We report a measurement of the parity-violating asymmetry in fixed target electron-electron (Møller) scattering: A_(PV) = [-175 ± 30(stat)± 20(syst)] X 10^(-9). This first direct observation of parity nonconservation in Møller scattering leads to a measurement of the electron’s weak charge at low energy Q^e_W = -0:053 ± 0:011. This is  consistent with the standard model expectation at the current level of precision: sin^2θ_W = (M_Z)_(MS) = 0:2293 ± 0:0024(stat) ± 0:0016(syst) ± 0:0006(theory)

Anthony, P. L.

Bega, K.

Carr, R.

Gao, J.

Gustafsson, K.

Hughes, E. W.

Jones, G. M.

Mastromarino, P.

McKeown, R. D.

English

Caltech Authors - Main

P H Y S I C A L R E V I E W L E T T E R S week ending7 MAY 2004VOLUME 92, NUMBER 18Observation of Parity Nonconservation in Møller Scattering
P. L. Anthony,7 R. G. Arnold,3 C. Arroyo,3 K. Baird,7 K. Bega,2 J. Biesiada,1,4 P. E. Bosted,3 M. Breuer,3 R. Carr,2
G. D. Cates,10 J-P. Chen,9 E. Chudakov,9 M. Cooke,1 F. J. Decker,7 P. Decowski,6 A. Deur,10 W. Emam,8 R. Erickson,7
T. Fieguth,7 C. Field,7 J. Gao,2 K. Gustafsson,2,* R. S. Hicks,3 R. Holmes,8 E.W. Hughes,2 T. B. Humensky,4 G. M. Jones,2
L. J. Kaufman,3 Yu. G. Kolomensky,1 K. S. Kumar,3 D. Lhuillier,5 R. Lombard-Nelsen,5 P. Mastromarino,2 B. Mayer,5
R. D. McKeown,2 R. Michaels,9 M. Olson,7 K. D. Paschke,3 G. A. Peterson,3 R. Pitthan,7 K. Pope,6,† D. Relyea,4,7
S. E. Rock,3 O. Saxton,7 G. Shapiro,1,† J. Singh,10 P. A. Souder,8 Z. M. Szalata,7 W. A. Tobias,10 B.T. Tonguc,8 J. Turner,7
B. Tweedie,1 A. Vacheret,5 D. Walz,7 T. Weber,7 J. Weisend,7 D. Whittum,7 M. Woods,7 and I. Younus8
(SLAC E158 Collaboration)
1University of California, Berkeley, California 94720, USA
2California Institute of Technology, Pasadena, California 91125, USA
3University of Massachusetts, Amherst, Massachusetts 01003, USA
4Princeton University, Princeton, New Jersey 08544, USA
5CEA Saclay, DAPNIA/SPhN, F-91191 Gif-sur-Yvette, France
6Smith College, Northampton, Massachusetts 01063, USA
7Stanford Linear Accelerator Center, Menlo Park, California 94025, USA
8Syracuse University, Syracuse, New York 13244, USA
9Thomas Jefferson Laboratory, Newport News, Virginia 23606, USA
10University of Virginia, Charlottesville, Virginia 22903, USA
(Received 11 December 2003; published 7 May 2004)181602-1We report a measurement of the parity-violating asymmetry in fixed target electron-electron
(Møller) scattering: APV  175 30stat  20syst  109. This first direct observation of parity
nonconservation in Møller scattering leads to a measurement of the electron’s weak charge at low
energy QeW  0:053 0:011. This is consistent with the standard model expectation at the current
level of precision: sin2WMZMS  0:2293 0:0024stat  0:0016syst  0:0006theory.
DOI: 10.1103/PhysRevLett.92.181602 PACS numbers: 11.30.Er, 12.15.Mm, 13.66.Jn, 13.88.+eof hadronic targets restricted the interpretation of the
experimental results at the quantum loop level.
to 5:5 1011 electrons in  270 ns pulses at 120 Hz,
was produced by optical pumping of a strained GaAsPrecision measurements of weak neutral current
(WNC) processes mediated by Z0 exchange stringently
test the standard model of electroweak interactions.
While most WNC measurements have been performed
at high energy colliders, the comprehensive search for
new physics at TeV energies also requires precision mea-
surements at low momentum transfer (Q2 	 M2Z).
One class of such measurements involves the scattering
of longitudinally polarized electrons from unpolarized
targets, allowing the determination of a parity-violating
asymmetry APV 
 	R  	L=	R  	L, where 	RL is
the cross section for incident right(left)-handed electrons.
APV arises from the interference of the weak and electro-
magnetic amplitudes [1] and is sensitive toWNC coupling
constants and thus the weak mixing angle W.
The first observation of APV was made at the Stanford
Linear Accelerator Center (SLAC) using a deuteron target
[2]. That experiment established the basic experimental
technique to determine small asymmetries that typically
range from 0.1 to 100 parts per million (ppm). Subsequent
measurements yielded improved precision and accuracy
[3,4]. However, theoretical uncertainties related to the use0031-9007=04=92(18)=181602(4)$22.50 In this Letter we report the first observation of APV in
electron-electron (Møller) scattering. This purely lep-
tonic reaction has a large cross section and has little
theoretical uncertainty. The development of the 50 GeV
electron beam in SLAC End Station A (ESA) made
possible a measurement of APV [5] with a precision that
tests electroweak radiative corrections and probes physics
beyond the standard model at the TeV scale.
At 50 GeVand a center-of-mass scattering angle of 90,
APV in Møller scattering is predicted to be ’ 320 parts per
billion (ppb) [6] at tree level. Electroweak radiative cor-
rections [7,8] and the experimental acceptance reduce the
measured asymmetry by more than 50%. The principal
components of the experimental apparatus, designed to
measure APV to better than 10%, were the polarized
electron beam, a liquid hydrogen target, a spectrometer/
collimator system, and detectors. Møller-scattered elec-
trons were directed into a calorimeter by a magnetic
spectrometer. The asymmetry was measured by extract-
ing the fractional difference in the integrated calorimeter
response for incident right- and left-handed beam pulses.
The longitudinally polarized electron beam, with up2004 The American Physical Society 181602-1
P H Y S I C A L R E V I E W L E T T E R S week ending7 MAY 2004VOLUME 92, NUMBER 18photocathode [9] by circularly polarized laser light [10].
The sign of the laser circular polarization state deter-
mined the electron beam helicity. The helicity sequence
of the pulse train was made up of quadruplets consisting
of two consecutive pulses with pseudorandomly chosen
helicities, followed by their complements, yielding two
independent right-left ‘‘pulse pairs’’ every 33 ms.
Careful optimization of optical components [10] mini-
mized intrinsic intensity and position differences be-
tween right- and left-helicity beams that resulted from
imperfections in the laser light and the photocathode
response. Additionally, helicity-dependent corrections
were applied to the laser beam in a feedback loop using
periodic average measurements of beam asymmetries.
The beam intensity and position were measured at the
upstream and downstream ends of the accelerator with
typical accuracies per pulse pair of 50 ppm in intensity,
50 ppm in energy, and 2 m [11] in position. Cumulative
beam asymmetries at the target were reduced to
<500 ppb in intensity, <10 ppb in energy, and <50 nm
in position.
A schematic diagram of the apparatus in ESA is shown
in Fig. 1. The 0.5 MWelectron beam first passed through a
1.57 m long cylindrical cell filled with liquid hydrogen
[12]. The cell was part of a target loop consisting of a
motor, impeller, and heat exchanger, which circulated the
liquid hydrogen at  5 m=s. Aluminum meshes in the
fluid path surrounding the electron beam enhanced tur-
bulence and mixing. These features allowed the absorp-
tion of  500 W deposited by the beam while keeping
density fluctuations below 40 ppm per pulse pair.
Scattered particles with a laboratory scattering angle
between 4.4 and 7.5 mr over the full range of the azimuth
were selected by the magnetic spectrometer [13] while
the primary beam and forward angle photons passed
unimpeded to the beam dump. Sixty meters downstream
of the target, the charged particle flux was approximately
azimuthally symmetric about the beam axis. Møller elec-
trons in the range 13–24 GeV formed a ring spatially
separated from electrons scattered from target protons
(ep scattering). This Møller ring contained 2 107
electrons per pulse.
A scanning detector system provided a complete radial
and azimuthal map of the charged particle flux. Figure 2
compares the measured radial profile at one azimuthal
angle with Monte Carlo simulations of Møller and ep
scattering. The ep flux within the Møller ring was the
dominant background, estimated to be ’ 8%.
For the asymmetry measurement, the charged particle
flux was intercepted by the primary calorimeter, a 25 cmhydrogen
liquid
target
primary & scattered
polarized
beam
photons
dipoles quadrupole
collimator collimatorbeam
60 m
181602-2long cylindrical structure with a 15 (35) cm inner (outer)
radius. It was assembled by layering planes of flexible
fused-silica fibers between elliptical copper plates so as to
withstand a 100 Mrad radiation dose. The fibers directed
Cherenkov light to air light guides, each of which termi-
nated into a shielded photomultiplier tube (PMT). The
regions I, II, and III in Fig. 2 were covered by 30, 20, and
10 PMTs, respectively, providing radial and azimuthal
segmentation.
The small contribution of neutral particles, such as
photons and neutrons, to the calorimeter response was
measured in calibration runs. The asymmetry from pions
was measured by using ten quartz bars arranged in
azimuthal symmetry behind the Møller detector and
lead shielding. Eight ionization chambers arranged in
45 azimuthal sections intercepted charged particles
with lab  1 mr. This ‘‘luminosity’’ detector monitored
target density fluctuations and provided a check of the
null asymmetry expected at such small scattering angles.
The data sample, constituting a total flux of just over
1020 electrons on target, was collected at beam energies of
45.0 and 48.3 GeV. Because of g 2 precession as the
beam traversed a 24:5 bend after acceleration, the two
beam energies corresponded to opposite orientations of
longitudinal beam polarization in ESA. Roughly equal
statistics were thus accumulated with opposite signs for
the measured asymmetry, which suppressed many sys-
tematic effects. In addition, the state of a half-wave plate
in the laser line was toggled every other day, passively
reversing the sign of the electron beam polarization. This
guarded against helicity-correlated electronics cross talk.
For each beam pulse at 120 Hz, a distributed data
acquisition (DAQ) system was triggered to collect data
from the polarized source electronics and the digitized
integrated response of the detectors and beam monitors
with negligibly small electronic dead time. Alternate
DAQ triggers fell into two 60 Hz fixed-phase ‘‘time
slots.’’ Within these time slots, right-left pulse pairs
were formed for independent asymmetry analyses.
Loose requirements were imposed on beam quality and
beam monitor linearity. However, no helicity-dependent
cuts were applied, other than the demand that the beam
intensity asymmetry measured by two independent
monitors agreed to within 103 for each pulse pair. In
total, 8:6 107 pulse pairs satisfied all selection criteria.
The right-left asymmetry in the integrated detector re-
sponse for each pulse pair was computed and then cor-
rected for fluctuations in the beam trajectory.
To first order, six correlated beam parameters described
the trajectory of a beam pulse: intensity, energy, anddetectors
s
Mollers
ep's
0.7 m
FIG. 1 (color online). Schematic plan
view of the experimental configuration
in SLAC End Station A.
181602-2
TABLE I. Corrections  Ai and dilutions fi to Araw and asso-
ciated systematic uncertainties.
Source  A (ppb) f
Beam (first order) 41 3
Beam (higher order) 0 10
Transverse polarization 8 3
e  p! e  p 8 2 0:064 0:007
e  p! e  X 26 6 0:011 0:003
High energy photons 3 3 0:004 0:002
Synchrotron photons 0 5 0:002 0:001
Neutrons 5 3 0:003 0:001
Pions 1 1 0:001 0:001
FIG. 2. The charged particle radial profile at the calorimeter.
The points are the data scan, and the open histogram is the
Monte Carlo simulation. Møller (shaded) and ep (hatched)
contributions are also shown. Region I and III PMTs were
used to measure Møller and ep asymmetries, respectively.
P H Y S I C A L R E V I E W L E T T E R S week ending7 MAY 2004VOLUME 92, NUMBER 18horizontal and vertical position and angle. Each beam
parameter was measured by two independent monitors,
such that device resolution and systematic effects could be
studied.
Two methods were used to calibrate the detector sensi-
tivity to each beam parameter and thus remove beam-
induced random and systematic effects from the raw
asymmetry. One method used a calibration subset of the
pulses, where each beam parameter was modulated peri-
odically around its average value by an amount large
compared to nominal beam fluctuations with an 4%
duty cycle. The other method applied an unbinned least
squares linear regression to the pulses used for physics
analysis. They yielded statistically consistent results to
within 12 ppb. Final results were obtained with the latter,
statistically more powerful technique.
The integrated responses of region I PMTs (see Fig. 2)
were averaged to form the raw asymmetry Araw. Near-
perfect azimuthal symmetry reduced the sensitivity to
beam fluctuations and right-left asymmetries. The Araw
pulse-pair distribution had an rms of  200 ppm. The
cumulative beam asymmetry correction was 41
3 ppb. A correction due to an azimuthal modulation of
Araw [14] from a small nonzero transverse beam polar-
ization component was found to be 8 3 ppb.
Additional bias to Araw may arise from asymmetries in
unmeasured beam quantities, such as higher order mo-
ments of beam distributions. Region II PMT channels
were significantly more sensitive to such fluctuations
and helped to limit possible bias in Araw to 10 ppb.
Likewise, the luminosity detector was very sensitive to
higher order effects, where the cumulative raw right-left
asymmetry was 16 15stat ppb. This is consistent
with the theoretical expectation, providing additional
confirmation that higher order effects are under control.
A separate study limited the bias due to beam spot-size
fluctuations on Araw to 1 ppb, using data from a retractable181602-3wire array that was inserted into the beam during some of
the data collection.
The physics asymmetry Aphys was formed from Araw by
correcting for background contributions, detector linear-
ity, and beam polarization:
Aphys  1Pb
Araw 
P
i
 Ai
1P
i
fi
:
 Ai and dilutions fi for various background sources are
listed in Table I. The largest correction of 26 6 ppb
was due to electrons from inelastic electron- and photon-
proton interactions. The measured asymmetry in
region III PMTs was used as input, along with reasonable
assumptions for the kinematic extrapolation to region I.
The electron beam polarization was Pb  0:85 0:05,
measured every other day by a dedicated polarimeter
using Møller scattering of beam electrons off a magne-
tized foil placed just upstream of the hydrogen target. The
linearity of the calorimeter response was determined to
be   0:99 0:01.
Figure 3 shows Aphys for all data, divided into 24
sequential samples. Each Aphys measurement has sign
reversals depending on the beam energy and the state of
the half-wave plate. APV is obtained by correcting each
result by the appropriate sign. The combined result is
APV  175 30stat  20syst ppb;
establishing parity nonconservation in Møller scattering
at the 5	 level. APV is proportional to the product of the
electron’s vector and axial-vector neutral current cou-
plings, parametrized as the weak charge QeW :
APV  GFQ
2

2
p

1 y
1 y4  1 y4F bQ
e
W 
AQ2; yQeW;
where GF and  are the Fermi and fine structure con-
stants, respectively [15], and F b  1:01 0:01 ac-
counted for kinematically weighted hard initial and
final state radiation effects [16]. The effective analyzing
power A  3:28 0:06 ppm was determined from a181602-3
Data sample
0 5 10 15 20
 
(p
pb
)
ph
ys
A
-1000
-800
-600
-400
-200
0
200
400
600
800
 
(p
pb
)
ph
ys
A
45/IN
45/OUT
48/IN
48/OUT
 30 ppb± = -175 PVA
/df = 12.5/232χ
FIG. 3. Aphys for each of 24 data samples. Data collected with
half-wave plate inserted (removed) at a beam energy of 45 (48)
GeVare shown as solid (open) circles (triangles). The solid line
represents the grand average, with the expected modulation of
the asymmetry sign for each beam energy and half-wave plate
state. Only statistical uncertainties are shown.
P H Y S I C A L R E V I E W L E T T E R S week ending7 MAY 2004VOLUME 92, NUMBER 18Monte Carlo simulation that accounted for energy losses
in the target and systematic uncertainties in the spec-
trometer setup. The average values of the kinematic
variables were Q2  0:026GeV=c2 and y 
 Q2=s ’
0:6, where s is the square of the center-of-mass energy.
We find QeW  0:053 0:009stat  0:006syst,
consistent with the standard model expectation [7,15] of
0:046 0:003. As an example of the sensitivity of the
measurement, the result can be used to limit the scale "LL
of a new left-handed contact interaction characterized by
a term in the Lagrangian [17,18] L  4=2"2LL  $eLeL. At 95% C.L. a tree-level calculation yields
"LL  7:2 TeV and "LL  5:1 TeV, for potential posi-
tive and negative deviations, respectively.
In the context of the standard model, we find
sin2WMZMS  0:2293 0:0024stat  0:0016syst
 0:0006theory:
The last error comes from the Q2 evolution to the Z pole.
The reported APV result is the most precise measure-
ment of any asymmetry in electron scattering. The con-
sistency of the result with the theoretical prediction
provides significant new limits on TeV scale physics,
comparable in sensitivity and complementary to other
WNC measurements at low Q2 [19]. Data from the first
of three E158 run periods were used; the measurement
accuracy is expected to improve by more than a factor of
2 when analysis of all the data is complete. The experi-
mental techniques described in this Letter demonstrate
the feasibility of measuring asymmetries with accuracies
better than 10 ppb, applicable to new experiments under
development [4].
We thank the SLAC staff for their efforts in helping
develop and operate the E158 apparatus, and especially181602-4A. Brachmann and T. Maruyama for their essential work
on the polarized electron source. This work was sup-
ported by Department of Energy Contract No. DE-
AC03-76SF00515, and by the Division of Nuclear
Physics at the Department of Energy and the Nuclear
Physics Division of the National Science Foundation in
the United States and the Commissariat a` l’E´ nergie
Atomique and the Centre National de la Recherche
Scientifique in France.*Present address: Helsinki Institute of Physics, Finland.
†Deceased.
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Observation of Parity Nonconservation in Møller Scattering

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Observation of Parity Nonconservation in Møller Scattering

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