Accessing weak neutral-current coupling $C_{3q}$ using positron and electron beams at Jefferson Lab

Electroweak neutral-current couplings are important parameters of the Standard Model of particle physics. The product of lepton and quark couplings, $C_{1q}$, $C_{2q}$ and $C_{3q}$, or $g_{AV}^{eq}$, $g_{VA}^{eq}$ and $g_{AA}^{eq}$, can be accessed in lepton scattering off a nucleon or nuclear target. Recent parity violation electron scattering experiments at Jefferson Lab have improved the precision of the $C_{1q,2q}$ couplings. On the other hand, the $C_{3q}$ couplings can only be measured by comparing scattering cross sections between a lepton and an anti-lepton beam, and have been measured only once at CERN. In this talk, we present the definitions and current knowledge of the $C_{1q,2q,3q}$ and how to access them in charged lepton scattering. We found the DIS cross section asymmetry between an electron and a positron beam scattering off an isoscalar target arise purely from $C_{3q}$. We present at the end exploratory calculations for possible measurements of $C_{3q}$ using the planned SoLID spectrometer and a positron beam at Jefferson Lab.