  In this work, we investigate numerical evolution of massive Kaluza-Klein (KK)
modes of a Dirac field on a thick brane. We deduce the Dirac equation in
five-dimensional spacetime, and obtain the time-dependent evolution equation
and Schr\"odinger-like equation of the extra-dimensional component. We use the
Dirac KK resonances as the initial data and study the corresponding dynamics.
By monitoring the decay law of the left- and right-chiral KK resonances, we
compute the corresponding lifetimes and find that there could exist long-lived
KK modes on the brane. Especially, for the lightest KK resonance with a large
coupling parameter and a large three momentum, it will have an extremely long
lifetime.
