Neutral weak currents in pion electroproduction on the nucleon

Parity violating asymmetry in inclusive ${\pi }^0$ or ${\pi }^{+}$ meson production by longitudinally polarized electrons on unpolarized protons, is calculated as a function of the momentum transfer square $k^2$ and the total energy W of the $\pi N$ system. We consider the Δ contribution in the s channel, the standard Born contributions and the vector mesons (ρ and ω) exchanges in the t channel. The parity-odd term is the sum of two contributions. The main term (found to be linear in $k^2)$ comes from the isovector component of the electromagnetic currents. It is model independent and can be calculated exactly in terms of fundamental constants. The second term is isoscalar in nature. Near threshold and in the Δ region, it is found to be much smaller (in absolute value) than the isovector one.