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Abstract In this work, we investigate the 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 Schrödinger-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.
Zhu et al. (Wed,) studied this question.