  The forward-backward asymmetry is an important measurable quantity which can
enable independent determination of the neutral-current couplings of fermions.
In this paper, we extend the definition of the asymmetry from the partonic
level to the hadronic level by calculating this asymmetry of the hadron pair in
the semi-inclusive electron position annihilation process. Semi-inclusive
implies that a back-to-back jet is also measured in addition to the hadron
pair. Due to the limitation of the factorization theorem, we calculate this
process up to leading order twist-4 level by applying the collinear expansion
formalism. After obtaining the differential cross section, we calculate the
forward-backward asymmetries and show them in terms of the corresponding
di-hadron fragmentation functions. Di-hadron fragmentation functions are
introduced to describe the hadron pair productions in the fragmentation
process. With available parameterization of the functions, we present a
numerical estimation of the forward-backward asymmetry. On the flip side,
measurements of the forward-backward asymmetry would give strict restrictions
of parameterizations of the di-hadron fragmentation functions. We also present
a numerical estimation of the twist-4 di-hadron fragmentation functions in
order to illustrate their contributions.
