VOLUME 87, N
UMBER 20 PHYSICAL REVIEW LETTERS 12N
OVEMBER 2001
Longitudinal Electroproduction of Charged Pions from
1
H,
2
H, and
3
He
D. Gaskell,
10,1
A. Ahmidouch,
8
P. Ambrozewicz,
13
H. Anklin,
3,14
J. Arrington,
1
K. Assamagan,
4
S. Avery,
4
K. Bailey,
1
O. K. Baker,
4,14
S. Beedoe,
8
B. Beise,
6
H. Breuer,
6
D. S. Brown,
6
R. Carlini,
14
J. Cha,
4
N. Chant,
6
A. Cowley,
6
S. Danagoulian,
8
D. De Schepper,
1
J. Dunne,
14
D. Dutta,
9
R. Ent,
14
L. Gan,
4
A. Gasparian,
4
D. F. Geesaman,
1
R. Gilman,
12,14
C. Glashausser,
12
P. Gueye,
4
M. Harvey,
4
O. Hashimoto,
15
W. Hinton,
4
G. Hofman,
2
C. Jackson,
8
H. E. Jackson,
1
C. Keppel,
4,14
E. Kinney,
2
D. Koltenuk,
11
G. Kyle,
7
A. Lung,
14
D. Mack,
14
D. McKee,
7
J. Mitchell,
14
H. Mkrtchyan,
18
B. Mueller,
1
G. Niculescu,
4
I. Niculescu,
4
T. G. O’Neill,
1
V. Papavassiliou,
7
D. Potterveld,
1
J. Reinhold,
1
P. Roos,
6
R. Sawafta,
8
R. Segel,
9
S. Stepanyan,
18
V. Tadevosyan,
18
T. Takahashi,
15
L. Tang,
4,14
B. Terburg,
5
D. Van Westrum,
2
J. Volmer,
17
T. P. Welch,
10
S. Wood,
14
L. Yuan,
4
B. Zeidman,
1
and B. Zihlmann
14,16
1
Argonne National Laboratory, Argonne, Illinois 60439
2
University of Colorado, Boulder, Colorado 76543
3
Florida International University, Miami, Florida 33119
4
Hampton University, Hampton, Virginia 23668
5
University of Illinois, Champaign, Illinois 61801
6
University of Maryland, College Park, Maryland 20742
7
New Mexico State University, Las Cruces, New Mexico 88003
8
North Carolina A & T State University, Greensboro, North Carolina 27411
9
Northwestern University, Evanston, Illinois 60201
10
Oregon State University, Corvallis, Oregon 97331
11
University of Pennsylvania, Philadelphia, Pennsylvania 19104
12
Rutgers University, Piscataway, New Jersey 08855
13
Temple University, Philadelphia, Pennsylvania 19122
14
Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606
15
Tohoku University, Sendai 982, Japan
16
University of Virginia, Charlottesville, Virginia 22901
17
Vrije Universiteit, NL-1081 HV Amsterdam, The Netherlands
18
Yerevan Physics Institute, 375036 Yerevan, Armenia
(Received 25 May 2001; published 23 October 2001)
Separated longitudinal and transverse cross sections for charged pion electroproduction from
1
H,
2
H,
and
3
He were measured at Q
2
苷 0.4 共GeV兾c兲
2
for two values of the invariant mass, W 苷 1.15 GeV
and W 苷 1.60 GeV, in a search for a mass dependence which would signal the effect of nuclear pions.
This is the first such study that includes recoil momenta significantly above the Fermi surface. The
longitudinal cross section, if dominated by the pion-pole process, should be sensitive to nuclear pion
currents. Comparisons of the longitudinal cross section target ratios to a quasifree calculation reveal a
significant suppression in
3
He at W 苷 1.60 GeV. The W 苷 1.15 GeV results are consistent with simple
estimates of the effect of nuclear pion currents, but are also consistent with pure quasifree production.
DOI: 10.1103/PhysRevLett.87.202301 PACS numbers: 25.30.Rw, 13.60.Le, 25.10. +s, 25.30.Fj
Conventional pictures of the nucleon-nucleon force, in
which pion-exchange currents play a significant role, pre-
dict a mass dependent modification of the pion field in
nuclei [1]. Early measurements of the mass dependence
of the F
2
structure function in deep inelastic scattering
(DIS) appeared to confirm this expectation when a large
enhancement was seen at x , 0.2 [2]. This was quickly
attributed to contributions from excess pions in the nucleus
[3]. However, later DIS measurements observed a much
smaller enhancement of F
2
at low x [4,5]. Studies of the
Drell-Yan reaction, which is sensitive to antiquark distribu-
tions in nuclei, revealed no mass dependence at low x [6].
Polarization transfer measurements, first 共
p,
p
0
兲 [7] and
later 共
p,
n兲 [8], of the ratios of longitudinal to transverse
spin-isospin response functions in nuclei saw no evidence
for the expected enhancement of the response ratio as pre-
dicted by models including nuclear pion effects. While
evidence of large effects from pions in nuclei seems to be
lacking in the above experiments, the interpretation is am-
biguous. Recent calculations of both the mass dependence
of DIS [9] and the Drell-Yan reaction [10] that explain the
existing data include contributions from excess pions in
nuclei. Furthermore, later analysis of the 共
p,
n兲 results in-
dicates that the enhancement of the response ratio due to
pion-exchange contributions to the longitudinal response
may have been masked by an unexpected enhancement of
the transverse response [11]. Clearly, a more direct probe
of the pion field of the nucleus is needed.
To the extent that the pion-pole process (i.e., scatter-
ing of virtual pions into the continuum) dominates, lon-
gitudinal charged pion electroproduction directly probes
the virtual pion field of nuclei. If current models of the
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VOLUME 87, N
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OVEMBER 2001
nucleon-nucleon force are correct, one expects a suppres-
sion of the pion field in nuclei relative to the free nu-
cleon at low values of the virtual pion momentum,
k 艐
0.1
0.2 GeV兾c (in the pole process k, the virtual pion
momentum, is equivalent to the 3-momentum transfer to
the nucleus) and an enhancement at moderate pion mo-
mentum, k 艐 0.3
0.6 GeV兾c. Furthermore, these mod-
els predict the modification of the pion field in
3
He to be
significant and in
4
He to be comparable to that in heavier
nuclei. These modifications should manifest themselves in
measurable changes to the longitudinal pion electroproduc-
tion cross section. An earlier measurement of the unsepa-
rated
p
1
electroproduction cross section from the deuteron
at k 艐 0.18 GeV兾c measured a ratio of 0.80 6 0.05 rela-
tive to hydrogen [12]. This result motivated further study,
in particular the isolation of the longitudinal response to
increase sensitivity to the nuclear pion field.
In Jefferson Lab experiment E91003, charged pion
electroproduction from
1
H,
2
H, and
3
He was measured.
Data were taken for Q
2
苷 0.4 共GeV兾c兲
2
at kinematics
corresponding to the negative enhancement region (k 苷
0.20 GeV兾c and W 苷 1.60 GeV) and the positive en-
hancement region (k 苷 0.47 GeV兾c and W 苷 1.15 GeV)
of the pion excess distribution of Ref. [1]. The experiment
was carried out in Hall C using electron beam energies
that ranged from 0.845 GeV to 3.245 GeV. Electrons
were detected in the High Momentum Spectrometer and
pions in the Short Orbit Spectrometer.
Electrons were selected using a gas
ˇ
Cerenkov counter
containing C
4
F
10
at 0.42 atmospheres. Pions were iden-
tified using time-of-flight information from two pairs of
scintillating hodoscope arrays to reject protons at posi-
tive polarity and a gas
ˇ
Cerenkov containing Freon-12 at
atmospheric pressure to reject electrons at negative polar-
ity. Backgrounds from random coincidences and the alu-
minum walls of the cryogenic targets were subtracted in
the charge-normalized yields. These yields were also cor-
rected for dead times and efficiencies. Cuts on the re-
constructed missing mass excluded the region above the
two-pion threshold.
The pion electroproduction cross section can be written
as the product of a virtual photon flux (G) and a virtual
photon cross section (evaluated in the laboratory frame),
ds
dV
e
dE
e
dV
p
dM
x
苷 G
ds
dV
p
dM
x
, (1)
where M
x
is the missing mass of the recoiling system,
M
2
x
苷 共q 1 P
A
2 p
p
兲
2
. The virtual photon flux is given
by
G 苷
a
2p
2
E
0
e
E
e
1
Q
2
1
1 2e
W
2
2 M
2
2M
. (2)
We take M to be the proton mass so that equal laboratory
cross sections result in equal virtual photon cross sections
regardless of target mass. The virtual photon cross section
can be written
ds
dV
x
dM
x
苷
ds
T
dV
p
dM
x
1e
ds
L
dV
p
dM
x
1e
ds
TT
dV
p
dM
x
3 cos2f
pq
1
q
2e共1 1e兲
ds
LT
dV
p
dM
x
cosf
pq
,
(3)
where e describes the longitudinal polarization of the vir-
tual photon. In the parallel kinematics of E91003, the inter-
ference terms (s
LT
and s
TT
) are small, and, for complete
f
pq
coverage, integrate to zero.
To compare the longitudinal cross sections from
1
H,
2
H,
and
3
He, it is necessary to integrate the cross sections over
the missing mass peak. In this case the cross section can
be expressed (after integrating over f
pq
)
Z
DM
x
ds
dV
p
dM
x
苷
Z
DM
x
ds
T
dV
p
dM
x
1e
Z
DM
x
ds
L
dV
p
dM
x
, (4)
where DM
x
is the region of missing mass within the ex-
perimental acceptance. In the case of the free proton, the
missing mass is just a radiation and resolution broadened
d function at the neutron mass. For
2
H and
3
He, the Fermi
motion of the bound nucleons broadens the distributions,
and the missing mass coverage is limited by the acceptance
of the spectrometers. At the k 苷 0.20 GeV兾c kinematics
the coverage is nearly complete, while at k 苷 0.47 GeV兾c
a significant fraction (10%
30%) of the missing mass dis-
tribution is outside the experimental acceptance, as illus-
trated in Fig. 1.
The (unseparated) missing mass integrated cross sec-
tions were measured at two values of e for each k (W)
dσ/dΩ
π
dM
x
(µb/GeV/sr)
k=0.2 GeV/c
M
x
(GeV)
k=0.47 GeV/c
0
500
1000
1500
1.9 1.95 2
0
100
200
300
1.9 1.95 2
FIG. 1. M
x
acceptance for the
2
H共e, e
0
p
1
兲nn data at low
(top) and high (bottom) k. The points are cross sections with
statistical errors only and the curves are quasifree calculations
(normalized to the data) that include NN final state interaction
effects.
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OVEMBER 2001
M
x
(GeV)
Normalized Yield
π
+
/2
π
-
3
He(e,e
,
π
+
)
3
H
3
He(e,e
,
π
+
)Dn/pnn
3
He(e,e
,
π
-
)ppp
0
2
4
6
8
10
12
14
16
2.78 2.8 2.82 2.84 2.86 2.88 2.9 2.92
FIG. 2. Missing mass distributions for p
1
and p
2
production
from
3
He at k 苷 0.20 GeV兾c. The p
1
data have been divided
by 2 for comparison with the p
2
data. The coherent
3
H fi-
nal state is clearly distinguishable from the Dn兾pnn continuum
states.
setting, and the missing mass integrated longitudinal and
transverse cross sections were extracted via a Rosenbluth
separation [Eq. (4)]. The experimental cross sections were
extracted using a Monte Carlo simulation of the experi-
ment that included detailed descriptions of the spectrome-
ters, decay of the pions in flight, multiple scattering,
ionization energy loss, and radiative effects. The simu-
lation used the MAID [13] model of charged pion
electroproduction from nucleons to account for variations
of the cross section across the acceptance. For electropro-
duction from
2
H and
3
He, the MAID model was imple-
mented in a quasifree approximation in combination with
realistic nucleon momentum distributions [14,15]. The
3
He calculation also included a missing energy distribution
[fit from 共e, e
0
p兲 data [16]] which was used to model the
Dn strength relative to the pnn strength in the
3
He共e, e
0
p
1
兲
reaction. Effects from nucleon-nucleon final state inter-
actions were also included via a simple Jost function
prescription [17]. An iterative procedure was used to
optimize the pion electroproduction model and match the
resulting Monte Carlo distributions to the data. Details
of the analysis and iteration procedure can be found in
Ref. [18].
In
p
1
and p
2
electroproduction from
2
H, it is appro-
priate to describe the process as quasifree since there are
no bound nn or pp states. This is also the case for p
2
production from
3
He where the final state is ppp.How-
ever, for p
1
production from
3
He, one has the
3
H (triton)
bound state in addition to the Dn and pnn continuum states
available. At the high-k kinematics, this state is not in the
experimental acceptance and should be greatly suppressed
by the
3
He form factor. At low k, the
3
H peak is clearly
visible in the data (see Fig. 2) and the cross sections for the
coherent and continuum processes can be independently
extracted. In this Letter, we focus on the continuum final
states and present results only for the combined Dn
兾pnn
cross section in the
3
He共e, e
0
p
1
兲 reaction.
The separated cross sections are given in Table I. The
2
H and
3
He cross sections also include the experimental
missing mass range over which they have been integrated.
These separated cross sections are given in the laboratory
frame at Q
2
苷 0.4 共GeV兾c兲
2
and u
pq
苷 1.72
±
.
The longitudinal cross section ratios, R
L
, are presented
in Table II. These ratios do not directly relate to the
pion field modification due to the limited M
x
acceptance.
Rather than attempt to extrapolate the measured spectra to
full M
x
acceptance, we compare the measured ratios to a
calculation over the same region of M
x
in which the pro-
cess is treated as quasifree, i.e., in the absence of pion ex-
cess or other nuclear effects beyond binding. In this way,
we take into account the limited M
x
acceptance as well
TABLE I. Longitudinal and transverse separated cross sections for A共e, e
0
p
6
兲. s
L共T兲
denotes
R
DM
x
ds
L共T 兲
dV
p
dM
x
(in the laboratory). Uncertainties on the cross sections are statistical (systematic).
3
He共e, e
0
p
1
兲 cross sections have been divided by two (the number of protons) for comparison
with the other targets.
Target
DM
x
(GeV) s
L
共mb兾sr兲 s
T
共mb兾sr兲
k 苷 0.20 GeV兾c, W 苷 1.60 GeV, e 苷 0.49, 0.89
1
H · · · 34.6 6 1.4共4.4兲 27.3 6 1.0共2.9兲
D(p
1
) M
x
, 2.01 29.7 6 1.1共3.8兲 25.3 6 0.9共2.5兲
D(p
2
) M
x
, 2.01 46.8 6 1.2共4.2兲 11.3 6 0.8共2.0兲
3
He (p
1
) M
x
, 2.94 19.3 6 1.4共2.6兲 18.1 6 1.0共1.8兲
3
He (p
2
) M
x
, 2.94 25.9 6 1.2共2.7兲 13.3 6 0.8共1.6兲
k 苷 0.47 GeV兾c, W 苷 1.15 GeV, e 苷 0.44, 0.86
1
H · · · 18.4 6 1.0共2.0兲 9.2 6 0.6共1.1兲
D(p
1
) 1.90 , M
x
, 1.97 13.4 6 1.1共1.4兲 6.2 6 0.7共0.7兲
D(p
2
) 1.90 , M
x
, 1.97 16.9 6 1.0共1.5兲 1.8 6 0.6共0.5兲
3
He (p
1
) 2.85 , M
x
, 2.93 9.6 6 0.9共1.1兲 5.5 6 0.7共0.6兲
3
He (p
2
)
2.85 , M
x
, 2.93
11.6 6 0.9共1.1兲 2.2 6 0.6共0.4兲
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TABLE II. Experimental and quasifree calculations of longitudinal cross section ratios. Un-
certainties on the experimental ratios are statistical (systematic). The experimental ratios are
not corrected for pion-nucleon final state interactions, although these effects are expected to be
small in all cases but the
3
He, p
1
data at high k.
Ratio
R
exp
L
R
q.f.
L
R
exp
L
兾R
q.f.
L
k 苷 0.20 GeV兾c, W 苷 1.60 GeV
D兾
1
H 共p
1
兲 0.86 6 0.05共0.11兲 0.95 6 0.03 0.90 6 0.12
3
He兾D 共p
2
兲 0.55 6 0.03共0.06兲 0.95 6 0.02 0.58 6 0.07
3
He兾H 共p
1
兲 0.56 6 0.05共0.09兲 0.92 6 0.05 0.61 6 0.12
k 苷 0.47 GeV兾c, W 苷 1.15 GeV
D兾
1
H 共p
1
兲 0.73 6 0.07共0.07兲 0.67 6 0.04 1.09 6 0.16
3
He兾D 共p
2
兲 0.69 6 0.07共0.06兲 0.70 6 0.04 0.99 6 0.14
3
He兾H 共p
1
兲
0.52 6 0.06共0.07兲
0.49 6 0.05 1.07 6 0.21
as the kinematic variation of the fundamental g
ⴱ
-N cross
section due to the Fermi motion of the bound nucleon.
The quasifree ratios are calculated using the pion elec-
troproduction model and momentum space wave functions
used in the Monte Carlo simulation and are shown with
the measured ratios in Table II. The model dependence
of the calculated ratio is estimated by comparing the re-
sult with the value obtained by using a flat cross section
in place of the electroproduction model. The uncertainty
in the quasifree calculation of the ratio varies from 2%
to 10%— generally largest in the
3
He兾
1
H ratio. Figure 3
shows the experimentally determined ratios compared to
the quasifree calculated ratios, i.e., R
exp
L
兾R
q.f.
L
as a function
of k for the free nucleon. Error bars include the uncertainty
in the quasifree calculation as well as the experimental sta-
tistical and systematic uncertainties.
At k 苷 0.20 GeV兾c, a suppression of the longitudinal
cross section in
3
He relative to
1
H and
2
H is clearly evident
k (GeV/c)
R
exp
L
/ R
q.f.
L
D/H (π
+
)
3
He/H (π
+
)
3
He/D (π
-
)
0
0.5
1
1.5
0 0.1 0.2 0.3 0.4 0.5 0.6
FIG. 3. Longitudinal cross section ratios compared to a
quasifree calculation. Note that the calculation is integrated
over the same region of the quasifree peak as is sampled
experimentally. The experimental ratios are not corrected for
pion-nucleon final state interactions (these effects should be
less than 5%, except for the
3
He, p
1
data at high k). The
3
He
ratios have been shifted in k for viewing purposes.
while the
2
Hto
1
H ratio is consistent with unity within the
uncertainties. At k 苷 0.47 GeV兾c, all of the super-ratios
are consistent with unity, indicating that the longitudinal
strength in
2
H and
3
He is not significantly enhanced rela-
tive to the free nucleon. In all cases, the measured ratios
are somewhat suppressed due to final state interactions be-
tween the outgoing pion and the spectator nucleons. This
suppression is expected to be less than 5%, except for the
3
He共e, e
0
p
1
兲 data at high k. In this case, the final pion mo-
mentum is 0.29 GeV兾c and the pion rescattering effects on
the spectator pn pair can be large. In a simple factoriza-
tion approximation, the suppression due to rescattering is
0.75 [19]. Applying this calculation to kinematics where
other estimates are available [20–22], we estimate the un-
certainty in the rescattering suppression to be about 20%.
Hence, the
3
He兾
1
H共p
1
兲 super-ratio of 1.07 might be more
accurately interpreted as 1.43, albeit with large experimen-
tal uncertainties (60.28) in addition to the uncertainty in
the rescattering calculation.
While the pole term is believed to be the single largest
piece of the longitudinal cross section at E91003 kine-
matics, it is unclear to what extent other processes may
contribute. One can check for pole-term dominance by
comparing the longitudinal p
2
兾p
1
ratios in
2
H. A de-
viation from unity indicates the presence of isoscalar
terms which, since the pole term is pure isovector, must
come from other Born terms. At k 苷 0.47 GeV兾c
(k 苷 0.20 GeV兾c), the longitudinal p
2
兾p
1
ratio is
1.27 6 0.16 (1.58 6 0.19). These ratios clearly deviate
from unity, but do not give enough information to deter-
mine how the isoscalar backgrounds affect the measured
ratios.
One can use the pion-excess calculations of Ref. [1]
together with the formalism of Ref. [23] [Eq. (18)] to
estimate the modifications to the nuclear response (and
hence the super-ratios of Fig. 3) which might be expected
in the best-case scenario of pole dominance. Such a cal-
culation indicates that, at low k, the suppression should be
艐1% (14%)in
2
H(
3
He) relative to the free nucleon. At
high k, the expected enhancement is 6% (13%)in
2
H(
3
He)
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OVEMBER 2001
(note that this implies a 7% enhancement in the
3
He兾D
super-ratio). The measured super-ratios are largely consis-
tent with these simple estimates, though contributions from
non-pole terms could dilute or enhance the experimental
signal. The suppression seen in the
3
He data at low
k is
larger than the naive expectation, but this may come about
from the exclusion of the
3
H final state which would give
additional longitudinal strength to the
p
1
data. It should
be noted that while the high k results are consistent with
the estimated pion-excess effects, they are also consistent
with pure quasifree production.
Longitudinal pion electroproduction holds great promise
as a probe of the pion field of nuclei. The results reported
here show a clear suppression of the longitudinal strength
at low k, and at high k are consistent with estimates derived
from pion-excess calculations. Further measurements at
kinematics where the longitudinal p
2
兾p
1
ratio is consis-
tent with pole dominance (as is the case in Ref. [24]) and
extending the measurement to higher missing mass, where
it has been suggested that nucleon-nucleon correlations are
important [23], would greatly simplify the interpretation of
this type of experiment. Furthermore, extending the mea-
surements to
4
He would provide the opportunity to probe a
nucleus with potentially twice the enhancement, but where
detailed microscopic calculations are still feasible.
We thank Lothar Tiator for providing the
FORTRAN code
for the MAID model. This research was supported by the
U.S. National Science Foundation and the U.S. Department
of Energy.
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