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Accessing weak neutral-current coupling $g_{AA}^{eq}$ using positron and electron beams at Jefferson Lab

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.