  The hybrid gauge transformation and its nontrivial phenomenological
implications are investigated using the noncommutative gauge theory with the
Seiberg-Witten map expanded scenario. Particularly, the $e^+e^- \to\mu^+ \mu^-$
process is studied with a generalized noncommutative standard model (NCSM)
including massive neutrinos and neutrino-photon interaction. In this model, the
hybrid gauge transformation in the lepton sector is naturally introduced
through the requirement of gauge invariance of the seesaw neutrino mass term.
It is shown that in the NCSM without hybrid gauge transformation the
noncommutative correction to the scattering amplitude of the $e^+e^- \to\mu^+
\mu^-$ process appears only as a phase factor, predicting no new physical
deviation in the cross section. However, when the hybrid feature is considered,
the noncommutative effect appears in the single channel process. The cross
section and angular distribution are analyzed in the laboratory frame including
Earth's rotation. It is proposed that pair production of muons in the upcoming
TeV International Linear Collider (ILC) can provide an ideal opportunity for
exploring not only the NC space-time, but also the mathematical structure of
the corresponding gauge theory.
