Quantum decay in renormalizable field theories: Quasiparticle formation, Zeno and anti-Zeno effects

In a renormalizable theory the survival probability of an unstable quantum state features divergences as a consequence of the rapid growth of the density of states with energy. Introducing a high energy cutoff $\Lambda$, the transient dynamics during a time scale $\simeq 1∕\Lambda$ describes the renormalization of the bare into a "quasiparticle" state which decays on longer time scales. During this early transient the decay law features Zeno behavior $e^{-{(t∕t_Z)}^2}$ with the Zeno time-scale $t_Z\propto 1∕{\Lambda }^{3∕2}$. We introduce a dynamical renormalization framework that allows to separate consistently the dynamics of formation of the quasiparticle state and its decay on longer time scales by introducing a renormalization time scale along with alternative "schemes". The survival probability obeys a renormalization group equation with respect to this scale. We find a transient suppression of the decay law for large Lorentz factor as a consequence of the narrowing of the phase space for decay different from the usual time dilation. In the presence of higher mass thresholds, the energy uncertainty associated with transient dynamics leads to an anti Zeno enhancement with a transient acceleration of the decay into heavier particles. There remains memory of the transient effects in the survival probability even at long time. We discuss possible consequences of these effects in cosmology.