Polarization components in π0photoproduction at photon energies up to 5.6 GeV
W. Luo,1E. J. Brash,2,3R. Gilman,3,4M. K. Jones,3M. Meziane,5L. Pentchev,5C. F. Perdrisat,5A. J. R.
Puckett,6,7V. Punjabi,8F. R. Wesselmann,8A. Ahmidouch,9I. Albayrak,10K. A. Aniol,11J. Arrington,12A.
Asaturyan,13O. Ates,10H. Baghdasaryan,14F. Benmokhtar,15W. Bertozzi,6L. Bimbot,16P. Bosted,3W.
Boeglin,17C. Butuceanu,18P. Carter,2S. Chernenko,19E. Christy,10M. Commisso,14J. C. Cornejo,11S.
Covrig,3S. Danagoulian,9A. Daniel,20A. Davidenko,21D. Day,14S. Dhamija,17D. Dutta,22R. Ent,3S.
Frullani,23H. Fenker,3E. Frlez,14F. Garibaldi,23D. Gaskell,3S. Gilad,6Y. Goncharenko,21K. Hafidi,12D.
Hamilton,24D. W. Higinbotham,3W. Hinton,8T. Horn,3B. Hu,1, ∗J. Huang,6G. M. Huber,18E. Jensen,2H.
Kang,25C. Keppel,10M. Khandaker,8P. King,20D. Kirillov,19M. Kohl,10V. Kravtsov,21G. Kumbartzki,4
Y. Li,10V. Mamyan,14D. J. Margaziotis,11P. Markowitz,17A. Marsh,2Y. Matulenko,21, †J. Maxwell,14
G. Mbianda,26D. Meekins,3Y. Melnik,21J. Miller,27A. Mkrtchyan,13H. Mkrtchyan,13B. Moffit,6
O. Moreno,11J. Mulholland,14A. Narayan,22Nuruzzaman,22S. Nedev,28E. Piasetzky,29W. Pierce,2N.
M. Piskunov,19Y. Prok,2R. D. Ransome,4D. S. Razin,19P. E. Reimer,12J. Reinhold,17O. Rondon,14M.
Shabestari,14A. Shahinyan,13K. Shestermanov,21, †S.ˇSirca,30I. Sitnik,19L. Smykov,19, †G. Smith,3L.
Solovyev,21P. Solvignon,12I. I. Strakovsky,31R. Subedi,14R. Suleiman,3E. Tomasi-Gustafsson,32,16A.
Vasiliev,21M. Veilleux,2S. Wood,3Z. Ye,10Y. Zanevsky,19X. Zhang,1Y. Zhang,1X. Zheng,14and L. Zhu10
1Lanzhou University, Lanzhou 730000, Gansu, People’s Republic of China
2Christopher Newport University, Newport News, Virginia 23606, USA
3Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606, USA
4Rutgers, The State University of New Jersey, Piscataway, New Jersey 08855, USA
5The College of William and Mary, Williamsburg, Virginia 23187, USA
6Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
7Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
8Norfolk State University, Norfolk, Virginia 23504, USA
9North Carolina A&T state University, Greensboro, North Carolina 27411, USA
10Hampton University, Hampton, Virginia 23668, USA
11California State University, Los Angeles, Los Angeles, California 90032, USA
12Argonne National Laboratory, Argonne, Illinois 60439, USA
13Yerevan Physics Institute, Yerevan 375036, Armenia
14University of Virginia, Charlottesville, Virginia 22904, USA
15Carnegie Mellon University, Pittsburgh, PA 15213, USA
16Institut de Physique Nucl´ eaire, CNRS,IN2P3 and Universit´ e Paris Sud, Orsay Cedex, France
17Florida International University, Miami, Florida 33199, USA
18University of Regina, Regina, SK S4S OA2, Canada
19JINR-LHE, Dubna, Moscow Region, Russia 141980
20Ohio University, Athens, Ohio 45701, USA
21IHEP, Protvino, Moscow Region, Russia 142284
22Mississippi State University, Starkeville, Mississippi 39762, USA
23INFN, Sezione Sanit` a and Istituto Superiore di Sanit` a, 00161 Rome, Italy
24University of Glasgow, Glasgow G12 8QQ, Scotland, United Kingdom
25Seoul National University, Seoul 151-742, South Korea
26University of Witwatersrand, Johannesburg, South Africa
27University of Maryland, College Park, Maryland 20742, USA
28University of Chemical Technology and Metallurgy, Sofia, Bulgaria
29Unviversity of Tel Aviv, Tel Aviv, Israel
30Jozef Stefan Institute, 3000 SI-1001 Ljubljana, Slovenia
31The George Washington University, Washington, DC 20052, USA
32CEA Saclay, F-91191 Gif-sur-Yvette, France
(Dated: September 26, 2011)
We present new data for the polarization observables of the final state proton in the1H(? γ,? p)π0
reaction. These data can be used to test predictions based on hadron helicity conservation (HHC)
and perturbative QCD (pQCD). These data have both small statistical and systematic uncertainties,
and were obtained with beam energies between 1.8 and 5.6 GeV and for π0scattering angles larger
than 75◦in center-of-mass (c.m.) frame. The data extend the polarization measurements data
base for neutral pion photoproduction up to Eγ = 5.6 GeV. The results show non-zero induced
polarization above the resonance region. The polarization transfer components vary rapidly with
the photon energy and π0scattering angle in c.m. frame. This indicates that HHC does not hold
and that the pQCD limit is still not reached in the energy regime of this experiment.
arXiv:1109.4650v2 [nucl-ex] 23 Sep 2011
One of the major goals of nuclear physics is to under-
stand the mechanism of exclusive reactions, like meson
photoproduction. Measurements of both cross sections
and polarization observables help form an understand-
ing of the dynamics of meson production. The neutral
pion photoproduction process has been extensively stud-
ied for several decades at low photon energies, Eγ< 2.5
GeV, both theoretically and experimentally. Prominent
structures in the cross section data indicate that π0pho-
toproduction is dominated by the excitation of baryon
resonances. As further evidence of this mechanism, two
observables, the induced recoil proton polarization P and
the linearly polarized photon asymmetry Σ, are well char-
acterized below 1.5 GeV. Eight independent observables
are required to determine the four helicity amplitudes
without discrete ambiguities in this reaction [1, 2]. A
more recent Jefferson Lab Hall A experiment  obtained
data for the three polarization components and confirmed
the importance of polarization observables as a powerful
tool to search for resonance states. The contribution of
these polarization results in constraining multipole analy-
ses was investigated in Ref. , the conclusion was more
data were needed to constrain the multipoles above 1
Above the known resonance region, the cross sec-
tion for meson photoproduction is expected to be struc-
tureless and approximately follow the constituent quark
counting rules , which can be derived from pQCD. A
scaling behavior for a variety of different cross sections
has been observed for a number of exclusive reactions at
high transverse momenta [6–11]. But the recent Hall A
precise real Compton scattering cross section results 
give a scaling parameter near 8 for a kinematic range of
s = 5-11 and −t = 2-7 GeV2which is in strong disagree-
ment with pQCD-predicted value (n≈6). The structure-
less cross section data do not rule out the possibility of
overlapping high-mass resonance states with large width.
To determine the amplitudes which contribute to a par-
ticular energy bin, partial-wave analysis is required.
As a consequence of pQCD, with the assumption that
orbital angular momentum can be neglected, HHC 
predicts that the polarization components of the pro-
ton above the baryon resonance region should have a
smooth dependence on Eγ and approach limits estab-
lished by HHC in the absence of baryon resonance in the
1H(? γ,? p)π0reaction. Strong variation of the polarization
variables above 2 GeV might be an indication of the con-
tribution of high-mass resonances.
Two experiments were carried out by the GEp-III and
GEp-2γ collaborations in Hall C at Jefferson Lab. GEp-
III measured the elastic proton form factor ratio to high
four-momentum transfer, Q2, using the recoil polariza-
tion method in the ep elastic reaction . GEp-2γ mea-
sured the kinematic dependence of the ratio at fixed Q2
. Due to its relatively larger cross section at high Q2
and kinematical similarity in phase space to the ep elas-
0.20.4 0.60.81 1.2 1.4
determined random background
MC ep elastic
MC + random background
FIG. 1: The π0event selection at an incident photon energy
Eγ = 3.951 GeV. The distributions of the predicted energy
deposition in the BigCal are plotted for the data (red solid
line), the random background (green solid line) determined
from time of flight spectra, the Monte Carlo simulation of π0
events (light blue dotted line), and the MC simulation of ep
elastic events (blue dashed line). The black solid line is the
sum of the MC simulation of π0s, ep elastic events and the
measured random background. The simulated curves have
been scaled to match the data. The two vertical lines are
described in the text.
tic reaction, neutral pion production was the major con-
tribution to the background of these experiments. The
other reactions are suppressed by the ep elastic kinematic
settings. These pions come from real photoproduction as
well as electroproduction. The angular and energy selec-
tivity of these experiments restricted the contribution of
electroproduction to very low values of Q2, i.e., quasi-
real photons, resulting in final states indistinguishable
from photoproduction induced by real Bremsstrahlung
photons. Therefore, the polarization observables of the
protons in these two reactions are similar as proven by a
previous experiment . In this paper, these two reaction
channels are not distinguished and are collectively called
neutral pion photoproduction.
A high luminosity longitudinally polarized electron
beam (79-86% polarization) was scattered from a 20 cm
liquid hydrogen target. In the six kinematic settings of
the experiments, the incident electron energy was 1.87,
2.84, 3.63, 4.05 and 5.71 GeV (two settings with Ee =
5.71 GeV). The beam helicity was flipped at 30 Hz. The
beam polarization was monitored by the Hall C Møller
polarimeter  with an accuracy of 1.0%.
endpoint, the circular polarization of the Bremsstrahlung
photons is nearly equal to the longitudinal polarization of
the incident electron, while the linear polarization com-
ponent vanishes .
TABLE I: The proton polarization components for the process1H(? γ,? p)π0. The Eγ is the incident photon energy calculated
by the proton angle and momentum, θc.m.
is the angle of π0in c.m. frame for each bin of Eγ, χ is the proton spin precession
angle inside the HMS.
1.845 ± 0.038
2.704 ± 0.050
2.776 ± 0.025
3.304 ± 0.050
3.402 ± 0.050
3.498 ± 0.050
3.569 ± 0.030
3.858 ± 0.050
3.951 ± 0.050
5.550 ± 0.050
5.631 ± 0.030
5.552 ± 0.050
5.643 ± 0.040
143.3 ± 2.5
97.1 ± 2.3
96.1 ± 2.3
82.5 ± 2.3
81.6 ± 2.5
79.7 ± 2.3
79.4 ± 2.5
124.7 ± 4.2
123.3 ± 4.6
112.6 ± 4.0
112.2 ± 5.3
138.1 ± 4.0
137.3 ± 5.3
0.331 ± 0.003 ± 0.006
0.508 ± 0.007 ± 0.005
0.465 ± 0.009 ± 0.005
0.082 ± 0.014 ± 0.009
0.074 ± 0.008 ± 0.009
0.080 ± 0.009 ± 0.008
0.094 ± 0.018 ± 0.008
0.061 ± 0.024 ± 0.007
0.064 ± 0.018 ± 0.003
0.098 ± 0.041 ± 0.007
0.025 ± 0.054 ± 0.002
0.198 ± 0.015 ± 0.021
0.189 ± 0.016 ± 0.009
± stat. ± syst.Clab
0.073 ± 0.006 ± 0.005
0.255 ± 0.013 ± 0.004
0.263 ± 0.017 ± 0.003
0.358 ± 0.024 ± 0.009
0.362 ± 0.014 ± 0.009
0.343 ± 0.016 ± 0.008
0.293 ± 0.031 ± 0.010
0.742 ± 0.077 ± 0.020
0.699 ± 0.057 ± 0.018
-0.078 ± 0.080 ± 0.009
-0.162 ± 0.104 ± 0.009
0.732 ± 0.016 ± 0.026
0.772 ± 0.017 ± 0.019
± stat. ± syst.P ± stat. ± syst.
-0.503 ± 0.014 ± 0.012
0.138 ± 0.030 ± 0.009
0.023 ± 0.036 ± 0.009
0.215 ± 0.053 ± 0.014
0.210 ± 0.030 ± 0.012
0.151 ± 0.034 ± 0.010
0.237 ± 0.066 ± 0.012
-0.176 ± 0.020 ± 0.011
-0.174 ± 0.015 ± 0.009
0.387 ± 0.053 ± 0.034
0.347 ± 0.070 ± 0.033
The scattered protons were detected in the Hall C
High Momentum Spectrometer (HMS) . The proton
trajectories were measured by drift chambers located in
the HMS focal plane. The polarization of the proton
was measured by the Focal Plane Polarimeter (FPP) in
the HMS detector hut downstream from the HMS drift
chambers. The FPP, consisting of two 55 cm CH2 an-
alyzer blocks, each followed by a pair of drift cham-
bers, measured the asymmetry of the charged particles
in ? p+CH2→ charged particle + X to extract the proton
An electromagnetic calorimeter (BigCal), with a front
area of 1.2 × 2.2 m2, and consisting of 1744 4×4 cm2
lead-glass blocks, was placed at the six positions match-
ing the acceptance of the HMS for the elastic ep reaction.
BigCal provides no discrimination between electrons and
photons and gives the impact position with similar res-
olution for both. The BigCal energy resolution changed
from 10%/√E to 23%/√E during the experiment be-
cause of radiation damage to the lead-glass. By contrast,
the coordinate resolution of about 8 mm is not measur-
ably affected by radiation damage. The primary trigger
of the experiment was a coincidence between signals from
the BigCal and from the HMS within a ±50 ns timing
In π0photoproduction, the meson decays into two pho-
tons directly following its production.
opening angle between these two decay photons corre-
sponds to the two photons sharing the energy of the π0
equally in the lab frame. As the opening angle increases,
one photon will take more energy from the π0and its
track will be closer to the incident π0track direction. Ei-
ther of the π0decay photons with energy greater than the
BigCal hardware energy threshold (set typically at about
half the ep elastic scattered electron energy) hitting the
BigCal will produce a BigCal trigger. If the event was in
coincidence with a proton in the HMS, it was recorded.
In two kinematic settings where the electron beam en-
ergy was 5.71 GeV, the BigCal coincidence acceptance
with the HMS was large enough to detect both photons.
These data with lower statistics were also analyzed and
the results were found to be consistent with the “one
photon detected” results. In this paper, only the “one
photon detected” results will be shown.
To identify π0events when one photon was detected in
the BigCal, the π0decay photon energy predicted from
the proton angle, momentum and the π0decay photon
angle was compared with the energy measured in the
BigCal. A good linear correlation was seen between the
measured and predicted energies. We applied a 3σ cut on
the ratio of the measured and predicted photon energy to
identify the π0events. The major background events in
the π0photoproduction channel come from the ep elas-
tic radiative tail and from random coincidence events.
To reduce random background, a 3σ cut around the Big-
Cal and HMS coincidence time peak was applied. The
ep elastic radiation tail contamination was estimated by
comparing the data to Monte Carlo simulation. Back-
ground events came from heavier meson photoproduction
and multiple π0photoproduction were also estimated by
the simulation. Only the data near the Bremsstrahlung
endpoint with less than 1.0% contamination from these
two types of reactions were kept in the analysis.
Figure 1 shows the distribution of the predicted π0de-
cay photon energy E?
indicates the hardware energy threshold of BigCal, and
the right vertical dashed line indicates the E?
limit selected to optimize the signal to background ratio
calo. The left vertical dashed line
and statistics. Events between the two vertical dashed
lines were selected and used in the analysis. At an inci-
dent photon energy of 3.951 GeV, the elastic background
contamination ratio in the selected range of E?
and the random background contamination is 1.5% after
all cuts were applied. The polarization components of
both kinds of background were studied separately and
corrections were applied to the final results.
Elastic events were used to calibrate the FPP analyz-
ing power and determine the instrumental asymmetry at
each kinematic setting. With the knowledge of the beam
polarization and of the spin precession in the HMS ,
polarization transfer in the ep elastic reaction allows the
determination of both the CH2analyzing power and the
ratio of the proton electromagnetic form factors. To take
into account the proton momentum difference between
elastic events and π0events, the analyzing power of π0
events was obtained by correcting the ep elastic results
according to the analyzing power momentum dependence
. As the induced polarization in ep elastic scattering
is zero in the one photon exchange mechanism, the instru-
mental asymmetry could be extracted by Fourier analy-
sis of the helicity sum spectrum of ep elastic events. The
same cut on hit position of the protons in the focal plane
of ep elastic events was applied to the π0events to make
sure the calibrated analyzing power and the instrumental
asymmetry are valid. This cut also further suppressed
the heavier meson (e.g., η) production contribution to
the data by requiring higher proton momentum in the
HMS. After all these calibrations were done, the induced
and transferred polarization components of the proton in
π0photoproduction at the target were extracted by the
maximum likelihood method described in Ref. .
The high statistics of π0events allows us to divide the
data into several incident photon energy bins. The bin
size was selected to be greater than the reconstructed in-
cident photon energy resolution (less than 12 MeV for all
kinematics) and to keep enough events to calculate the
polarization components in each bin. Systematic uncer-
tainties were estimated by analyzing the sensitivity of the
polarization components to background corrections, the
beam polarization, the instrumental asymmetry, the ana-
lyzing power calibration and the tracking reconstruction
systematics for each bin. For the polarization transfer
components, the uncertainties from the ep elastic back-
ground estimation are dominant because the polarization
components are very different in ep elastic events. The
systematic uncertainties of the induced polarization com-
ponent are dominated by the instrumental asymmetry
correction. Overall, the systematic uncertainties are less
than ±0.026 for the polarization transfer components and
do not exceed ±0.034 for the induced polarization com-
The results are listed in Table I. No induced polariza-
tion data for the last kinematics in the table are available
because the spin precession inside the HMS at this set-
ting leads to very large systematic uncertainties. The lab
coordinate system is defined by ˆ z =ˆkproton/|ˆkproton|, ˆ y
=ˆkproton×ˆkγ/|ˆkproton×ˆkγ| and ˆ x = ˆ y×ˆ z, whereˆkproton
(ˆkγ) is the recoil proton (incident photon) momentum.
are the longitudinal, the induced (along
ˆ y) and the transverse polarization components in the lab
Several theoretical models predict the polarization ob-
servables in the1H(? γ,? p)π0reaction; they are partial-
wave analyses SAID  and MAID  (Eγ
1.65 GeV), a quark model sub-process calculation by
Afanasev et al. , and a pQCD prediction from Farrar
et al. .
In SAID, both an energy-dependent and a set of
energy-independent partial-wave analyses of single-pion
photoproduction data were performed. The latest SP09
 solution extends from threshold to 2.7 GeV of inci-
dent photon energy in the laboratory.
Assuming helicity conservation, the induced polariza-
tion P and the transverse polarization transfer Cc.m.
pion photoproduction are zero. From pQCD scaling ar-
guments, the longitudinal polarization transfer Cc.m.
constant at fixed θc.m.
, but HHC alone does not deter-
mine the value of this constant.
Farrar et al. predicted the helicity amplitudes for pion
photoproduction by explicitly calculating all lowest-order
Feynman diagrams . Several nucleon and pion wave
functions were used in the calculation. The predicted
cross sections are highly sensitive to the choices of wave
functions and they do not agree with the data in general.
The calculated curves shown in Fig. 2 used asymptotic
distribution amplitudes for both the proton and the pion.
Afanasev et al.  used a pQCD approach to cal-
culate the longitudinal polarization Cc.m.
toproduction in the limit xBjorken→ 1. This model as-
sumes helicity conservation and that the pQCD approach
is justified for high meson transverse momentum.
Figure 2 presents the comparison of the new Hall C re-
sults with data from previous experiment and the avail-
able models. Not all the data of  are shown in the
figure. The theoretical predictions are calculated for the
given π0c.m. angles shown in the panels and have been
converted from the c.m. frame to the lab frame. In the
lower incident photon energy regime (Eγ < 2.7 GeV),
these new data agree with the world data except for the
induced polarization in Fig. 2 j. A strong θc.m.
dence for P at Eγ = 2.5 GeV was found in the previ-
ous measurement . This discrepancy very likely comes
from the difference in θc.m.
the previous measurement. While the SAID model gives
good overall predictions for energies lower than 3 GeV,
it disagrees with the data in Fig. 2 panels a), j) and h);
this can be understood since above 1 GeV the multipoles
are still under-constrained in the model. For the larger
incident photon energies (Eγ> 3.0 GeV), the new data
z , P and Clab
of meson pho-
between the new data and
Polarization Transfer C
K. Wijesooriya 
Polarization Transfer C
Induced Polarization P
FIG. 2: Top to bottom: polarization transfer Clab
angles of π0in c.m. frame. The “old data” could be found in the SAID data base . The three curves labeled Afanasev
model , Farrar model  and SAID SP09  are described in the text. Only the statistical uncertainties are shown.
x , Clab
z , and induced polarization P in the lab frame. Left to right: different
are the first measurements at the given θc.m.
sults still show strong energy dependence in Clab
at 120 degrees, and a strong angle dependence in Clab
at Eγ ≈ 5.6 GeV. Such behavior was not predicted by
the models based on HHC. It appears, based on our few
examples, that the strong kinematic dependences in the
SAID fit at low energies continue up to 5.6 GeV.
To conclude, the precise new polarization data for π0
photoproduction from the proton presented here extend
the world data set to Eγ= 5.6 GeV. In the lower energy
region, the new data are in good agreement with previous
measurements and the SAID predictions. But the new
data of Eγ < 2.7 GeV do not give a further constraint
on the multipole fit alone; more lower energy data from
MAMI-C will be very useful  for this purpose. At
higher energy, the new data show no evidence of HHC
at Eγ = 5.6 GeV. Furthermore, the polarization trans-
fer components vary drastically as a function of θc.m.
Eγ≈ 5.6 GeV and this is not predicted by any theoretical
model. The high energy data may allow interpretation in
terms of the quark handbag mechanism, providing access
to polarization-dependent Generalized Parton Distribu-
tions, as discussed in , . More theoretical predic-
tions would be highly desirable and the interpretation of
. The re-
the data would help achieve a complete understanding of
the mechanism of this reaction.
We thank A. Afanasev for discussions of his model, and
acknowledge the Hall C technical staff and the Jefferson
Lab Accelerator Division for their outstanding support
during the experiment. This work was supported in part
by the U.S. Department of Energy, the U.S. National
Science Foundation, the Italian Institute for Nuclear re-
search, the French Commissariat ` a l’Energie Atomique
(CEA) and the Centre National de la Recherche Sci-
entifique (CNRS), and the Natural Sciences and Engi-
neering Research Council of Canada. This work is sup-
ported by DOE contract DE-AC05-06OR23177, under
which Jefferson Science Associates, LLC, operates the
Thomas Jefferson National Accelerator Facility.
∗Corresponding author: firstname.lastname@example.org
 I. Barker, A. Donnachie, and J. Storrow, Nuclear Physics
B 95, 347 (1975), ISSN 0550-3213.
 W.-T. Chiang and F. Tabakin, Phys. Rev. C 55, 2054
6 Download full-text
 K. Wijesooriya et al., Phys. Rev. C 66, 034614 (2002).
 R. A. Arndt, I. I. Strakovsky, and R. L. Workman, Phys.
Rev. C 67, 048201 (2003).
 S. J. Brodsky and G. R. Farrar, Phys. Rev. Lett. 31,
 R. L. Anderson et al., Phys. Rev. D 14, 679 (1976).
 C. Bochna et al., Phys. Rev. Lett. 81, 4576 (1998).
 J. E. Belz et al., Phys. Rev. Lett. 74, 646 (1995).
 S. J. Freedman et al., Phys. Rev. C 48, 1864 (1993).
 E. C. Schulte et al., Phys. Rev. Lett. 87, 102302 (2001).
 L. Y. Zhu et al. (Jefferson Lab Hall A Collaboration),
Phys. Rev. Lett. 91, 022003 (2003).
 A. Danagoulian et al., Phys. Rev. Lett. 98, 152001
 S. J. Brodsky and G. P. Lepage, Phys. Rev. D 24, 2848
 A. J. R. Puckett et al., Phys. Rev. Lett. 104, 242301
 M. Meziane et al., Phys. Rev. Lett. 106, 132501 (2011).
 M. Hauger et al., Nucl. Instrum. Methods A 462, 382
 H. Olsen and L. C. Maximon, Phys. Rev. 114, 887 (1959).
 H. Blok et al., Phys. Rev. C 78, 045202 (2008).
 K. Makino and M. Berz, Nucl. Instrum. Methods A 427,
 L. S. Azghirey et al., Nucl. Instrum. Methods A 538, 431
 R. A. Arndt, W. J. Briscoe, I. I. Strakovsky, and R. L.
Workman, Phys. Rev. C 66, 055213 (2002).
 D. Drechsel, S. Kamalov, and L. Tiator, The European
Physical Journal A - Hadrons and Nuclei 34, 69 (2007),
 A. Afanasev, C. E. Carlson, and C. Wahlquist, Physics
Letters B 398, 393 (1997).
 G. R. Farrar, K. Huleihel, and H. Zhang, Nuclear Physics
B 349, 655 (1991), ISSN 0550-3213.
 M. Dugger et al. (CLAS Collaboration), Phys. Rev. C
79, 065206 (2009).
 M. Sikora, Ph.D. thesis, Edinburgh Univ. (2011).
 A. V. Afanasev, arXiv:hep-ph/9808291 (1998).
 H. W. Huang, R. Jakob, P. Kroll, and K. Passek-
Kumericki, Eur. Phys. J. C33, 91 (2004).