  Low-energy neutral-current couplings arising in the Standard Model of
electroweak interactions can be constrained in lepton scattering off hydrogen
or a nuclear fixed target. Recent polarized electron scattering experiments at
Jefferson Lab (JLab) have improved the precision in the parity-violating types
of effective couplings. On the other hand, the only known way to access the
parity-conserving counterparts is to compare scattering cross sections between
a lepton and an anti-lepton beam. We review the current knowledge of both types
of couplings and how to constrain them. We also present exploratory
calculations for a possible measurement of $g_{AA}^{eq}$ using the planned
SoLID spectrometer combined with a possible positron beam at JLab.
