  A quantity of particular experimental interest is the forward-backward
asymmetry in the angular distribution of positively and negatively charged
fermions produced in $Z^0$ decays. Measurements of this asymmetry can enable
independent determinations of the neutral-current couplings of these fermions,
i.e. the $Z^0$ boson couplings for left- and right-handed fermions,
respectively. Due to the quark confinement, however, it is difficult to
determine the electroweak interactions of quarks, especially for light quarks.
In the hadron production electron positron annihilation process, the parton
model with factorization theorem gives a reliable approximate description.
Quantities are thus expressed in terms of fragmentation functions in the
annihilation process. In this paper, we consider the vector meson production in
the inclusive electron positron annihilation process and calculate the
forward-backward asymmetry in the hadronic level. Calculations are carried out
by applying the collinear expansion in the parton model at leading order
twist-4. We note here this process provides not only a tool for analyzing the
hadronic weak interactions but also an opportunity for understanding the parton
model of the strong interaction. In other words, the results can be used to
test the electroweak and strong interactions simultaneously.
