<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>γ</mml:mi><mml:mi>Z</mml:mi></mml:mrow></mml:math> -exchange contributions in low-energy parity-violating <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>e</mml:mi><mml:mi>p</mml:mi></mml:mrow></mml:math> scattering

In this work, the $\ensuremath{\gamma}Z$-exchange contributions in low-energy elastic parity-violating $ep$ scattering are discussed with approximation ${m}_{e}=0$. By expanding $\ensuremath{\gamma}pp$ and $Zpp$ interactions on momentum of photon considering both leading-order next-to-leading order interactions, we calculate amplitudes diagrams. After performing loop integral, expand results low energy limit, obtain analytic expressions for amplitudes. Numerical comparisons show that very close to full over a large region. We investigate power behaviors these find some enhanced by kinematic factor limit. Additionally, cases, imaginary parts from next-to-leading-order at same as those interactions. Furthermore, corresponding physical observable quantity ${A}_{\text{PV}}$ also discussed. Combining all properties together, conclude describe helicity region ${\ensuremath{\alpha}}_{e}\ensuremath{\ll}Q/{M}_{N}\ensuremath{\sim}\ensuremath{\delta}/{M}_{N}^{2}\ensuremath{\ll}1$, where ${\ensuremath{\alpha}}_{e}$ is fine structure constant, ${M}_{N}$ mass proton, $Q$ $\ensuremath{\delta}$ small quantities related transfer center-of-mass energy.