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The hybrid gauge transformation and its nontrivial phenomenologicalimplications are investigated using the noncommutative gauge theory with theSeiberg-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, thehybrid gauge transformation in the lepton sector is naturally introducedthrough the requirement of gauge invariance of the seesaw neutrino mass term.It is shown that in the NCSM without hybrid gauge transformation thenoncommutative correction to the scattering amplitude of the $e^+e^- \to\mu^+\mu^-$ process appears only as a phase factor, predicting no new physicaldeviation in the cross section. However, when the hybrid feature is considered,the noncommutative effect appears in the single channel process. The crosssection and angular distribution are analyzed in the laboratory frame includingEarth's rotation. It is proposed that pair production of muons in the upcomingTeV International Linear Collider (ILC) can provide an ideal opportunity forexploring not only the NC space-time, but also the mathematical structure ofthe corresponding gauge theory.

TeV Scale Phenomenology of $e^+e^- \to\mu^+ \mu^-$ Scattering in the Noncommutative Standard Model with Hybrid Gauge Transformation