A Precision Measurement of the Weak Mixing Angle in Moller Scattering at Low Q^2

Abstract

The electroweak theory has been probed to a high level of precision at the mass scale of the Z{sup 0} through the joint contributions of LEP at CERN and the SLC at SLAC. The E158 experiment at SLAC complements these results by measuring the weak mixing angle at a Q{sup 2} of 0.026 (GeV/c){sup 2}, far below the weak scale. The experiment utilizes a 48 GeV longitudinally polarized electron beam on unpolarized atomic electrons in a target of liquid hydrogen to measure the parity-violating asymmetry A{sup PV} in Moeller scattering. The tree-level prediction for A{sup PV} is proportional to 1-4 sin{sup 2} {theta}{sub W}. Since sin{sup 2} {theta}{sub W} {approx} 0.25, the effect of radiative corrections is enhanced, allowing the E158 experiment to probe for physics effects beyond the Standard Model at the TeV scale. This work presents the results from the first two physics runs of the experiment, covering data collected in the year 2002. The parity-violating asymmetry A{sup PV} was measured to be A{sup PV} = -158 ppb {+-} 21 ppb (stat) {+-} 17 ppb (sys). The result represents the first demonstration of parity violation in Moeller scattering. The observed value of A{sup PV} corresponds to a measurement of the weak mixing angle of sin{sup 2} {theta}{sub W}{sup eff} = 0.2380 {+-} 0.0016(stat) {+-} 0.0013(sys), which is in good agreement with the theoretical prediction of sin{sup 2} {theta}{sub W}{sup eff} = 0.2385 {+-} 0.0006 (theory).