Simulations of the Sterile Neutrino Oscillations with a Crossing-Width Term

In this paper, we present an algorithm to generate the collider events of the GeV-scale oscillating sterile neutrinos with the ready-made event generation tools in the case that the crossing-widths among the nearly-degenerate fermionic fields arise. We prove the validity of our algorithm, and adopt some tricks for practical calculations. The formulations of the particle oscillation processes are also improved in the framework of the quantum field theory, offering us the ability to simulate the flying distances of the oscillating intermediate sterile neutrinos while regarding them as the internal lines in the Feynmann diagrams.