients are identical when looking at the central part
of the quasielastic spectrum. Comparisons showed com-
plete consistency between the extracted values of Cxand
Czwhen comparing the inner and outer dummy foils for
all kinematics, or when comparing the central part of the
quasielastic peak to the off-peak contributions.
We note that for each Q2setting, three measurements
were taken. One with the elastic peak positioned at the
central momentum of the spectrometer, and two where
the elastic peak was shifted up (down) by 2% in mo-
mentum. This allowed us to verify that the result was
independent of the position of the events on the focal
plane. However, dummy events were typically taken at
only one of these three settings, and the extracted endcap
contribution and quasielastic recoil polarizations taken
from that measurement were applied to all three settings.
Because of these limitations, we take a conservative ap-
proach and apply a 50% systematic uncertainty to the
size of the endcap contribution when making the correc-
tion for these events. In addition, because we could not
make a precise determination of Cxand Czwithout aver-
aging over a larger kinematic region, we apply an uncer-
tainty to Cxand Cz of 0.02 and 0.05 respectively. Note
that typical values for these polarization components in
this experiment are 0.1–0.3.
In the original analysis , the Ytg cut was loose and
so there was a large contribution from endcap scatter-
ing (up to several percent of the hydrogen elastic scat-
tering) which had to be subtracted. Because the tight
cuts used on the elastic events were also applied to the
Dummy spectra used to correct for endcap scattering,
the statistical uncertainty on these subtractions could be
very large. Therefore, fluctuations in the low statistics
dummy measurements led to large uncertainties and sig-
nificant fluctuations in the dummy-subtracted measure-
ments. In the present analysis, the endcap contributions
are greatly reduced, with a maximum contribution well
below 1%, such the that conservative systematic uncer-
tainties assumed for the dummy normalization and po-
larization coefficients yield only small uncertainties in the
final result. The cost was a decrease in the statistics of
the hydrogen elastic events, but in the end the statistical
uncertainty after the dummy subtraction was sometimes
smaller, even with the tighter cuts. Note that for a few
settings, additional runs were included, improving the
statistics by 5–15%, but this was a small effect compared
to the modified cuts.
Additionally, in the previous analysis the systematic
uncertainties from the endcap contribution were folded
into the reported statistical uncertainties after the back-
ground reduction. In our new analysis, this effect has
been separated out as a systematic uncertainty, some-
what reducing the reported statistical uncertainty. How-
ever, the largest effect on the uncertainty is, a noted,
from the reduction of the amount of endcap contribution
in the ”good” events.
In addition, the estimated systematics are somewhat
larger than in the previous analysis, due to a more de-
tailed analysis of the uncertainty in the spin precession
through the spectrometer, taking into account an optical
model for the spectrometer magnetic field including the
Note that the proton energy loss, which can be sig-
nificant for the low Q2kinematics, was more carefully
evaluated, leading to a change in the average Q2for each
bin compared to the original analysis . Correction for
the energy loss was performed on an event-by-event ba-
sis, rather than using the average values for each kine-
matic setting. For the 362 MeV running, where the pro-
ton was detected at small angles, applying an average
energy loss is insufficient. Figure 3 shows DpKin vs.
Ytgfor one of the 362 MeV runs with an average proton
energy loss is applied to all events. Positive Ytg values
correspond to the front (upstream) portion of the target,
where all events exit through the side of the target, and
thus travel through a constant amount of hydrogen and
aluminum endcap, and can be well corrected assuming
a fixed energy loss. Events that exit through the down-
stream end of the target have reduced energy loss, as
they pass through a reduced amount of material, yield-
ing a Ytg-dependent position for the elastic peak. This
yields a reduced proton energy loss, and thus a higher ap-
parent proton momentum after applying the correction
for the nominal energy loss. For these kinematics, we use
a Ytg-dependent cut, cut corresponding to a two-sigma
region around the elastic peak for each region of Ytg, as
indicated by the graphical cut displayed in Fig. 3.
TABLE II: Kinematic-dependent cuts applied to the data.
The Ytg cut is chosen to significantly suppress any contribu-
tions from the target endcap (as shown in Fig. 3).
Ytg cutδp/p cut
28.3 −0.022 < Ytg < 0.018 |δp/p| < 0.045
23.9 −0.022 < Ytg < 0.018 |δp/p| < 0.045
18.8 −0.018 < Ytg < 0.012 |δp/p| < 0.045
14.1 −0.014 < Ytg < 0.010 |δp/p| < 0.045
47.0 −0.025 < Ytg < 0.020 |δp/p| < 0.040
44.2 −0.025 < Ytg < 0.020 |δp/p| < 0.040
40.0 −0.028 < Ytg < 0.022 |δp/p| < 0.040
34.4 −0.024 < Ytg < 0.020 |δp/p| < 0.040
The kinematic-dependent cuts are detailed in Table II.
In addition, several cuts were applied to all kinematics.
FIG. 3: (Color online) The reconstructed target position, Ytg
vs. DpKin, the deviation of the momentum from the ex-
pected elastic peak position.
energy loss is applied, but there is a significant difference for
events on the upstream side of the target, which exit through
the side wall of the target, and events which occur nearer
the downstream end of the target and have less energy loss.
The band indicates the graphical cut placed on these runs, to
approximate a two-sigma range for each Ytg value.
A correction for the average
A cut was applied on the out-of-plane angle, |θtg| < 0.06,
and the in-plane angle, |φtg| < 0.03, to ensure events were
inside of the angular acceptance of the spectrometer. A
two-sigma cut was applied on the DpKin peak, with a
Ytg-dependence cut for the low energy kinematics to ac-
count for the position-dependent average energy loss as
shown in Figure 3. The tracks before and after the Car-
bon analyzer were used to determine the scattering loca-
tion and scattering angle in the analyzer. Events were
required to have the secondary scattering occur within
the analyzer, and angle between 5 and 50◦were accepted.
In addition, we apply a cone test to ensure that there is
complete azimuthal acceptance in the FPP. We do this
by requiring that the FPP would have accepted events
with any azimuthal angle given the reconstructed vertex
and scattering angle. This ensures that that any asym-
metry in the acceptance or distribution of events does not
lead to a different in the scattering angle distribution for
vertical and horizontal rescattering. A significant dif-
ference between the rescattering distribution for vertical
and horizontal rescattering events would yield a different
average analyzing power, and the analyzing power would
not cancel out in the ratio of polarization components.
The cone test cut ensures that the distribution of rescat-
tering angles is independent of the azimuthal angle, so
that it will drop out in the ratio, as discussed in more
detail in Ref. .
The combination of the more restrictive cuts on the
elastic events and the associated reduction in contami-
nation due to scattering from the target windows leads
to a reduction in the extracted ratio that is typically
at the 1–2% level. The largest effect is due to the im-
proved correction for endcap scattering, mainly due to
TABLE III: Systematic uncertainties. See text for details.
(GeV2) (endcap) (optics) (cuts)
cuts which significantly reduced the size of this contri-
bution. There is also a 1% reduction in the coincidence
settings, where there are negligible endcap contributions,
which is due to the tighter cuts on the proton kinemat-
ics. Tight elastic kinematics cuts using just the proton
will remove events where there is a larger than average
error in the reconstruction of the proton scattering an-
gle or momentum due to multiple scattering or imper-
fect track reconstruction. While these errors are small,
the reconstructed kinematics are used to determine the
spin propagation through the spectrometer, and thus the
impact of the poor reconstruction may be amplified in
evaluating the spin precession.
The results of the reanalysis are given in Table IV and
shown in Figure 4, which presents the updated results
along with previous measurements and a selection of fits.
The updated analysis yielded a systematic decrease of
∼1% in the extracted ratio, except for the highest Q2
point which decreased by 5%. Note that the analyzing
power has been extracted  from these data, but the
quality of this extraction does not impact these results,
as the analyzing power cancels out in the ratio of Eq. 1
The results in Fig. 4 show that the original conclusions
of  are largely unaffected. The new results confirm the
observation that µpGE/GM < 1 even for these low Q2
values, with the change from previous Rosenbluth sep-
arations being driven mainly by a change in GE, with
a smaller change in GM. The previous hint of a local
minimum near Q2= 0.35−0.4 GeV2was a consequence
of the point near 0.5 GeV2, and there is no longer any
indication for this in our measurement. These results
further support the observation that the decrease of the
ratio below unity occurs at low Q2, and thus we expect
that there will be a slightly larger impact on the extrac-
tion of strange quark contributions, as discussed in the
original paper .
Figure 5 shows the measurements compared to a set
of theoretical curves. The first type of calculations are
Punjabi et al.
Crawford et al.
Paolone et al.
X. Zhan et al.
Bernauer et al.
Friedrich & Walcher fit
Updated global fit
Arrington, Melnitchouk & Tjon fit
FIG. 4: (Color online) The proton form factor ratio as a
function of four-momentum transfer Q2, shown with previ-
ous extractions with total uncertainties ≤3%. The curves are
various fits [17, 32, 40, 58], while the dot-dashed curve and
associated error bands show the result of the fit to the recent
Mainz measurements .
based on the constituent quark models, which was quite
successful in describing the ground state baryon static
properties. To calculate the form factors, relativistic ef-
fects need to be considered. Miller  performed a cal-
culation in the light-front dynamics including the effect
from the pion cloud. Boffi et al.  performed a cal-
culation in the point form frame in the Goldstone bo-
son exchange model with point-like constituent quarks.
Faessler et al.  used a chiral quark model where pi-
ons are included perturbatively and dress the bare con-
stituent quarks by mesons in a Lorentz covariant fashion.
Another large group of calculations are based on the Vec-
tor Meson Dominance (VMD) picture, in which the scat-
tering amplitude is written as an intrinsic form factor of a
bare nucleon multiplied by an amplitude derived from the
interaction between the virtual photon and a vector me-
son. This type of models usually involve a number of free
parameters for the meson mass and coupling strength.
Lomon [11, 62, 65] performed the VMD fits by including
additional vector mesons and pQCD constraint at large
Q2. Belushkin et al.  performed a calculation using
dispersion relation analysis with additional contribution
from ρπ and K¯K continua. More recently, de Melo et
al.  performed a calculation in the light-front VMD
model by considering the non-valence contribution of the
nucleon state. While most of the theoretical curves are a
few percent higher, the calculations of Miller  and de
Melo et al.  generally reproduce the large deviation
from 1 in this low Q2region, emphasizing the pion cloud
TABLE IV: Experimental Results. R is given along with its
statistical and systematic uncertainties. The last column (f) is
the fractional contribution from scattering in the target end-
caps, along with the statistical uncertainty; a 50% systematic
uncertainty is also applied. The contribution is negligible for
the coincidence settings. For Q2= 0.474 GeV2, dummy mea-
surements were taken at all three sub-settings, and the range
of results is given. The final entry is the average of the four
low Q2points, which are of lower statistical precision.
R = µpGE/GM
0.8250 ± 0.0483 ± 0.0162
0.9433 ± 0.0414 ± 0.0144
0.9882 ± 0.0420 ± 0.0132
0.9833 ± 0.0349 ± 0.0124
0.9320 ± 0.0123 ± 0.0119
0.9318 ± 0.0098 ± 0.0108 –/0.40(2)
0.9172 ± 0.0109 ± 0.0105
0.9225 ± 0.0160 ± 0.0127
0.2460.9465 ± 0.0204 ± 0.0137 n/a
or non-valence effect. However, a deeper understanding
of such mechanism is still required to explain the current
The reanalysis yields a small but systematic disagree-
ment between the polarization transfer measurements
and the polarized target extraction from the MIT-Bates
BLAST experiment  at the upper range of Q2, which
is somewhat larger than the systematic uncertainties in
our results.However, the new results are in consis-
tent with the most recent polarization transfer measure-
ment , and slightly below the recent analysis of Mainz
cross section measurements , which lie between the
Jefferson Lab polarization transfer data and the BLAST
polarized target results. While our results and the recent
E08-007 measurement  extraction used recoil polar-
ization, Phase-II of E08-007  will use a polarized tar-
get to make measurements of comparable or better pre-
cision for Q2from 0.015 to 0.4, providing a check of the
two techniques for 0.25 < Q2< 0.4 where there will be
high-precision measurements using both techniques.
This small systematic shift of the low Q2form factors
impacts on other measurements as well. For example, it
was recently pointed out  that the reduction in the
form factor yields an agreement between studies of the
asymmetry in the D(e,e′p)n reaction at low missing mo-
mentum in polarized target measurements at NIKHEF
and MIT-Bates [67–69], and recent measurements at Jef-
ferson Lab . Similarly, this small shift in GEand GM
at low Q2modifies the expected asymmetry in parity-
violating elastic electron–proton scattering, which serves
as the baseline when extracting the strange-quark con-
tribution to the proton form factors [33–36]. The effect
is relatively small for any given extraction, especially at
forward angles, due to a partial cancellation due to the
Punjabi et al.
Crawford et al.
Paolone et al.
X. Zhan et al.
Boffi et al. PFCCQM
Faessler et al. LCQM
Belushkin, Hammer & Meissner
de Melo et al.
µpGE/GM vs. Q2, compared to several low-Q2models. The
curves shown are Millers light-front cloudy-bag model calcula-
tion ; Boffis point-form chiral constituent quark model cal-
culation ; Fasslers light-front quark model calculation ;
Lomons vector-meson dominance model ; the dispersion
analysis of Belushkin, Hammer and Meissner ; and the
model of de Melo, et al. .
(Color online) The proton form factor ratio
changes in GEand GM. However, because this is a sys-
tematic correction to all such measurements, the updated
form factors could have a small net contribution on the
extracted strange-quark contributions.
The form factors at very low Q2are important in both
extracting the proton size and as input to other finite-size
corrections in atomic physics, e.g. the Zemach radius in
hyperfine splitting [5–7]. A new extraction of the proton
charge radius, including these new results, was presented
in Ref. . This analysis yielded an RMS charge radius
of 0.875(10) fm, consistent with the CODATA value 
and recent extraction from cross section measurements
from Mainz . Combined, these independent extrac-
tions based on the electron–proton interaction yield a
radius of 0.8772(46) fm , more than seven standard
deviations from the recently published PSI muonic hy-
drogen Lamb shift measurement  of 0.8418(7) fm. As
yet, it is still unclear what yields this discrepancy, and
extensive examinations of the corrections applied to both
techniques [71–76] have found no error or inconsistency
which would explain the discrepancy, although a recent
work has proposed a mechanism which could yield such
a discrepancy .
Note that while the new polarization data presented
here and in Ref.  are somewhat high in Q2to directly
constrain the charge radius, they nonetheless play an im-
portant role in the extraction. The radius is related to
the Q2dependence of the form factor as Q2→ 0, which
must be fit using data over a finite Q2range.
higher order terms in the Q2expansion need to be con-
strained  to obtain a measure of the radius. More
importantly, knowledge of the relative normalization of
the different cross section measurements at very low Q2
have typically been the dominant source of uncertainty in
the extraction of the radius, as a shift in the normaliza-
tion between large and small scattering angles can shift
strength from GEto GMin Q2-dependent fashion, yield-
ing a modification of the extracted radius. By constrain-
ing the ratio of GE to GM, the polarization data allow
for more reliable cross normalization of the different data
Since the charge radius is proportional to the deriva-
tive of the form factor at Q2=0, a new, high precision
measurement of the form factor ratio at very low Q2
values , scheduled to run at the beginning of 2012
may shed more light on this discrepancy. At very low
Q2, measurements of the ratio µpGE/GM can allow for
a much improved extraction of the magnetic form fac-
tor at very low Q2, as well as the magnetization radius,
which have been difficult to extract precisely using un-
polarized cross section measurement. This will provide
improved measurements to help constrain models of the
proton structure, and also provide improved information
on the magnetization distribution in the proton which en-
ters into the hyperfine splitting in hydrogen and muonic
hydrogen [5–7]. These new results have also recently been
incorporated in an extraction of the infinite-momentum
frame charge and magnetization densities for the pro-
ton , where the densities are extracted along with
their uncertainties, which at large distance are impacted
by the form factor uncertainties in the present Q2range.
VI.SUMMARY AND CONCLUSIONS
In summary, we present an updated form factor ex-
traction from the data of Ref. . We find a somewhat
lower value for µPGE/GMthan the initial extraction for
the entire dataset, consistent with two recent high preci-
sion measurements [39, 40]. The new analysis does not
change our previous conclusion, i.e., that there is clear
indication of a ratio smaller than unity, even for low Q2,
indicating the necessity of including relativistic effects in
any calculation of the form factors. Both the form fac-
tors and proton charge radius extraction from various e–p
scattering measurements are in agreement, and there is
still a significant disagreement with the charge radius as
extracted from muonic hydrogen .
This work was supported by the U.S. Department
of Energy, including contract DE-AC02-06CH11357, the
U.S. National Science Foundation, the Israel Science
Foundation, the Korea Research Foundation, the US-
Israeli Bi-National Scientific Foundation, and the Adams
Fellowship Program of the Israel Academy of Sciences
and Humanities. Jefferson Science Associates operates
the Thomas Jefferson National Accelerator Facility un-
der DOE contract DE-AC05-06OR23177.
 G. Ron et al., Phys. Rev. Lett. 99, 202002 (2007).
 J. J. Kelly, Phys. Rev. C 66, 065203 (2002).
 P. J. Mohr, B. N. Taylor, and D. B. Newell, Rev. Mod.
Phys. 80, 633 (2008).
 R. Pohl et al., Nature 466, 213 (2010).
 S. J. Brodsky, C. E. Carlson, J. R. Hiller, and D. S.
Hwang, Phys. Rev. Lett. 94, 022001 (2005).
 C.E.Carlson, V. Nazaryan,
arXiv:physics.atom-ph/0805.2603 (2008), 0805.2603.
 C. E. Carlson, V. Nazaryan, and K. Griffioen (2011),
 G. A. Miller, Phys. Rev. Lett. 99, 112001 (2007).
 G. A. Miller and J. Arrington, Phys. Rev. C78, 032201
 G. A. Miller, E. Piasetzky, and G. Ron, Phys. Rev. Lett.
101, 082002 (2008).
 C. Crawford et al., Phys. Rev. C82, 045211 (2010).
 A. I. Akhiezer, L. N. Rozentsweig, and I. M. Shmuske-
vich, Sov. Phys. JETP 6, 588 (1958).
 N. Dombey, Rev. Mod. Phys. 41, 236 (1969).
 R. G. Arnold, C. E. Carlson, and F. Gross, Phys. Rev.
C 23, 363 (1981).
 A. I. Akhiezer and M. P. Rekalo, Sov. Phys. Dokl. 13,
 M. K. Jones et al., Phys. Rev. Lett. 84, 1398 (2000).
 O. Gayou et al., Phys. Rev. Lett. 88, 092301 (2002).
 V. Punjabi et al., Phys. Rev. C 71, 055202 (2005),
Erratum-ibid. C 71, 069902 (2005).
 A. J. R. Puckett et al., Phys. Rev. Lett. 104, 242301
 J. Arrington, Phys. Rev. C 68, 034325 (2003).
 P. A. M. Guichon and M. Vanderhaeghen, Phys. Rev.
Lett. 91, 142303 (2003).
 J. Arrington, W. Melnitchouk, and J. A. Tjon, Phys.
Rev. C76, 035205 (2007).
 C. E. Carlson and M. Vanderhaeghen, Ann. Rev. Nucl.
Part. Sci. 57, 171 (2007).
 C. E. Hyde-Wright and K. de Jager, Ann. Rev. Nucl.
Part. Sci. 54, 217 (2004).
 J. Arrington, C. D. Roberts, and J. M. Zanotti, J. Phys.
G34, S23 (2007).
 C. F. Perdrisat, V. Punjabi, and M. Vanderhaeghen,
Prog. Part. Nucl. Phys. 59, 694 (2007).
 J. Arrington, K. de Jager, and C. F. Perdrisat (2011), *
Temporary entry *, 1102.2463.
 A. V. Belitsky, X.-d. Ji, and F. Yuan, Phys. Rev. Lett.
11 Download full-text
91, 092003 (2003).
 S. J. Brodsky, J. R. Hiller, D. S. Hwang, and V. A. Kar-
manov, Phys. Rev. D 69, 076001 (2004).
 J. P. Ralston and P. Jain, Phys. Rev. D 69, 053008
 G. A. Miller, Phys. Rev. C 68, 022201 (2003).
 J. Friedrich and T. Walcher, Eur. Phys. J. A17, 607
 D. S. Armstrong et al. (G0), Phys. Rev. Lett. 95, 092001
 K. A. Aniol et al. (HAPPEX), Phys. Lett. B 635, 275
 K. A. Aniol et al. (HAPPEX), Phys. Rev. Lett. 96,
 A. Acha et al. (HAPPEX), Phys. Rev. Lett. 98, 032301
 I. Sick, Phys. Lett. B 576, 62 (2003).
 P. G. Blunden and I. Sick, Phys. Rev. C 72, 057601
 J. C. Bernauer et al., Phys. Rev. Lett. 105, 242001
 X. Zhan et al. (2011), 1102.0318.
 G. Miller, A. Thomas, J. Carroll, and J. Rafelski (2011),
 M. N. Rosenbluth, Phys. Rev. 79, 615 (1950).
 O. Gayou et al., Phys. Rev. C 64, 038202 (2001).
 I. A. Qattan et al., Phys. Rev. Lett. 94, 142301 (2005).
 J. Arrington, Phys. Rev. C 69, 022201(R) (2004).
 P. G. Blunden, W. Melnitchouk, and J. A. Tjon, Phys.
Rev. Lett. 91, 142304 (2003).
 Y. C. Chen, A. Afanasev, S. J. Brodsky, C. E. Carl-
son, and M. Vanderhaeghen, Phys. Rev. Lett. 93, 122301
 J. Arrington, Phys. Rev. C 69, 032201(R) (2004).
 J. Arrington, D. M. Nikolenko, et al., Proposal for
positron measurement at VEPP-3, nucl-ex/0408020.
 W. Brooks, A. Afanasev, J. Arrington, K. Joo, B. Raue,
L. Weinstein, et al., Jefferson Lab experiment E04-116.
 M. Kohl, AIP Conf. Proc. 1160, 19 (2009).
 C. B. Crawford et al., Phys. Rev. Lett. 98, 052301 (2007).
 R. Gilman, A. Sarty, S. Strauch, et al., Jefferson Lab
 J. Glister et al. (2010), 1003.1944.
 J. Alcorn et al., Nucl. Inst. & Meth. A522, 294 (2004).
 G. Ron, J. Arrington, D. Day, R. Gilman, D. Higin-
botham, A. Sarty, et al., Measurement of the Proton
Elastic Form Factor Ratio at Low Q2, Jefferson Lab Ex-
periment Proposal E08-007 (2008).
 J. Glister et al., Nucl. Instrum. Meth. A606, 578 (2009).
 J. Arrington and I. Sick, Phys. Rev. C76, 035201 (2007).
 G. A. Miller, Phys. Rev. C 66, 032201 (2002).
 S. Boffi et al., Eur. Phys. J. A14, 17 (2002).
 A. Faessler, T. Gutsche,
K. Pumsa-ard, Phys. Rev. D 73, 114021 (2006).
 E. L. Lomon (2006), nucl-th/0609020.
 M. A. Belushkin, H. W. Hammer, and U. G. Meissner,
Phys. Rev. C 75, 035202 (2007).
 J. P. B. C. de Melo, T. Frederico, E. Pace, S. Pisano, and
G. Salme, Phys. Lett. B671, 153 (2009).
 E. L. Lomon, Phys. Rev. D 64, 035204 (2001).
 D. Higinbotham, AIP Conf.Proc. 1257, 637 (2010),
 I. Passchier, L. van Buuren, D. Szczerba, R. Alarcon,
T. Bauer, et al., Phys.Rev.Lett. 88, 102302 (2002).
 B. D. Milbrath et al. (Bates FPP), Phys. Rev. Lett. 80,
 B. D. Milbrath et al., Phys. Rev. Lett. 82, 2221(E)
 B. Hu, M. Jones, P. Ulmer, H. Arenhovel, O. Baker, et al.,
Phys.Rev. C73, 064004 (2006).
 V. Barger, C.-W. Chiang, W.-Y. Keung, and D. Marfatia
(2010), * Temporary entry *, 1011.3519.
 U. Jentschura, Eur.Phys.J. D61, 7 (2011).
 A. De Rujula, Phys.Lett. B693, 555 (2010).
 I. C. Cloet and G. A. Miller, Phys.Rev. C83, 012201
 A. De Rujula, Phys.Lett. B697, 26 (2011).
 M. O. Distler, J. C. Bernauer, and T. Walcher, Phys.Lett.
B696, 343 (2011).
 S. Venkat, J. Arrington, G. A. Miller, and X. Zhan,
Phys.Rev. C83, 015203 (2011).
V. E. Lyubovitskij, and