The MOLLER Experiment Physics:

The MOLLER experiment will measure the parity violating asymmetry in the number of polarized electrons scattered off unpolarized electrons in a liquid hydrogen target:

A_{msr} = \frac{\sigma_R - \sigma_L}{\sigma_R + \sigma_L}.

Where \sigma_R ( \sigma_L ) is the scattering cross-section using incident right (left) handed electrons. A non-zero asymmetry constitutes parity nonconservation, dominated at Q^2 \ll M^2_Z by the interference between the weak and electromagnetic amplitudes.

The leading order Feynman diagrams relevant for Møller scattering, involving both direct and exchange diagrams that interfere with each other, are

Attach:LeadingDiagrams.png Δ

The total unpolarized cross section, dominated by photon exchange, is given by

{d\sigma\over d\Omega} = {\alpha^2\over 2mE}{(3+\cos^2\theta)^2\over\sin^4\theta} = {\alpha^2\over 4mE}{\frac{1+y^4+(1-y)^4}{y^2(1-y)^2}}

The parity-violating asymmetry A_{PV} , due to the interference between the photon and Z_0 boson exchange diagrams above is given by

A_{PV} = mE{G_F\over\sqrt{2}\pi\alpha}{4\sin^2\theta\over(3+\cos^2\theta)^2}Q^e_W = mE{G_F\over\sqrt{2}\pi\alpha}\frac{2y(1-y)}{1+y^4+(1-y)^4}Q^e_W.

Where Q^e_W = 1 - 4\sin^2\theta_W .