Measurement of the Differential Cross Section for the Reaction $gamma$n→ $pi$^$$-$$ p from Deuterium
arXiv:0903.1260v1 [nucl-ex] 6 Mar 2009
A measurement of the differential cross section for the reaction γn → π−p from
W. Chen,1T. Mibe,2D. Dutta,3H. Gao,1J.M. Laget,7,4M. Mirazita,5P. Rossi,5S. Stepanyan,4I.I. Strakovsky,6
M.J. Amaryan,27,37M. Anghinolfi,20H. Bagdasaryan,27, ∗M. Battaglieri,20M. Bellis,10B.L. Berman,6
A.S. Biselli,15,29C. Bookwalter,17D. Branford,14W.J. Briscoe,6W.K. Brooks,34,4V.D. Burkert,4S.L. Careccia,27
D.S. Carman,4L. Casey,11P.L. Cole,19,4P. Collins,8V. Crede,17A. Daniel,2N. Dashyan,37R. De Vita,20
E. De Sanctis,5A. Deur,4S. Dhamija,16R. Dickson,10C. Djalali,32G.E. Dodge,27D. Doughty,12,4
H. Egiyan,25,36P. Eugenio,17G. Fedotov,31A. Fradi,21M. Gar¸ con,7G.P. Gilfoyle,30K.L. Giovanetti,23
F.X. Girod,7, †W. Gohn,13R.W. Gothe,32K.A. Griffioen,36M. Guidal,21H. Hakobyan,34,37C. Hanretty,17
N. Hassall,18D. Heddle,12, 4K. Hicks,2M. Holtrop,25C.E. Hyde,27, 28Y. Ilieva,32D.G. Ireland,18B.S. Ishkhanov,31
E.L. Isupov,31H.S. Jo,21J.R. Johnstone,18K. Joo,13,35D. Keller,2M. Khandaker,26P. Khetarpal,29A. Klein,27
F.J. Klein,11,4L.H. Kramer,16,4V. Kubarovsky,4S.E. Kuhn,27S.V. Kuleshov,22V. Kuznetsov,24K. Livingston,18
H.Y. Lu,32N. Markov,13M.E. McCracken,10B. McKinnon,18C.A. Meyer,10T Mineeva,13V. Mokeev,31,4
B. Moreno,21K. Moriya,10P. Nadel-Turonski,11R. Nasseripour,32, ‡S. Niccolai,21I. Niculescu,23, 6M.R. Niroula,27
M. Osipenko,20,31A.I. Ostrovidov,17K. Park,32,24S. Park,17S. Anefalos Pereira,5O. Pogorelko,22S. Pozdniakov,22
J.W. Price,9S. Procureur,7D. Protopopescu,18B.A. Raue,16,4G. Ricco,20M. Ripani,20B.G. Ritchie,8G. Rosner,18
F. Sabati´ e,7,27M.S. Saini,17J. Salamanca,19C. Salgado,26R.A. Schumacher,10Y.G. Sharabian,4,37D.I. Sober,11
D. Sokhan,14S. Strauch,32M. Taiuti,20D.J. Tedeschi,32S. Tkachenko,27M. Ungaro,13M.F. Vineyard,33,30
D.P. Watts,18, §L.B. Weinstein,27D.P. Weygand,4M.H. Wood,32A. Yegneswaran,4J. Zhang,27and B. Zhao13
(The CLAS Collaboration)
1Duke University, Durham, North Carolina 27708
2Ohio University, Athens, Ohio 45701
3Mississippi State University, Mississippi State, MS 39762
4Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606
5INFN, Laboratori Nazionali di Frascati, 00044 Frascati, Italy
6The George Washington University, Washington, DC 20052
7CEA-Saclay, Service de Physique Nucl´ eaire, 91191 Gif-sur-Yvette, France
8Arizona State University, Tempe, Arizona 85287-1504
9California State University, Dominguez Hills, Carson, CA 90747
10Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
11Catholic University of America, Washington, D.C. 20064
12Christopher Newport University, Newport News, Virginia 23606
13University of Connecticut, Storrs, Connecticut 06269
14Edinburgh University, Edinburgh EH9 3JZ, United Kingdom
15Fairfield University, Fairfield CT 06824
16Florida International University, Miami, Florida 33199
17Florida State University, Tallahassee, Florida 32306
18University of Glasgow, Glasgow G12 8QQ, United Kingdom
19Idaho State University, Pocatello, Idaho 83209
20INFN, Sezione di Genova, 16146 Genova, Italy
21Institut de Physique Nucleaire ORSAY, Orsay, France
22Institute of Theoretical and Experimental Physics, Moscow, 117259, Russia
23James Madison University, Harrisonburg, Virginia 22807
24Kyungpook National University, Daegu 702-701, Republic of Korea
25University of New Hampshire, Durham, New Hampshire 03824-3568
26Norfolk State University, Norfolk, Virginia 23504
27Old Dominion University, Norfolk, Virginia 23529
28Universit´ e Blaise Pascal, Laboratoire de Physique Corpusculaire CNRS/IN2P3 F-63177 Aubi` ere France
29Rensselaer Polytechnic Institute, Troy, New York 12180-3590
30University of Richmond, Richmond, Virginia 23173
31Skobeltsyn Nuclear Physics Institute, Skobeltsyn Nuclear Physics Institute, 119899 Moscow, Russia
32University of South Carolina, Columbia, South Carolina 29208
33Union College, Schenectady, NY 12308
34Universidad T´ ecnica Federico Santa Mar´ ıa, Casilla 110-V Valpara´ ıso, Chile
35University of Virginia, Charlottesville, Virginia 22901
36College of William and Mary, Williamsburg, Virginia 23187-8795
37Yerevan Physics Institute, 375036 Yerevan, Armenia
(Dated: March 6, 2009)
We report a measurement of the differential cross section for the γn → π−p process from the
CLAS detector at Jefferson Lab in Hall B for photon energies between 1.0 and 3.5 GeV and pion
center-of-mass (c.m.) angles (θc.m.) between 50◦and 115◦. We confirm a previous indication of a
broad enhancement around a c.m. energy (√s) of 2.2 GeV at θc.m. = 90◦in the scaled differential
cross section, s7 dσ
dt. Our data show the angular dependence of this enhancement as the scaling
region is approached in the kinematic region from 70◦to 105◦.
PACS numbers: 13.60.Le, 24.85.+p, 25.10.+s, 25.20.-x
The γn → π−p, γp → π+n and γp → π0p reactions
are essential probes of the transition from meson-nucleon
degrees of freedom to quark-gluon degrees of freedom
in exclusive processes. The Constituent Counting Rule
(CCR) [1, 2] was proposed as a signature for the search
of such a transition. According to CCR, the differential
cross section for high energy exclusive two-body reactions
at a fixed c.m. angle scales as dσ/dt ∝ s−(n−2). Here n is
the total number of point-like particles and gauge fields in
the initial plus final states and s and t are the invariant
Mandelstam variables for the total energy squared and
the four-momentum transfer squared, respectively. In the
last decade or so, an all-orders demonstration of counting
rules for hard exclusive processes has been shown arising
from correspondence between the anti-de Sitter space and
the conformal field theory , which connects superstring
theory to QCD.
The differential cross section for many exclusive reac-
tions [4, 5], at high energy and large momentum transfer,
appears to obey the CCR, and in recent years, the scal-
ing behavior has been observed also in deuteron photo-
disintegration [6, 7, 8, 9, 10] at a surprisingly low trans-
verse momentum value above about 1.1 GeV/c [8, 10].
In addition to the early onset of scaling, some exclusive
processes such as pp [11, 12] and πp [12, 13] elastic scat-
tering, show a striking oscillation in the scaled differen-
tial cross section about the predicted quark counting rule
The CCR scaling behavior was studied in π0 and
π+photoproduction from the proton [14, 15, 16], and
in π−for the first time in the Thomas Jefferson National
Accelerator Facility (Jefferson Lab) Hall A experiment
E94-104 [15, 16] using a deuterium target and an un-
tagged bremsstrahlung photon beam. The data of the
γn → π−p process exhibit an overall CCR scaling behav-
ior at θc.m.= 70◦and 90◦, similar to what was observed
in the π+channel at similar c.m. angles. The data 
from both the γn → π−p and the γp → π+n processes
at θc.m. = 90◦seem to hint at some oscillatory scaling
behavior. Such oscillatory scaling behavior could be ex-
plained as suggested recently by Refs. [17, 18, 19]. The
data also suggest that a transverse momentum of around
1.2 GeV/c might be the scale governing the onset of scal-
ing, consistent with what has been observed in deuteron
photodisintegration [8, 10]. One very interesting feature
of the data is an apparent enhancement in the scaled dif-
ferential cross section at θc.m. = 90◦and at√s range
approximately from 1.8 GeV to 2.5 GeV. Furthermore,
the scaled differential cross section drops by a factor of
about 4 in a very narrow c.m. energy region (few hun-
dreds of MeV) around 2.5 GeV.
The sudden drop in the scaled differential cross section
may shed light on the transition between the aforemen-
tioned physical pictures. It is important to understand
the nature of the enhancement followed by the dramatic
drop in the scaled cross section and to test the onset of
scaling behavior in pion photoproduction. This requires
a detailed investigation of the pion photoproduction cross
section in the√s range from 1.8 to 2.5 GeV with very
fine photon energy bins. (However, this energy range
would not allow for a confirmation or refutation of the
oscillatory scaling behavior hinted by experiment E94-
104 .) In this paper, we report such a detailed study
using high statistics data from the Jefferson Lab CEBAF
Large Acceptance Spectrometer (CLAS)  in Hall B
taken during the g10 running period .
The CLAS instrumentation was designed to provide
large coverage of charged particles (8◦≤ θ ≤ 140◦). It
is divided into six sectors by six superconducting coils
which generate a toroidal magnetic field. Each sector
acts as an independent detection system that includes
drift chambers (DC), Cerenkov counters (CC), scintil-
lation counters (SC) and electromagnetic calorimeters
(EC). The drift chambers determine the trajectories of
charged particles. With the magnetic field generated by
the superconducting coils, the momenta of the charged
particle can be determined from the curvature of the tra-
jectories. The scintillation counters measure the time-
of-flight and provide charged particle identification when
combined with the momentum information from the drift
chambers. Details about the CLAS can be found in
A 24-cm long liquid-deuterium target was employed
with the target cell positioned 25 cm upstream from the
CLAS nominal center. A tagged-photon beam  gen-
erated by a 3.8-GeV electron beam incident on a gold ra-
diator with a radiation length of 10−4, corresponded to a
maximum√s of 2.8 GeV for the process of interest. The
event trigger required at least two charged particles in
different sectors. Two magnetic field settings were used
during the experiment, corresponding to a low-field set-
ting (with toroidal magnet current I=2250 A) for better
forward angle coverage , and a high-field setting (I=3375
A) for better momentum resolution. About 1010triggers
were collected during the g10 running period of about
The raw data collected from the experiment were first
processed to calibrate and convert the information from
the detector subsystems to physical variables for detected
particles such as energy, momentum, position and timing
information. The events of interest for which the photon
coupled to the neutron inside the deuteron, were selected
by ensuring a proton and a π−in the final state. The dif-
ference of the reconstructed time of photon and charged
particles at the reaction vertex was required to be within
1 ns to ensure that they came from the same accelera-
tor electron bunch, which had a period of 2.004 ns. The
momentum of the spectator proton in the deuteron is
mostly below 200 MeV/c and is therefore not detected by
CLAS. The 4-momentum of the undetected proton was
reconstructed by energy-momentum conservation. Only
events with missing mass around the proton mass were
selected to make sure that the missing particle was the
undetected proton. Shown in Fig. 1(a) is a typical recon-
structed missing mass squared distribution. A 3σ cut was
applied to identify the proton. Monte Carlo simulations
for the γn → π−p process based on a phase space gener-
ator have been carried out to determine the acceptance.
In the simulation, the neutron momentum distribution
inside the deuteron is based on the deuteron wave func-
tion obtained from the Bonn potential . Fig. 1(b)
shows the reconstructed proton momentum from the ex-
perimental data and the simulation. The excellent agree-
ment between the data and the Monte Carlo for a missing
momentum below 200 MeV/c justified the cut we used
(shown by the dashed line) in our analysis to select the
quasifree events of γn → π−p from deuterons.
To extract the cross section, the aforementioned phase
space based simulation is used to correct for events lost
due to geometrical constraints and detector inefficiencies.
The response of the CLAS detector was simulated in
GEANT. More than 108of events were generated and
passed through the simulation. The simulated data were
then processed to incorporate the subsystem efficiencies
and resolutions extracted from the experiment. The DC
wire efficiency and SC efficiency were studied in detail.
The “excluded-layer method”  was used to study the
DC wire efficiency and identify the bad DC regions. The
SC efficiency was extracted by studying the SC occupan-
cies. The correction due to the SC inefficiency is about
20% for the γn → π−p channel. All the simulated data
were then processed by the same software used in the
real data processing and analysis.
the events that passed the simulation and the generated
events is a product of the detector efficiency and the ac-
The final state interaction (FSI) effects must be taken
into account before one extracts cross sections on the neu-
The ratio between
tron since a deuteron target is used. The FSI correction
is estimated according to the Glauber formulation 
and this correction is about 20%.
The differential cross section in the c.m. frame of the
γn system is then given by
where tGis the correction  for the FSI, ǫ is the prod-
uct of the detector efficiency and acceptance, N is the
number of events, Nγis the total number of photons in-
cident on the target, and A, NA, L, ρ are deuteron atomic
mass, Avogadro’s number, target length and target den-
sity, respectively. The scaled differential cross section is
mentum in the c.m. frame, respectively. The results from
the high magnetic field setting are consistent with those
from the low magnetic field setting within systematic un-
There are three major sources of systematic uncertain-
ties: the luminosity, the FSI correction, and the back-
ground. We studied the target thickness fluctuations as
seen by the beam, as well as the run-dependent, and
beam-current-dependent fluctuations of the normalized
yield. All of them contribute to the uncertainty in the
luminosity, and in total this uncertainty is less than 5%.
The uncertainty of the Glauber calculation for the FSI
correction was estimated to be 5% in Ref. . To study
the model uncertainty in calculating the FSI correction,
we carried out another calculation using the approach
of Ref. . Both methods agree within 10%. A 10%
systematic uncertainty to the differential cross section is
assigned for the FSI correction. The background in the
missing mass peak region is about 2% - 7% depending
on the photon energy and an example is shown in Fig. 1
(left). According to Monte Carlo simulations, the back-
ground could come from the poorly reconstructed real
events due to the DC resolution. Therefore, no back-
ground was subtracted in this analysis, instead the fitted
background was assigned as the systematic uncertainty.
The overall systematic uncertainty is between 11% to
13% on the extracted differential cross sections.
Fig. 2 shows the scaled differential cross section s7 dσ
as a function of√s for θc.m. = 90◦for three different
channels. The results from this experiment are shown in
the middle panel as red solid circles with statistical un-
certainties, and the systematic uncertainty is shown as a
band. The error bars for E94-104  include both the
statistical and systematic uncertainties, while only sta-
tistical uncertainties are shown for the π0data  and
the π+data . All other world data are collected from
c.m.are the photon energy and π−mo-
Missing Mass Squared (GeV
Gauss + Linear Background Fit
Missing Momentum (GeV/c)
200 MeV/c Cut
squared of the spectator proton fitted with a Gaussian plus
linear function.The arrow indicates the mass squared of
the proton; (b): Reconstructed spectator proton momentum
(missing momentum) from this experiment together with a
Monte Carlo simulation.
(color online).(a): Reconstructed missing mass
γ p → π+ n
CLAS g10 (this work)
γ n → π- p
1 1.52 2.53 3.54
γ p → π° p
CLAS g1c (2007)
s7dσ/dt (107GeV14 nb/GeV2)
FIG. 2: (color online). Scaled differential cross section s7 dσ
a function of√s for θc.m. = 90◦for three different channels.
The upper panel is for the γp → π+n process, the middle
panel is for the γn → π−p process, and the lower panel is for
the γp → π0p process. The green solid squares are results
from Ref.  and the results from this experiment are shown
as red solid circles. Results from Dugger et al.  on neutral
pion production are shown as blue solid squares. The blue
open squares are recent CLAS data on π+production .
The SAID FA08 results  are shown as the magenta curves
in all three panels. The prediction from a Regge approach 
is shown in the top and middle panels by black curves. The
black open circles are the world data collected from Refs. [4,
Refs. [4, 29]. There are three distinct features shown in
the data: a broad enhancement around√s of 2.1 GeV; a
marked fall-off of the differential cross section in a narrow
energy window of about 300 MeV above this enhance-
ment; and the suggested  onset of the CCR scaling
for√s around 2.8 GeV. The second feature was sug-
θc.m. ≈ 50o
θc.m. ≈ 55o
θc.m. ≈ 70o
θc.m. ≈ 75o
θc.m. ≈ 90o
θc.m. ≈ 95o
θc.m. ≈ 100o
θc.m. ≈ 105o
θc.m. ≈ 110o
θc.m. ≈ 115o
FIG. 3: (color online). Scaled differential cross section s7 dσ
as a function of√s for θc.m. = 50◦to 115◦. The arrows indi-
cate the location of√s corresponding to a transverse momen-
tum value of 1.1 GeV/c. The green solid squares are results
from Ref. . The results from this experiment are shown
as red solid circles. The black open circles and open squares
are the world data collected from Refs. [4, 29] and , re-
spectively. Errors on the data from CLAS are the quadratic
sums of the statistical and systematic uncertainties. The blue
dashed lines indicate the known resonances, and the red dot-
ted lines illustrate the angular dependent feature of the broad
enhancement structure discussed in the text.
gested by Jefferson Lab experiment E94-104  (shown
as green solid squares) and the π−p total scattering cross
section data . The drastic fall-off of the cross sec-
tion has now been firmly established by the results from
this experiment. Also shown are the results of the SAID
FA08 partial wave analysis  (magenta), the MAID07
model  (blue), and the prediction from a Regge ap-
proach  (black).
The Regge approach does not describe our data and
the deviation is speculated to be due to baryon reso-
nances . While the SAID FA08 fit has been greatly
improved by the CLAS π0 and the π+data , it
does not give as good a description of the data near the
peak of the enhancement. Further, it lacks the constraint
on the π−channel and does not describe our data well
above 2.4 GeV in√s. The precision data presented here
will help to further constrain the SAID fit and will allow
for a determination of the corresponding neutron electro-
magnetic parameters for 4-star PDG resonances. These
studies will be reported in a future publication.
Fig. 3 shows the scaled differential cross section s7 dσ
as a function of√s for θc.m.= 50◦to 115◦with an angu-
lar bin size of 5◦for the γn → π−p process. As in Fig. 2,
the systematic uncertainties are shown as bands in Fig. 3.
The blue arrows indicate the location of√s correspond-
ing to a pion transverse momentum (pT) of 1.1 GeV/c.
This pT value was suggested to govern the scaling onset
by Refs. [8, 10]. We note the large discrepancy between
our results and those from Ref.  at θc.m.= 75◦and
95◦. We also note that the SAID fits [27, 28] did not in-
clude data from Ref. . An angular-dependent feature
in the scaled differential cross section is clearly seen in our
data. The aforementioned broad enhancement around a
√s value of 2.1 GeV at θc.m. = 90◦seems to shift as
a function of θc.m.from√s of 1.80 GeV at 50◦to 2.45
GeV at 105◦as shown by the red dotted lines. Our stud-
ies show that such behavior is not an artifact of the s7
scaling factor. It is not clear whether this enhancement
dies off for θc.m. > 105◦or whether it shifts to further
higher energies. The blue dotted lines indicate the loca-
tions of the nucleon resonances around 1.2 GeV and 1.5
GeV which, as expected, do not change with θc.m.. How-
ever, such an angular dependent scaling behavior is not
present in the π+and π0channels from the proton .
Our preliminary studies show that such a behavior is not
due to the FSI correction, while more complete calcula-
tions are in progress.
The approach to the scaling region is seen in Fig. 3
at the highest pT kinematics, from θc.m.= 70◦to 105◦.
In the forward angle kinematics of 50◦, higher energies
are necessary to reach a pT value of 1.1 GeV/c, sug-
gested by the deuteron photodisintegration data [8, 10]
as the value for the onset of the scaling behavior. It is
very important to extend this experiment to much higher
photon energies, such as is feasible at 6 GeV at Jeffer-
son Lab currently and at 11 GeV at the energy-upgraded
Jefferson Lab facility in the future, and to carry out sim-
ilar measurements on the γp → π+n and the γp → π0p
processes, and polarization measurements for all three
channels. Such studies will be essential in understanding
the nature of the observed enhancement, the running be-
havior of the enhancement structure in the π−channel,
and to understand where and how the transition from the
nucleon-meson to the quark-gluon degrees of QCD takes
We acknowledge the outstanding efforts of the staff
of the Accelerator and Physics Divisions at Jefferson
Lab who made this experiment possible.
was supported in part by the U.S. Department of En-
ergy, the National Science Foundation, the Italian Is-
tituto Nazionale di Fisica Nucleare, the French Centre
National de la Recherche Scientifique and Commissariat
` a l’Energie Atomique, and the Korea Science and Engi-
neering Foundation. Jefferson Science Associates (JSA)
operates the Thomas Jefferson National Accelerator Fa-
cility for the U.S. Department of Energy under contract
∗Current address:University of Virginia, Charlottesville,
†Current address:Thomas Jefferson National Accelerator
Facility, Newport News, Virginia 23606
‡Current address:The George Washington University,
Washington, DC 20052
§Current address:Edinburgh University, Edinburgh EH9
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