The Qweak Experiment: A Search for New Physics at the TeV Scale via a   Measurement of the Proton's Weak Charge
  We propose a new precision measurement of parity-violating electron scattering on the proton at very low Q^2 and forward angles to challenge predictions of the Standard Model and search for new physics. A unique opportunity exists to carry out the first precision measurement of the proton's weak charge, $Q_W =1 - 4\sin^2\theta_W$. A 2200 hour measurement of the parity violating asymmetry in elastic ep scattering at Q^2=0.03 (GeV/c)^2 employing 180 $\mu$A of 85% polarized beam on a 35 cm liquid Hydrogen target will determine the proton's weak charge with approximately 4% combined statistical and systematic errors. The Standard Model makes a firm prediction of $Q_W$, based on the running of the weak mixing angle from the Z0 pole down to low energies, corresponding to a 10 sigma effect in this experiment. 
R. D. Carlini, J.M. Finn, S. Kowalski, S. A. Page, D. S. Armstrong, A.   Asaturyan, T. Averett, J. Benesch, J. Birchall, P. ...
physics.ins-det nucl-ex