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Results and Physics Plots
This plot shows simulation results for the expected radial distribution
of scattered electrons at the MØLLER Detector.
There are contributions from both electron-electron (ee)
scattering and electron-proton (ep) scattering. The E158
spectrometer focuses the ee Møller signal onto
regions I and II of the Detector, while the ep (Mott) electrons are at
larger radii and are studied with the ep Detector. The Mott
electrons do give a small background of ~7% in the MØLLER
Detector region, which needs to be determined and
corrected for. |
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Quartz scanners, readout by phototubes, were used to check the
simulation model of the E158 spectrometer. Here we show the
observed data in black, together with simulation results in green.
The agreement is very good and allows us to estimate with confidence the
background corrections and to determine the uncertainty in the
correction.
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The Asymmetry (in parts per billion, ppb) observed in the MØLLER
Detector is shown as a function of data sample; the length of each data
sample was ~2 days in Runs I and II and ~1 day in Run III. The
sign of the Asymmetry should be opposite for the two different beam
energies studied (45 and 48 GeV) and also for the two states (IN or OUT)
of a halfwave plate in the laser system for the Polarized Electron
Source. A pink line is shown to guide the eye for the expected
asymmetry, while the points with error bars indicate the data. The
data are well behaved statistically and give the result, APV
= (-131 ± 14) ppb. The Møller Asymmetry,
APV, is defined as
where SR and SL are
the scattering rates for incident right- and left-polarized electron
beams. Every 16 milli-seconds, the experiment records data for 1
right-polarized and 1 left-polarized electron beam pulse
and forms a pulse-pair asymmetry, APVi for the ith
pulse-pair. Each beam pulse has ~500 billion beam
electrons; ~20 million of these scatter from an electron in the
liquid hydrogen target and hit the MÖLLER
Detector. Each pulse pair measures APVi
to a precision of 200 parts per million. The entire
experiment consists of analyzing ~300 million pulse pairs over a period
of 4 months in 2002 and 2003 to reach the final precision of 14 parts
per billion.
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The E158 APV result determines the weak mixing angle
parameter, sin2qWeff,
at low momentum transfer, Q. The result is shown here, together
with results from other experiments and a
theoretical prediction (black
curve) from Czarnecki and Marciano. The gray region about the
black theory curve represents the theoretical uncertainty in the
"running" (evolution) of the weak mixing angle from the Z0
mass energy scale of the SLD and LEP experiments to low energy.
This plot summarizes the primary physics result for the E158 experiment.
E158 measures the weak mixing angle parameter to be 4% greater than
the result at high energy obtained from SLD and LEP, demonstrating the
"running" of the weak mixing angle with a significance of 6.2 standard
deviations. The result is consistent with the Standard Model
(SM)
Prediction. In addition to the results from SLAC E158 and the SLD
and LEP experiments, we also plot low energy results from an Atomic
Parity Violation (APV) experiment using Cesium,
QW(Cs), and a neutrino-nucleon
scattering experiment,
NuTeV. The APV experiment was carried out
by a group at Boulder, Colorado and the NuTeV experiment was performed
at Fermilab. The APV result is from data taken in the 1990s, and
as recently as 2000 indicated a discrepancy of 2.5
standard deviations
with the Standard Model predictions. Since 2000,
improved atomic theory calculations indicate the discrepancy to be
within 1 standard deviation of the SM prediction. The NuTeV
result, however, disagrees with the SM prediction by 3 standard
deviations. Studies are ongoing to check for contributions and
uncertainties from conventional effects -- strong and electroweak
radiative corrections, isospin symmetry violation or an asymmetric
strange sea. A distinct advantage for the E158 experiment is that
the theoretical prediction is quite precise because of the simple
electron-electron scattering process.
The electron's weak charge is approximately
given by QW(e) = -(1-4sin2qWeff).
E158 finds QW(e) = -0.041
± 0.006,
approximately ½ the value expected if there were no
running!
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The low energy weak mixing angle results can be evolved
to a common energy scale at the Z0 mass (using the Standard
Model) for direct comparison. The result from E158 is the most
precise low energy determination of the weak mixing angle and of the
electron's weak charge. (The PDG2002 result shown is the
Particle Data Group's
compilation of the results from the SLD and LEP experiments.)
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