Polarization transfer in the 4He(e,e'p)3H reaction at Q2=0.8 and 1.3 (GeV/c)2.

Abstract

Proton recoil polarization was measured in the quasielastic 4He(e,e'p)3H reaction at Q{2}=0.8 and 1.3  (GeV/c){2} with unprecedented precision. The polarization-transfer coefficients are found to differ from those of the 1H(e,e'p) reaction, contradicting a relativistic distorted-wave approximation and favoring either the inclusion of medium-modified proton form factors predicted by the quark-meson coupling model or a spin-dependent charge-exchange final-state interaction. For the first time, the polarization-transfer ratio is studied as a function of the virtuality of the proton.

Full text

Page 1

arXiv:1002.2188v8 [nucl-ex] 23 Aug 2010
Polarization Transfer in the4He(? e,e′? p)3H Reaction at Q2= 0.8 and 1.3 (GeV/c)2
M. Paolone,1S.P. Malace,1S. Strauch,1I. Albayrak,2J. Arrington,3B.L. Berman,4E.J. Brash,5B. Briscoe,4
A. Camsonne,6J.-P. Chen,6M.E. Christy,2E. Chudakov,6E. Cisbani,7B. Craver,8F. Cusanno,7R. Ent,6
F. Garibaldi,7R. Gilman,9,6O. Glamazdin,10J. Glister,11,12D.W. Higinbotham,6C.E. Hyde-Wright,13
Y. Ilieva,4C.W. de Jager,6X. Jiang,9M.K. Jones,6C.E. Keppel,2E. Khrosinkova,14E. Kuchina,9
G. Kumbartzki,9B. Lee,15R. Lindgren,8D.J. Margaziotis,16D. Meekins,6R. Michaels,6K. Park,6L. Pentchev,17
C.F. Perdrisat,17E. Piasetzky,18V.A. Punjabi,19A.J.R. Puckett,20X. Qian,21Y. Qiang,20R.D. Ransome,9
A. Saha,6A.J. Sarty,11E. Schulte,9P. Solvignon,3R.R. Subedi,14L. Tang,2D. Tedeschi,1V. Tvaskis,2
J.M. Udias,22P.E. Ulmer,13J.R. Vignote,23F.R. Wesselmann,19B. Wojtsekhowski,6and X. Zhan20
(The E03-104 Collaboration)
1University of South Carolina, Columbia, South Carolina 29208
2Hampton University, Hampton, Virginia 23668
3Argonne National Laboratory, Argonne, Illinois
4The George Washington University, Washington, DC 20052
5Christopher Newport University, Newport News, Virginia 23606
6Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606
7INFN, Sezione Sanit´ a and Istituto Superiore di Sanit´ a, Laboratorio di Fisica, I-00161 Rome, Italy
8University of Virginia, Charlottesville, Virginia 22904
9Rutgers, The State University of New Jersey, Piscataway, New Jersey 08854
10Kharkov Institute of Physics and Technology, Kharkov 310108, Ukraine
11Saint Mary’s University, Halifax, Nova Scotia, Canada
12Dalhousie University, Halifax, Nova Scotia, Canada
13Old Dominion University, Norfolk, Virginia 23529
14Kent State University, Kent, Ohio 44242
15Seoul National University, Seoul, Korea
16California State University, Los Angeles, Los Angeles, California 90032
17College of William and Mary, Williamsburg, Virginia 23187
18Tel Aviv University, Tel Aviv 69978, Israel
19Norfolk State University, Norfolk, Virginia 23504
20Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
21Duke University, Durham, North Carolina 27708
22Universidad Complutense de Madrid, E-28040 Madrid, Spain
23Instituto de Estructura de la Materia, CSIC, E-28006 Madrid, Spain
(Dated: August 24, 2010)
Proton recoil polarization was measured in the quasielastic4He(? e,e′? p)3H reaction at Q2= 0.8
(GeV/c)2and 1.3 (GeV/c)2with unprecedented precision. The polarization-transfer coefficients
are found to differ from those of the1H(? e,e′? p) reaction, contradicting a relativistic distorted-wave
approximation, and favoring either the inclusion of medium-modified proton form factors predicted
by the quark-meson coupling model or a spin-dependent charge-exchange final-state interaction. For
the first time, the polarization-transfer ratio is studied as a function of the virtuality of the proton.
PACS numbers: 13.40.Gp,13.88.+e,21.65.-f,27.10.+h
Electron-nucleon scattering is a powerful tool for prob-
ing the structure of nucleons.
cess to high-quality polarized electron beams has al-
lowed the nucleon’s electromagnetic properties to be ex-
plored through measurement of polarization observables.
In elastic electron-nucleon scattering, the polarization-
transfer technique allows measurement of the Sachs form-
factor ratio GE/GM, that is directly proportional to the
ratio of transverse and longitudinal polarization observ-
ables P′
x/P′
zin the single-photon exchange approximation
[1, 2]. This technique [3] benefits from a large cancella-
tion of systematic uncertainties, unlike the Rosenbluth
separation technique, which relies on repeated cross-
section measurements. Several recent experiments have
For over a decade, ac-
extracted GE/GMof the proton using this method [4–7].
The question of if and how the nucleon structure is
modified within the nuclear medium has been hotly de-
bated since the discovery of the nuclear EMC effect,
which showed that quark momentum distributions within
nuclei differ from those within free nucleons. Indeed, a
deviation of GEand GM of a nucleon immersed in a nu-
clear medium from their free-space values is predicted by
Lu et al. [8, 9] using the quark-meson coupling (QMC)
model. These results are consistent with experimental
constraints from the Coulomb Sum Rule; see [10, 11].
In addition to the QMC model, many other model cal-
culations predict the in-medium modification of nucleon
structure; for recent examples see [12–15]. Ciofi degli Atti

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2
et al. predict that the proton form factors are strongly
correlated with the excitation of the residual system and
the virtuality of the ejected proton [16].
The polarization-transfertechnique can be used to help
settle this question using quasi-elastic nucleon knockout.
In that case, the ratio GE/GM remains approximately
proportional to P′
x/P′
z, allowing modifications of the form
factors to be determined. However, in-medium nucleon
interactions complicate this picture, and even raise the
question as to whether the concept of medium modifi-
cations is a meaningful one, due to the complex nature
of the in-medium interaction. Predictions from Schiav-
illa [17] contend that final-state interactions (FSIs) in-
cluding charge exchange processes and meson exchange
currents lead to a quenching of 10% in the polarization-
transfer ratio P′
x/P′
zin the quasielastic scattering re-
action4He(? e,e′? p)3H compared with the free-space re-
action1H(? e,e′? p). The correct treatment of FSIs in a
model calculation is essential to separate any uncon-
ventional medium effects from FSIs, since both influ-
ence the polarization-transfer observables. To help settle
this debate precision measurements are needed with the
polarization-transfer coefficients P′
in a region of low (< 100 MeV/c) missing momentum,
where such FSI complications are minimized, and as a
function of the virtuality of the ejected proton. Depen-
dence on the latter is a simple and straightforward corol-
lary of models with medium modifications.
ThisLetterreportson
polarization-transfer coefficients P′
quasi-elastic
ferson Lab in Hall A: experiment E03-104. Data were
taken at four-momentum transfers of Q2= 0.8 and
1.3 (GeV/c)2within a missing-momentum range < 160
MeV/c. The4He target was chosen for its high nuclear
density and relative theoretical modeling simplicity. A
recent study of the EMC effect [18] has shown that
the effect on nucleons in
effect on nucleons in12C. The low missing-momentum
regime was chosen to reduce the contribution from
many-body effects, although a weaker contribution from
in-medium modification effects is expected. Additional
1H(? e,e′? p) scattering data also were taken to provide
unmodified proton scattering measurements as a basis
for comparison. The carbon analyzing power of the
polarimeter was also extracted from the1H(? e,e′? p) data.
Kinematic settings for the present experiment are
given in Table I. For both1H(? e,e′? p) and4He(? e,e′? p)3H,
the scattered electron and ejected proton were detected
in coincidence in two high-resolution spectrometer arms.
For the nine1H settings, the central momenta for the pro-
ton were adjusted in 2% increments from −8% to +8% in
order to produce similar coverage of the focal plane, as in
4He(? e,e′? p)3H scattering. This allowes for detailed stud-
ies of the spin transport and other instrumental effects.
Beam currents up to 80 µA and beam polarizations of
x/P′
zmapped in detail
measurementsof
in the
the
x
and P′
z
4He(? e,e′? p)3H reaction preformed at Jef-
4He is comparable to the
85% were used. The proton spectrometer was equipped
with a focal plane polarimeter (FPP) which measures the
asymmetry of polarized protons scattered from a carbon
analyzer [4]. The spin precession of the proton in the
magnetic field of the spectrometer was calculated using
the COSY software [19]. A maximum likelihood method
was then employed in conjunction with the beam helicity,
the carbon analyzing power, and the proton spin preces-
sion to extract the polarization of the ejected proton at
the target [20]. The large amount of statistics accumu-
lated in this experiment have allowed the extraction of
µGE/GM from the data with strict missing-energy and
missing-momentum cuts to prevent any effects from di-
luting the polarization observables. For4He(? e,e′? p)3H
scattering, tight cuts on the reconstructed missing mass
spectrum were used to ensure that quasi-elastic knockout
of the proton leaves the undetected3H intact. Radiative
effects due to single-photon emission [21], as well as ra-
diative corrections from two-photon exchange to the po-
larization ratio P′
x/P′
z[22], are predicted to be less than
0.5%. Radiative effects on the ratio were minimized with
missing-energy and missing-momentum cuts, but no spe-
cific radiation corrections were applied to the data.
Figure 1 shows our results for the polarization-transfer
coefficients as a function of the missing momentum. Here,
the sign of the missing momentum is positive if the
component of the missing-momentum vector along the
momentum-transfer direction is positive. The individual
polarization-transfer coefficients from the4He(? e,e′? p)3H
normalized to the1H(? e,e′? p) reaction, (P′
(P′
z)He/(P′
z)H, and the double ratio R is shown along
with acceptance-corrected calculations from the Madrid
group [23, 24]. Here, R is defined as:
x)He/(P′
x)Hand
R =(P′
x/P′
(P′
x/P′
z)4He
z)1H
.(1)
The Madrid group calculations use a relativistic wave
function for the bound state that reproduces the ex-
clusive
culations are represented through bands whose varia-
tion in width depends on the nuclear current opera-
tors, cc1 and cc2 [26], and the optical potential mod-
els, MRW [27] and RLF [28], used. The light, medium,
and dark grey bands represent calculations from a rel-
ativistic plane-wave impulse-approximation (RPWIA),
relativistic distorted-wave impulse-approximation (RD-
WIA), and a RDWIA that includes an in-medium mod-
ified form factor as predicted by Lu et al.with the QMC
model [8], respectively. At both Q2= 0.8 (GeV/c)2and
1.3 (GeV/c)2the RPWIA and RDWIA calculations over-
estimate the data significantly. With RDWIA + QMC,
the calculation is in better agreement with the data. Un-
certainties from model wave functions, current operators,
or choice of MRW or RLF optical potentials are small
which allows discrimination between the data and the
conventional RDWIA calculations. The RDWIA calcula-
4He(e,e′p) cross section data [25].The cal-

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3
tions with medium-modified nucleon form factors predict
a greater divergence from standard RDWIA calculations
at missing momenta further from zero.
The expected effect on the hydrogen-normalized polar-
ization coefficients from in-medium modified form factors
can be estimated by comparing the ? ep elastic scattering
to the quasielastic case. In elastic scattering, the polar-
ization coefficients themselves can be expressed directly
as functions of P′
x/P′
z. One would expect a decrease
for (P′
x)He/(P′
x)Hand an increase for (P′
sistent with the overall observed quenching of R, which
is indeed consistent with our data for both observables.
These results are also in agreement with the full model,
RDWIA + QMC.
In Figure 2, results are shown as the polarization-
transfer double-ratio R plotted versus Q2. The results
agree with previous results [29] from Mainz [30] and JLab
experiment E93-049 [31] establishing the quenching of R
and its Q2dependence with previously unattained con-
fidence; additionally, the calculated µGE/GM values for
1H(? e,e′? p) are in good agreement with world data [4–
7]. The experimental results for R and µGE/GM are
also listed in Table II.With data for1H(? e,e′? p) and
4He(? e,e′? p)3H obtained under near identical experimen-
tal conditions, calculating the double-ratio R results in a
significant cancellation of systematic uncertainties.
The theoretical calculations shown in Figure 2 include
a RDWIA calculation with free-space proton form fac-
tors (dashed line), and RDWIA calculations that include
an in-medium modified form factor as predicted by Lu
et al.with the QMC model [8] (solid line) and an in-
medium modified form factor as predicted in the chiral
quark soliton model by Smith and Miller [14] (dash-dot
line). Theoretical calculations from Schiavilla [17] are in-
cluded in Figure 2 as a grey band, and assume a missing
momentum close to zero and have not been acceptance
corrected. Schiavilla shows with conventional many-body
calculations that a model with free-space nucleon form
factors can describe R as a function of Q2. The difference
in modeling the FSIs account for most of the discrepancy
between Schiavilla’s and the Madrid group’s calculations.
Schiavilla’s calculation includes MEC effects paired with
tensor correlations that suppress R by 4% and include
both a spin-dependent and a spin-independent charge-
exchange term in the final-state interaction that suppress
R by an additional 6%, all of which are not included in
the Madrid group’s calculations. The spin-orbit terms in
Schiavilla’s FSI calculations are not well constrained, and
the Monte Carlo technique employed in the model calcu-
lation introduces a statistical uncertainty represented in
the width of the grey band in Figure 2.
Figure 3 shows R as a function of the proton virtuality,
v = p2− m2
p. Here, p is the proton four-momentum in
the4He nucleus and is defined as p2= (mHe− Et)2−p2
in the impulse approximation, where Et and pt are re-
spectively the energy and momentum of the undetected
z)He/(P′
z)H, con-
t
triton. The dashed line is a linear fit to the data as-
suming R = 1 at v = 0, and is included as a simple
approximation of the expected trend in virtuality. The
RDWIA models including medium modified proton form
factors describe the data best. The Madrid group RD-
WIA + QMC calculations diverge from the conventional
RDWIA calculations as the virtuality moves further from
zero. Calculations from Schiavilla are not available as a
function of the missing momentum or the virtuality.
In summary, we have measured recoil polarization in
the4He(? e,e′? p)3H reaction at Q2values of 0.8 (GeV/c)2
and 1.3 (GeV/c)2.The data agree well with previ-
ously reported measurements from Mainz [30] and JLab
[31], but the increased precision challenges state-of-the-
art nuclear physics calculations, both with and without
medium modifications. Our data allow one to study the
dependence of polarization-transfer ratios as functions of
missing momentum and, for the first time, proton virtu-
ality. The data are in excellent agreement with model
calculations including the medium modification of the
proton form factors through the quark-meson coupling
model presented by Lu et al [8], and with a chiral quark
soliton model by Smith and Miller [14]. A model calcula-
tion by Schiavilla [17], which uses conventional free-space
nucleon form factors, but employs a different treatment
of in-medium nucleon interactions, including charge ex-
change processes, also agrees with the overall reduction
of the polarization-transfer ratios, albeit within large un-
certainties. Combining these data with similar preci-
sion induced-polarization data, directly sensitive to the
amount of in-medium nucleon interactions, may lead to
a definite statement in favor or against the effective use
of proton medium modifications.
The collaboration wishes to acknowledge the Hall A
technical staff and the Jefferson Lab Accelerator Divi-
sion for their terrific support. This work was supported
by the U.S. Department of Energy and the U.S. National
Science Foundation. Jefferson Science Associates oper-
ates the Thomas Jefferson National Accelerator Facility
under DOE contract DE-AC05-06OR23177.
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TABLE I: Table of kinematic settings for Experiment E03-104. Here E0is the incident beam energy, ppis the central momentum
setting of the proton spectrometer, θp is the central angle setting for the proton spectrometer, pe is the central momentum
setting of the electron spectrometer, and θe is the central angle setting for the electron spectrometer.
Kinematic
Setting
A1–9
A10
B1–9
B10
Q2
E0
pp
θp
pe
θe
(GeV/c)2(GeV) Target
0.8 1.987
0.81.987
1.3 2.637
1.32.637
(GeV/c)
0.991±8%
1.004
1.334±8% 45.289
1.353
(deg) (GeV/c)
50.668
49.115
(deg)
−29.440
−29.730
−29.221
−29.462
1H
4He
1H
4He
1.561
1.532
1.944
1.90943.920
TABLE II: Values for the polarization-transfer coefficients P′
four-momentum transfer settings. Uncertainties are listed as statistical then systematic. Systematic uncertainties in the ratios
(P′
xand P′
zof the ejected proton from the listed target at both
x)He/(P′
x)H, (P′
z)He/(P′
z)H, and the double ratio R mostly cancel, providing a systematic precision better than 5.0 × 10−4.
Q2(GeV/c)2
0.8
1.3
(P′
1.062 ± 0.009
1.064 ± 0.014
x)He/(P′
x)H
(P′
0.956 ± 0.010
0.954 ± 0.015
z)He/(P′
z)H
µGE/GM
R
0.901 ± 0.007 ± 0.010
0.858 ± 0.008 ± 0.019
0.900 ± 0.012
0.897 ± 0.019
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H
xx
)
/ (P’
He He
)
(P’(P’
xx
0.80.8
1.0 1.0
RPWIA
RDWIA
RDWIA + QMCRDWIA + QMC
RPWIA
RDWIA
H
)
/ (P’
)
H
zz
)
/ (P’
He
zz
)
(P’(P’
1.0 1.0
1.2 1.2
2
=0.8 (GeV/c)
2
Q
H
)
/ (P’
He
)
(GeV/c)
mm
pp
-0.1 -0.10.0
(GeV/c)
0.10.1
H
zz
)
/P’
/ (P’
xx
He
zz
)
/P’
(P’ (P’
xx
0.8 0.8
0.9 0.9
1.01.0
0.0
H
)
/P’
/ (P’
He
)
/P’
H
xx
)
/ (P’
HeHe
)
(P’(P’
xx
0.80.8
1.01.0
RPWIA
RDWIA
RDWIA + QMCRDWIA + QMC
RPWIA
RDWIA
H
)
/ (P’
)
H
zz
)
/ (P’
He
zz
)
(P’ (P’
1.01.0
1.2 1.2
2
=1.3 (GeV/c)
2
Q
H
)
/ (P’
He
)
(GeV/c)
mm
pp
-0.1-0.10.0
(GeV/c)
0.10.1
H
zz
)
/P’
/ (P’
xx
He
zz
)
/P’
(P’(P’
xx
0.80.8
0.90.9
1.01.0
0.0
H
)
/P’
/ (P’
He
)
/P’
FIG. 1: The individual polarization-transfer coefficients from
the double-ratio R versus the missing momentum pm for Q2= 0.8 (GeV/c)2(left) and Q2= 1.3 (GeV/c)2(right). The bands
represent RPWIA (light grey), RDWIA calculations (medium grey), and RDWIA + QMC calculations (dark grey) [25]. See
the text for a description of the models.
4He normalized to
1H, (P′
x)He/(P′
x)H and (P′
z)He/(P′
z)H, and
2
(GeV/c)
2
Q
0123
H)
z
/P’
x
/ (P’
He
z
)
/P’
(P’
x
0.8
1.0
E03-104
E93-049
MAMI
Madrid RDWIA
Madrid RDWIA + QMC
Madrid RDWIA + CQS
Schiavilla
FIG. 2: Experimental results for R versus Q2for E03-104
(black circles), E93-049 (open circles) [31] and MAMI (open
triangle) [30]. The curves represent RDWIA (dashed), RD-
WIA + QMC (solid), and RDWIA + CQS (dash-dot) calcu-
lations with the current operator cc2 and the MRW optical
potential [25]. The grey band represents Schiavilla’s model
[17]; See text for details.

Page 6

6
H
zz
)
/P’
/ (P’
xx
He
zz
)
/P’
(P’(P’
xx
0.80.8
0.90.9
1.01.0
2
= 0.8 (GeV/c)
2
Q
H
)
/P’
/ (P’
He
)
/P’
2)
22
(GeV/c
p
- m (GeV/c
p
- m
22
22
(p/c)(p/c)
-0.06-0.06 -0.04-0.04-0.02-0.020.000.00
H
zz
)
/P’
/ (P’
xx
He
zz
)
/P’
(P’(P’
xx
0.80.8
0.90.9
1.01.0
RPWIARPWIA
RDWIARDWIA
RDWIA + QMCRDWIA + QMC
2
= 1.3 (GeV/c)
2
Q
2)
H
)
/P’
/ (P’
He
)
/P’
FIG. 3: The double ratio R versus the proton virtuality for
Q2= 0.8 and 1.3 (GeV/c)2. The dashed line is a linear fit to
the data constrained to have a y intercept value of one at zero
virtuality. The bands represent RPWIA (light grey), RDWIA
calculations (grey), and RDWIA + QMC calculations (dark
grey)[25]. See the text for a description of the models.