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Results and Physics Plots

This plot shows simulation results for the expected radial distribution of scattered electrons at the MLLER Detector.  There are contributions from both electron-electron (ee)  scattering and electron-proton  (ep) scattering.  The E158 spectrometer focuses the ee Mller 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 MLLER Detector region, which needs to be determined and corrected for.

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.


The Asymmetry (in parts per billion, ppb) observed in the MLLER 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 Mller 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 MLLER 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.


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 the value expected if there were no running!


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.)

Last Update: 27 Apr 2005