We report the first measurement of the parity-violating asymmetry in elastic
electron scattering from the proton. The asymmetry depends on the neutral weak
magnetic form factor of the proton which contains new information on the
contribution of strange quark-antiquark pairs to the magnetic moment of the
proton. We obtain the value $G_M^Z= 0.34 \pm 0.09 \pm 0.04 \pm 0.05$ n.m. at
$Q^2=0.1$ (GeV/c)${}^2$.Comment: 4 pages TEX, text available at
  http://www.krl.caltech.edu/preprints/OAP.htm

A. Lung

B. Mueller

B. Terburg

B. W. Filippone

D. H. Beck

D. Kaplan

D. Nilsson

E. Candell

E. J. Beise

F. Duncan

G. Dodson

H. Gao

J. Napolitano

K. Abe

K. Dow

L. Cardman

M. Farkhondeh

M. J. Musolf

M. Pitt

N. Simicevic

P. A. Souder

R. C. DiBari

R. Carr

R. D. McKeown

R. M. Barnett

R. Mohring

S. Kowalski

S. P. Wells

S.-P. Li

T. Forest

W. Heil

W. Korsch

English

arXiv

We report the first measurement of the parity-violating asymmetry in elastic electron scattering from the proton. The asymmetry depends on the neutral weak magnetic form factor of the proton which contains new information on the contribution of strange quark-antiquark pairs to the magnetic moment of the proton. We obtain the value GMZ = 0.34±0.09±0.04±0.05 n.m. at Q^2 = 0.1 (GeV/c)^2

Mueller, B.

Beck, D. H.

Beise, E. J.

Candell, E.

Cardman, L.

Carr, R.

DiBari, R. C.

Dodson, G.

Dow, K.

Duncan, F.

Farkhondeh, M.

Filippone, B. W.

Forest, T.

Gao, H.

Korsch, W.

Kowalski, S.

Lung, A.

McKeown, R. D.

Mohring, R.

Napolitano, J.

Nilsson, D.

Pitt, M.

Simicevic, N.

Terburg, B.

Wells, S. P.

Caltech Authors - Main

VOLUME 78, NUMBER 20 P HY S I CA L REV I EW LE T T ER S 19 MAY 1997Measurement of the Proton’s Neutral Weak Magnetic Form Factor
B. Mueller,1 D.H. Beck,2 E. J. Beise,3 E. Candell,4,* L. Cardman,2,† R. Carr,1 R. C. DiBari,4 G. Dodson,5 K. Dow,5
F. Duncan,3 M. Farkhondeh,5 B.W. Filippone,1 T. Forest,2 H. Gao,2,‡ W. Korsch,1,§ S. Kowalski,5 A. Lung,3 R.D.
McKeown,1 R. Mohring,3 J. Napolitano,4 D. Nilsson,2 M. Pitt,1,k N. Simicevic,2,¶ B. Terburg,2 and S. P. Wells5,¶
(SAMPLE Collaboration)
1Kellogg Radiation Laboratory, California Institute of Technology, Pasadena, California 91125
2University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
3University of Maryland, College Park, Maryland 20742
4Rensselaer Polytechnic Institute, Troy, New York 12180
5Bates Linear Accelerator Center, Laboratory for Nuclear Science and Department of Physics,
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
(Received 24 February 1997)
We report the first measurement of the parity-violating asymmetry in elastic electron scattering from
the proton. The asymmetry depends on the neutral weak magnetic form factor of the proton which
contains new information on the contribution of strange quark-antiquark pairs to the magnetic moment
of the proton. We obtain the value GZM ­ 0.34 6 0.09 6 0.04 6 0.05 n.m. at Q2 ­ 0.1 sGeVycd2.
[S0031-9007(97)03181-5]
PACS numbers: 13.60.Fz, 11.30.Er, 13.40.Gp, 14.20.DhThe measurement of strange quark-antiquark (ss) ef-
fects in the nucleon offers a unique window to study the
effects of the qq “sea” at low momentum transfers. This
information is an important clue to the dynamical effects
of QCD that are responsible for form factors in the non-
perturbative regime, and may lead to new insight into the
origins of these effects.
It has been shown [1] that the neutral weak current
can be used to determine the ss contributions to nucleon
form factors. The magnetic moment is one important
nucleon property that can be studied in this fashion. The
neutral weak magnetic form factor of the proton can be
measured in parity-violating electron scattering, [2], thus
providing information on the ss content of the nucleon’s
magnetic moment. In this Letter, we report the first such
measurement and obtain the first direct experimental data
relevant to determination of the strange magnetic moment
of the proton.
To lowest order (tree-level), the neutral weak magnetic
form factor of the proton GZM can be related to nucleon
electromagnetic form factors and a contribution from
strange quarks:
GZM ­
1
4
sGpM 2 GnMd 2 sin2 uW G
p
M 2
1
4
GsM , (1)
where GpM and GnM are the (electromagnetic) nucleon
magnetic form factors, and uW is the weak mixing angle.
(Note that the weak mixing angle has recently been deter-
mined [3] with high precision: sin2 uW sMZd ­ 0.2315 6
0.0004.) Electroweak radiative corrections must be ap-
plied to the coefficients in Eq. (1), which have been com-
puted in Ref. [4]. Then measurement of the neutral weak
form factor GZM will allow (after combination with the
well known electromagnetic form factors) determination3824 0031-9007y97y78(20)y3824(4)$10.00of the strange magnetic form factor GsM . There has been
a variety of theoretical predictions for GsM in the limit of
zero momentum transfer (;ms) over the last few years,
and summaries of them are presented in Refs. [5] and [6].
The typical magnitude is 20.3 n.m. (nuclear magnetons),
although the predictions range from 20.73 to 10.42 n.m.
As mentioned above, the quantity GZM for the proton
can be measured via elastic parity-violating electron
scattering at backward angles [2]. The difference in cross
sections for right and left handed incident electrons arises
from interference of the electromagnetic and neutral weak
amplitudes, and so contains products of electromagnetic
and neutral weak form factors. The expression for elastic
scattering from the proton is given by
A ­
sR 2 sL
sR 1 sL
­
"
2GFQ2
pa
p
2
#
(2)
3
«G
g
EG
Z
E 1 tG
g
MG
Z
M 2
1
2 s1 2 4 sin2 uW d«0G
g
MG
Z
A
«sGgE d2 1 tsG
g
M d2
,
where «, t, and «0 ­
p
ts1 1 td s1 2 «2d are kinematic
quantities, and Q2 . 0 is the four-momentum transfer [5].
In addition to the electric and magnetic neutral weak form
factors, GZE and GZM , the numerator of this expression also
contains the neutral weak axial form factor:
GZA ­ 2
1
2
s1 1 RAdGA 1
1
2
GsA , (3)
where we take GA ­ 1.2601 from neutron beta decay
[3], GsA ­ Ds , 20.1 is from polarized deep inelastic
scattering [7], and RA , 20.34 is the axial radiative© 1997 The American Physical Society
VOLUME 78, NUMBER 20 P HY S I CA L REV I EW LE T T ER S 19 MAY 1997correction [4,5]. This axial radiative correction is quite
uncertain and we assign a 100% uncertainty to this
correction. The uncertainty due to the GsA term is about an
order of magnitude smaller than the radiative correction
uncertainty.
The SAMPLE experiment measures the parity-violating
asymmetry in the elastic scattering of 200 MeV incident
electrons at backward angles with an average Q2 .
0.1 sGeVycd2. For GsM ­ 0, the value of GZM (at Q2 ­
0.1 GeV2) is 0.40 and the expected asymmetry in the
SAMPLE experiment is 27.2 3 1026 or 27.2 ppm;
for GsM ­ 20.3 n.m., GZM ­ 0.48 and we would then
expect A ­ 28.3 ppm. At these kinematics the axial
term contributes about 20% of the asymmetry, so the
uncertainty due to the axial term is 60.7 ppm.
The experiment is performed at the MIT/Bates Linear
Accelerator Center using a 200 MeV polarized electron
beam incident on a liquid hydrogen target. The scattered
electrons are detected in a large solid angle (,2 sr)
air Cerenkov detector similar in design to that used in
Ref. [8]. The detector covers the angular region 130– ,
u , 170– corresponding to the range of momentum
transfers 0.10 , Q2 , 0.11 sGeVycd2.
The liquid hydrogen target is 40 cm long, and is part
of a high flow-rate recirculating liquid hydrogen system
with a heat exchanger to remove the ,500 watts of
heat deposited by the electron beam. Studies of the
performance [9] of the target indicate that with 40 mA of
beam the target can be maintained as a subcooled liquid
and that density fluctuations are less than 0.1%. The
fluctuations in the detected signal are then dominated by
counting statistics of the scattered particles.
The detector consists of ten large mirrors, each with
ellipsoidal curvature to focus the Cerenkov light onto
one of ten photomultiplier tubes. Each photomultiplier is
8 in. in diameter and is shielded from the target and room
background by a cast lead shield. In addition, 2 mm of
Pb on the scattering chamber wall is essential to reduce
the x-ray background in the detector to a reasonable level.
(This backround is due to Compton scattering of forward
bremsstrahlung in the liquid hydrogen target.)
A remotely controlled light shutter can cover each pho-
tomultiplier tube for background measurements. We typ-
ically take one third of our data with shutters closed to
monitor this background. We have determined that this
background is soft electromagnetic radiation (a thin Pb
shield eliminates it) and arises from showering in the tar-
get plus additional scattering from downstream of the ap-
paratus. Electromagnetic background generated by soft
bremsstrahlung will have negligible helicity dependence.
(The parity-violating asymmetry is proportional to the
squared momentum transfer to the proton which is ex-
tremely small.) Our measurements do verify an absence
of helicity dependence in this signal (see Table I).
In addition, we study the detector signals with covers
on the mirrors to analyze them for non-Cerenkov sourcesTABLE I. Components of detector signal.
Source Fraction Asymmetry (ppm)
Elastic electrons 54.8 6 4.0% 26.34 6 1.45 6 0.53
Shutter closed 22.6 6 0.5% 1.95 6 3.13 (Measured)
p decays 2.3 6 1.4% ,1 ppm (Ref. [11])
x rays (EM) 20.3 6 3.7% 0
of light. To further study these backgrounds, we de-
veloped a technique of accelerating “tracer bullets” of
,0.1 mA peak current interspersed with very weak beam
pulses with typical peak currents in the nA range. One
can then use more conventional pulse counting techniques
to study the Cerenkov detector response. This method
clearly shows the relative fraction of scintillation light
(events with only one photoelectron) relative to Cerenkov
light (events with several photoelectrons). The scintilla-
tion light is due to the interaction of the residual flux of
x rays and low energy gamma rays from the target with
the air in the detector and the rate agrees with a computer
simulation of this process. As indicated in Table I, this
background amounts to 20.3 6 3.7% of our total detector
signal and should have negligible helicity dependence (as
discussed in the previous paragraph).
The Cerenkov light is almost totally due to elastic scat-
tering of electrons from protons, with a small contribution
due to pion decays. The pion background is rather small
because the low incident beam energy (200 MeV) is close
to the production threshold. The pion yield has been cal-
culated using known photoproduction cross sections, and
the low p1 yield is verified by measurement of the rate
of delayed signals from muon decays just after the elec-
tron beam pulse ends. In addition, we used a NaI detec-
tor behind a mirror in coincidence to check the spectrum
of scattered electrons and compare with computer simu-
lations. The observed elastic scattering signal is in good
agreement with expectations.
The incident electron beam is pulsed at 600 Hz; each
detector signal is integrated over the ,15 msec of every
beam pulse and digitized. The beam intensity is similarly
integrated and digitized. The ratio of integrated detector
signal to the integrated beam signal is the normalized
yield which is proportional to the cross section (plus
background). We then measure the helicity dependent
asymmetry in the normalized yield which (after correction
for background, radiative effects, and beam polarization)
yields the parity-violating asymmetry A. All ten detectors
are combined in software during the data analysis.
The polarized electron source is a GaAs photoemission
source. The laser beam that is incident on the GaAs
crystal is circularly polarized by a ly4 Pockels cell. The
electron beam helicity is rapidly reversed by changing
the voltage on the Pockels cell to reverse the circular
polarization of the light. The helicity is randomly chosen
for each of ten consecutive beam pulses and then the
complement helicities are used for the next ten pulses.3825
VOLUME 78, NUMBER 20 P HY S I CA L REV I EW LE T T ER S 19 MAY 1997The asymmetry in the normalized yields is computed for
“pulse pairs” separated by 1y60 of a second to minimize
systematic errors. Each pulse pair asymmetry corresponds
to a measurement of the parity-violating cross section
asymmetry. These are then combined in 30 minute runs
corresponding to typically 0.5 3 106 measurements. An
active feedback system [10] keeps the helicity correlations
in the beam intensity averaged to zero to better than 1 ppm.
The beam helicity can be manually reversed by rotating
a ly2 plate which reverses the helicity of the light (and
the beam) relative to all electronic signals. We denote this
setting as “reverse” as opposed to the “normal” setting;
a real parity violation signal will appear to change sign
under this “slow reversal.” Electronic crosstalk and other
effects will not change under slow reversal, so this is
an important test that our signal is not some spurious
systematic effect.
The electron polarization is measured using a Moller
apparatus on the beam line and is typically 35%. A
Wien spin rotator located at the exit of the polarized
source is used to rotate the spin for investigation of
transverse spin asymmetries and minimize their effects
during parity violation measurements. Based on these
studies, the effect of transverse components of electron
polarization to the observed parity violation signal is
determined to be negligible.
The beam position and angle at the target in both
transverse dimensions (x and y), the beam energy, and
the “halo” of the beam are continuously monitored for
every beam pulse. If a helicity correlation is present, then
we can correct the detector normalized yield asymmetries
to remove its effect. In practice, these corrections are
generally less than 1 ppm per run and approximately
average to zero over many runs. Other properties, such
as the width of the beam, are studied during special runs
to verify the absence of helicity correlations.
We have acquired a significant data sample from two
runs: one in fall 1995 and one in spring 1996. Combin-
ing the data in each of the two data sets and comput-
ing the physics asymmetry, we obtain the asymmetries
shown in Fig. 1. The corrections to the raw measured
asymmetry are the background effects given in Table I
(1.82 6 0.13), the correction for (internal and external)
bremsstrahlung radiation (1.16 6 0.01), and the beam po-
larization [1ys0.348 6 0.015d]. These are combined to
give an overall multiplicative correction of 6.07 6 0.51.
We have assumed that the shutter closed background and
the x-ray background light have zero asymmetry, as ex-
pected for soft electromagnetic processes. Combining the
asymmetries from the two data sets yields the value for
the parity-violating asymmetry
A ­ 26.34 6 1.45 6 0.53 ppm ,
where the first uncertainty is statistical and the second
is the estimated systematic error. The neutral weak3826FIG. 1. Results for the parity-violating asymmetry measured
in the 1995 and 1996 running periods. For each running period
we display the result for the normal (squares) and reverse
(triangles) settings of slow helicity reversal, which are in good
agreement. The combined result for both helicity states and
both running periods is also shown (circle). The error bars
include statistical errors only. The hatched region indicates the
asymmetry band (due to the uncertain axial radiative correction)
for ms ­ GsM ­ 0.
magnetic form factor derived from this asymmetry is
GZM sQ
2 ­ 0.1 GeV2d ­ 0.34 6 0.09 6 0.04 6 0.05 n.m. ,
where the last uncertainty is due to the axial radiative
correction and other minor form factor uncertainties as-
sociated with extracting GZM from the measured asym-
metry. In the absence of a strange quark contribution
we expect GZM ­ 0.40 n.m.; our measurement of GZM
thus corresponds to a value of GsMsQ2 ­ 0.1 GeV2d ­
10.23 6 0.37 6 0.15 6 0.19 n.m.
If we do not assume the shutter closed background to be
identically zero but rather use the measured shutter closed
asymmetry (see Table I), then the result for A becomes
27.38 6 2.12 6 0.66 ppm where the statistical error is
increased by the shutter closed measurement. This value
is in good agreement with that obtained above.
In the future, for the full hydrogen data set we project
that the statistical error on GZM will be reduced to about
0.05 nm. (We have collected only about 20% of the
total data sample in these two runs.) Additional running
with deuterium will further reduce the uncertainty in
GZM by greatly reducing the error associated with the
axial radiative correction [12]. The deuterium asymmetry
contains the same fraction of axial correction but is almost
completely insensitive to GsM . As a result the ratio ApyAD
has the same sensitivity to GsM but almost no sensitivity
to RA.
Additional experiments to explore other features of
neutral weak currents and strange form factors of the nu-
cleon are planned at Mainz (MAMI-B) [13] and TJNAF
(formerly known as CEBAF) [14]. These experiments
will provide a new and unique window on the quark struc-
ture of the nucleon, and hopefully will provide important
VOLUME 78, NUMBER 20 P HY S I CA L REV I EW LE T T ER S 19 MAY 1997information towards a more complete understanding of
nucleon structure in the context of QCD.
The persistent efforts of the staff of the MIT/Bates fa-
cility to provide high quality beam and improve the ex-
periment are gratefully acknowledged. Financial support
for the construction of the Moller apparatus from CE-
BAF is acknowledged. This work was supported by NSF
Grants No. PHY-9420470 (Caltech), No. PHY-9420787
(Illinois), No. PHY-9457906yPHY-9229690 (Maryland),
No. PHY-9507412 (RPI), and DOE Cooperative Agree-
ment No. DE-FC02-94ER40818 (MIT/Bates).
*Deceased.
†Present address: Thomas Jefferson National Accelerator
Facility, Newport News, VA 23606.
‡Present address: Physics Division, Argonne National
Laboratory, Argonne, IL 60439.
§Present address: Department of Physics and Astronomy,
University of Kentucky, Lexington, KY 40506.
kPresent address: Department of Physics, Virginia
Polytechnic Institute and State University, Blacksburg,
VA 24061-0435.
¶Present address: Department of Physics, Louisiana TechUniversity, Ruston, LA 71270.
[1] D. Kaplan and A. Manohar, Nucl. Phys. B310, 527 (1988).
[2] R. D. McKeown, Phys. Lett. B 219, 140 (1989); D. H.
Beck, Phys. Rev. D 39, 3248 (1989).
[3] Particle Data Group, R.M. Barnett et al., Phys. Rev. D 54,
1 (1996).
[4] M. J. Musolf and B.R. Holstein, Phys. Lett. B 242, 461
(1990).
[5] M. J. Musolf et al., Phys. Rep. 239, 1 (1994).
[6] E. J. Beise et al., in Proceedings of SPIN96 Symposium
(Report No. nucl-exy9610011).
[7] K. Abe et al., Phys. Rev. Lett. 74, 346 (1995).
[8] W. Heil et al., Nucl. Phys. B327, 1 (1989).
[9] E. J. Beise et al., Nucl. Instrum. Methods Phys. Res.,
Sect. A 378, 383 (1996).
[10] P. A. Souder et al., Phys. Rev. Lett. 65, 694 (1990).
[11] S.-P. Li, E.M. Henley, and W.-Y. P. Hwang, Ann. Phys.
(N.Y.) 143, 372 (1982).
[12] Bates experiment 94-11 (M. Pitt and E. J. Beise,
spokespersons).
[13] Mainz proposal A4y1-93 94-11 (D. von Harrach,
spokesperson).
[14] TJNAF experiments E91-017 (D. Beck, spokesperson);
E91-010 (P. Souder and J. Finn, spokespersons); E91-004
(E. J. Beise, spokesperson).3827


Measurement of the Proton's Neutral Weak Magnetic Form Factor

We report the first measurement of the parity-violating asymmetry in elastic electron scattering from the proton. The asymmetry depends on the neutral weak magnetic form factor of the proton which contains new information on the contribution of strange quark-antiquark pairs to the magnetic moment of the proton. We obtain the value GMZ = 0.34±0.09±0.04±0.05n.m. at Q2 = 0.1 (GeV/c)2.National Science Foundatio

Beck, D.H.

Beise, E.J.

DiBari, R.C.

Filippone, B.W.

McKeown, R.D.

Wells, S.P.

SAMPLE Collaboration

Digital Repository at the University of Maryland

VOLUME 78, NUMBER 20 P H Y S I C A L R E V I E W L E T T E R S 19 MAY 1997Measurement of the Proton’s Neutral Weak Magnetic Form FactorB. Mueller,1 D. H. Beck,2 E. J. Beise,3 E. Candell,4,* L. Cardman,2,† R. Carr,1 R. C. DiBari,4 G. Dodson,5 K. Dow,5F. Duncan,3 M. Farkhondeh,5 B. W. Filippone,1 T. Forest,2 H. Gao,2,‡ W. Korsch,1,§ S. Kowalski,5 A. Lung,3 R. D.McKeown,1 R. Mohring,3 J. Napolitano,4 D. Nilsson,2 M. Pitt,1,k N. Simicevic,2,¶ B. Terburg,2 and S. P. Wells5,¶(SAMPLE Collaboration)1Kellogg Radiation Laboratory, California Institute of Technology, Pasadena, California 911252University of Illinois at Urbana-Champaign, Urbana, Illinois 618013University of Maryland, College Park, Maryland 207424Rensselaer Polytechnic Institute, Troy, New York 121805Bates Linear Accelerator Center, Laboratory for Nuclear Science and Department of Physics,Massachusetts Institute of Technology, Cambridge, Massachusetts 02139(Received 24 February 1997)We report the first measurement of the parity-violating asymmetry in elastic electron scattering fromthe proton. The asymmetry depends on the neutral weak magnetic form factor of the proton whichcontains new information on the contribution of strange quark-antiquark pairs to the magnetic momentof the proton. We obtain the valueGZM ­ 0.34 6 0.09 6 0.04 6 0.05 n.m. at Q2 ­ 0.1 sGeVycd2.[S0031-9007(97)03181-5]PACS numbers: 13.60.Fz, 11.30.Er, 13.40.Gp, 14.20.Dhhstnthnnhbucaetmntepman[6].,onssesakticticmoThe measurement of strange quark-antiquark (ss) ef-fects in the nucleon offers a unique window to study teffects of theqq “sea” at low momentum transfers. Thiinformation is an important clue to the dynamical effecof QCD that are responsible for form factors in the noperturbative regime, and may lead to new insight intoorigins of these effects.It has been shown [1] that the neutral weak currecan be used to determine thess contributions to nucleonform factors. The magnetic moment is one importanucleon property that can be studied in this fashion. Tneutral weak magnetic form factor of the proton canmeasured in parity-violating electron scattering, [2], thproviding information on thess content of the nucleon’smagnetic moment. In this Letter, we report the first sumeasurement and obtain the first direct experimental drelevant to determination of the strange magnetic momof the proton.To lowest order (tree-level), the neutral weak magneform factor of the protonGZM can be related to nucleonelectromagnetic form factors and a contribution frostrange quarks:GZM ­14sGpM 2 GnMd 2 sin2 uW GpM 214GsM , (1)where GpM and GnM are the (electromagnetic) nucleomagnetic form factors, anduW is the weak mixing angle.(Note that the weak mixing angle has recently been demined [3] with high precision: sin2 uW sMZd ­ 0.2315 60.0004.) Electroweak radiative corrections must be aplied to the coefficients in Eq. (1), which have been coputed in Ref. [4]. Then measurement of the neutral weform factor GZM will allow (after combination with thewell known electromagnetic form factors) determinatio3824 0031-9007y97y78(20)y3824(4)$10.00es-etteeshtanticr---kof the strange magnetic form factorGsM . There has beena variety of theoretical predictions forGsM in the limit ofzero momentum transfer (;ms) over the last few years,and summaries of them are presented in Refs. [5] andThe typical magnitude is20.3 n.m. (nuclear magnetons)although the predictions range from20.73 to 10.42 n.m.As mentioned above, the quantityGZM for the protoncan be measured via elastic parity-violating electrscattering at backward angles [2]. The difference in crosections for right and left handed incident electrons arisfrom interference of the electromagnetic and neutral weamplitudes, and so contains products of electromagneand neutral weak form factors. The expression for elasscattering from the proton is given byA ­sR 2 sLsR 1 sL­"2GFQ2pap2#(2)3´GgEGZE 1 tGgMGZM 212 s1 2 4 sin2 uW d´0GgMGZA´sGgE d2 1 tsGgM d2,where´, t, and´0 ­pts1 1 td s1 2 ´2d are kinematicquantities, andQ2 . 0 is the four-momentum transfer [5].In addition to the electric and magnetic neutral weak forfactors,GZE andGZM , the numerator of this expression alscontains the neutral weak axial form factor:GZA ­ 212s1 1 RAdGA 112GsA , (3)where we takeGA ­ 1.2601 from neutron beta decay[3], GsA ­ Ds , 20.1 is from polarized deep inelasticscattering [7], andRA , 20.34 is the axial radiative© 1997 The American Physical SocietyVOLUME 78, NUMBER 20 P H Y S I C A L R E V I E W L E T T E R S 19 MAY 1997eonlhaomtitioroptere-ofmneuesodtova-fithteris(ast-nallseal-ndec-ec-mu-odchrlytoredsentnn)ionAsglarnthees.correction [4,5]. This axial radiative correction is quituncertain and we assign a 100% uncertainty to thcorrection. The uncertainty due to theGsA term is about anorder of magnitude smaller than the radiative correctiuncertainty.The SAMPLE experiment measures the parity-violatinasymmetry in the elastic scattering of 200 MeV incideelectrons at backward angles with an averageQ2 .0.1 sGeVycd2. For GsM ­ 0, the value ofGZM (at Q2 ­0.1 GeV2) is 0.40 and the expected asymmetry in thSAMPLE experiment is27.2 3 1026 or 27.2 ppm;for GsM ­ 20.3 n.m., GZM ­ 0.48 and we would thenexpect A ­ 28.3 ppm. At these kinematics the axiaterm contributes about 20% of the asymmetry, so tuncertainty due to the axial term is60.7 ppm.The experiment is performed at the MIT/Bates LineAccelerator Center using a 200 MeV polarized electrbeam incident on a liquid hydrogen target. The scatterelectrons are detected in a large solid angle (,2 sr)air Cerenkov detector similar in design to that usedRef. [8]. The detector covers the angular region130± ,u , 170± corresponding to the range of momentutransfers0.10 , Q2 , 0.11 sGeVycd2.The liquid hydrogen target is 40 cm long, and is paof a high flow-rate recirculating liquid hydrogen systemwith a heat exchanger to remove the,500 watts ofheat deposited by the electron beam. Studies ofperformance [9] of the target indicate that with40 mA ofbeam the target can be maintained as a subcooled liqand that density fluctuations are less than 0.1%. Tfluctuations in the detected signal are then dominatedcounting statistics of the scattered particles.The detector consists of ten large mirrors, each wellipsoidal curvature to focus the Cerenkov light onone of ten photomultiplier tubes. Each photomultiplier8 in. in diameter and is shielded from the target and roobackground by a cast lead shield. In addition, 2 mmPb on the scattering chamber wall is essential to reduthe x-ray background in the detector to a reasonable lev(This backround is due to Compton scattering of forwabremsstrahlung in the liquid hydrogen target.)A remotely controlled light shutter can cover each phtomultiplier tube for background measurements. We tyically take one third of our data with shutters closedmonitor this background. We have determined that thbackground is soft electromagnetic radiation (a thin Pshield eliminates it) and arises from showering in the taget plus additional scattering from downstream of the aparatus. Electromagnetic background generated by sbremsstrahlung will have negligible helicity dependenc(The parity-violating asymmetry is proportional to thsquared momentum transfer to the proton which is etremely small.) Our measurements do verify an absenof helicity dependence in this signal (see Table I).In addition, we study the detector signals with coveon the mirrors to analyze them for non-Cerenkov sourcisngteernedinrtheuidhebythosmfceel.d--oisbr-p-ofte.x-cesesTABLE I. Components of detector signal.Source Fraction Asymmetry (ppm)Elastic electrons 54.8 6 4.0% 26.34 6 1.45 6 0.53Shutter closed 22.6 6 0.5% 1.95 6 3.13 (Measured)p decays 2.3 6 1.4% ,1 ppm (Ref. [11])x rays (EM) 20.3 6 3.7% 0of light. To further study these backgrounds, we dveloped a technique of accelerating “tracer bullets”,0.1 mA peak current interspersed with very weak beapulses with typical peak currents in the nA range. Ocan then use more conventional pulse counting techniqto study the Cerenkov detector response. This methclearly shows the relative fraction of scintillation ligh(events with only one photoelectron) relative to Cerenklight (events with several photoelectrons). The scintilltion light is due to the interaction of the residual flux ox rays and low energy gamma rays from the target wthe air in the detector and the rate agrees with a compusimulation of this process. As indicated in Table I, thbackground amounts to20.3 6 3.7% of our total detectorsignal and should have negligible helicity dependencediscussed in the previous paragraph).The Cerenkov light is almost totally due to elastic scatering of electrons from protons, with a small contributiodue to pion decays. The pion background is rather smbecause the low incident beam energy (200 MeV) is cloto the production threshold. The pion yield has been cculated using known photoproduction cross sections, athe low p1 yield is verified by measurement of the ratof delayed signals from muon decays just after the eletron beam pulse ends. In addition, we used a NaI dettor behind a mirror in coincidence to check the spectruof scattered electrons and compare with computer simlations. The observed elastic scattering signal is in goagreement with expectations.The incident electron beam is pulsed at 600 Hz; eadetector signal is integrated over the,15 msec of everybeam pulse and digitized. The beam intensity is similaintegrated and digitized. The ratio of integrated detecsignal to the integrated beam signal is the normalizyield which is proportional to the cross section (plubackground). We then measure the helicity dependasymmetry in the normalized yield which (after correctiofor background, radiative effects, and beam polarizatioyields the parity-violating asymmetryA. All ten detectorsare combined in software during the data analysis.The polarized electron source is a GaAs photoemisssource. The laser beam that is incident on the Gacrystal is circularly polarized by aly4 Pockels cell. Theelectron beam helicity is rapidly reversed by changinthe voltage on the Pockels cell to reverse the circupolarization of the light. The helicity is randomly chosefor each of ten consecutive beam pulses and thencomplement helicities are used for the next ten puls3825VOLUME 78, NUMBER 20 P H Y S I C A L R E V I E W L E T T E R S 19 MAY 1997foniounpindhgneiuleAdocetristoeriaeuuwinuieeel)aetfnaediodrsedndrstheon)ves--onbesedluectegnerystofu-tsc-tThe asymmetry in the normalized yields is computed“pulse pairs” separated by 1y60 of a second to minimizesystematic errors. Each pulse pair asymmetry correspoto a measurement of the parity-violating cross sectasymmetry. These are then combined in 30 minute rcorresponding to typically0.5 3 106 measurements. Anactive feedback system [10] keeps the helicity correlatioin the beam intensity averaged to zero to better than 1 pThe beam helicity can be manually reversed by rotata ly2 plate which reverses the helicity of the light (anthe beam) relative to all electronic signals. We denote tsetting as “reverse” as opposed to the “normal” settina real parity violation signal will appear to change sigunder this “slow reversal.” Electronic crosstalk and otheffects will not change under slow reversal, so thisan important test that our signal is not some spuriosystematic effect.The electron polarization is measured using a Molapparatus on the beam line and is typically 35%.Wien spin rotator located at the exit of the polarizesource is used to rotate the spin for investigationtransverse spin asymmetries and minimize their effeduring parity violation measurements. Based on thstudies, the effect of transverse components of elecpolarization to the observed parity violation signaldetermined to be negligible.The beam position and angle at the target in botransverse dimensions (x and y), the beam energy, andthe “halo” of the beam are continuously monitored fevery beam pulse. If a helicity correlation is present, thwe can correct the detector normalized yield asymmetto remove its effect. In practice, these correctionsgenerally less than 1 ppm per run and approximataverage to zero over many runs. Other properties, sas the width of the beam, are studied during special rto verify the absence of helicity correlations.We have acquired a significant data sample from truns: one in fall 1995 and one in spring 1996. Combing the data in each of the two data sets and comping the physics asymmetry, we obtain the asymmetrshown in Fig. 1. The corrections to the raw measurasymmetry are the background effects given in Tabl(1.82 6 0.13), the correction for (internal and externabremsstrahlung radiation (1.16 6 0.01), and the beam po-larization [1ys0.348 6 0.015d]. These are combined togive an overall multiplicative correction of6.07 6 0.51.We have assumed that the shutter closed backgroundthe x-ray background light have zero asymmetry, aspected for soft electromagnetic processes. Combiningasymmetries from the two data sets yields the valuethe parity-violating asymmetryA ­ 26.34 6 1.45 6 0.53 ppm,where the first uncertainty is statistical and the secois the estimated systematic error. The neutral we3826rdsnnssm.gis;rssrftsseonhrnesrelychnso-t-sdIndx-heordkFIG. 1. Results for the parity-violating asymmetry measurin the 1995 and 1996 running periods. For each running perwe display the result for the normal (squares) and reve(triangles) settings of slow helicity reversal, which are in gooagreement. The combined result for both helicity states aboth running periods is also shown (circle). The error bainclude statistical errors only. The hatched region indicatesasymmetry band (due to the uncertain axial radiative correctifor ms ­ GsM ­ 0.magnetic form factor derived from this asymmetry isGZM sQ2 ­ 0.1 GeV2d ­ 0.34 6 0.09 6 0.04 6 0.05 n.m.,where the last uncertainty is due to the axial radiaticorrection and other minor form factor uncertainties asociated with extractingGZM from the measured asymmetry. In the absence of a strange quark contributiwe expect GZM ­ 0.40 n.m.; our measurement ofGZMthus corresponds to a value ofGsMsQ2 ­ 0.1 GeV2d ­10.23 6 0.37 6 0.15 6 0.19 n.m.If we do not assume the shutter closed background toidentically zero but rather use the measured shutter cloasymmetry (see Table I), then the result forA becomes27.38 6 2.12 6 0.66 ppm where the statistical error isincreased by the shutter closed measurement. This vais in good agreement with that obtained above.In the future, for the full hydrogen data set we projethat the statistical error onGZM will be reduced to about0.05 nm. (We have collected only about 20% of thtotal data sample in these two runs.) Additional runninwith deuterium will further reduce the uncertainty iGZM by greatly reducing the error associated with thaxial radiative correction [12]. The deuterium asymmetcontains the same fraction of axial correction but is almocompletely insensitive toGsM . As a result the ratioApyADhas the same sensitivity toGsM but almost no sensitivityto RA.Additional experiments to explore other featuresneutral weak currents and strange form factors of the ncleon are planned at Mainz (MAMI-B) [13] and TJNAF(formerly known as CEBAF) [14]. These experimenwill provide a new and unique window on the quark struture of the nucleon, and hopefully will provide importanVOLUME 78, NUMBER 20 P H Y S I C A L R E V I E W L E T T E R S 19 MAY 1997o--r-F7-taia,c.,.e,n);004information towards a more complete understandingnucleon structure in the context of QCD.The persistent efforts of the staff of the MIT/Bates facility to provide high quality beam and improve the experiment are gratefully acknowledged. Financial suppofor the construction of the Moller apparatus from CEBAF is acknowledged. This work was supported by NSGrants No. PHY-9420470 (Caltech), No. PHY-942078(Illinois), No. PHY-9457906yPHY-9229690 (Maryland),No. PHY-9507412 (RPI), and DOE Cooperative Agreement No. DE-FC02-94ER40818 (MIT/Bates).*Deceased.†Present address: Thomas Jefferson National AcceleraFacility, Newport News, VA 23606.‡Present address: Physics Division, Argonne NationLaboratory, Argonne, IL 60439.§Present address: Department of Physics and AstronomUniversity of Kentucky, Lexington, KY 40506.kPresent address: Department of Physics, VirginPolytechnic Institute and State University, BlacksburgVA 24061-0435.¶Present address: Department of Physics, Louisiana Teftorly,hUniversity, Ruston, LA 71270.[1] D. Kaplan and A. Manohar, Nucl. Phys.B310, 527 (1988).[2] R. D. McKeown, Phys. Lett. B219, 140 (1989); D. H.Beck, Phys. Rev. D39, 3248 (1989).[3] Particle Data Group, R. M. Barnette al.,Phys. Rev. D54,1 (1996).[4] M. J. Musolf and B. R. Holstein, Phys. Lett. B242, 461(1990).[5] M. J. Musolf et al., Phys. Rep.239, 1 (1994).[6] E. J. Beiseet al., in Proceedings of SPIN96 Symposium(Report No. nucl-exy9610011).[7] K. Abe et al., Phys. Rev. Lett.74, 346 (1995).[8] W. Heil et al., Nucl. Phys.B327, 1 (1989).[9] E. J. Beise et al., Nucl. Instrum. Methods Phys. ResSect. A378, 383 (1996).[10] P. A. Souderet al., Phys. Rev. Lett.65, 694 (1990).[11] S.-P. Li, E. M. Henley, and W.-Y. P. Hwang, Ann. Phys(N.Y.) 143, 372 (1982).[12] Bates experiment 94-11 (M. Pitt and E. J. Beisspokespersons).[13] Mainz proposal A4y1-93 94-11 (D. von Harrach,spokesperson).[14] TJNAF experiments E91-017 (D. Beck, spokespersoE91-010 (P. Souder and J. Finn, spokespersons); E91-(E. J. Beise, spokesperson).3827

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Measurement of the Proton's Neutral Weak Magnetic Form Factor

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