Abstract
Taking a two interacting scalar toy model with interaction term $g\ensuremath{\phi}{\ensuremath{\chi}}^{2}$, we study the production of $\ensuremath{\chi}$ particles coming from the decay of an asymptotic and highly occupied beam of $\ensuremath{\phi}$ particles. We perform a nonperturbative analysis coming from parametric resonant instabilities and investigate the possibility that massive $\ensuremath{\chi}$ particles are produced from decays of massless $\ensuremath{\phi}$ particles from the beam. Although this process is not present in a perturbative analysis, our nonperturbative approach allows it to happen under certain conditions. For a momentum $p$ of the beam particles and a mass ${m}_{\ensuremath{\chi}}$ of the produced ones, we find that the decay is allowed if the energy density of the beam exceeds the instability threshold ${p}^{2}{m}_{\ensuremath{\chi}}^{4}/(2{g}^{2})$. We also provide an analytical expression for the spontaneous decay rate at the earliest time.
Highlights
The decay of a particle into other species is one of the simplest and most relevant effects in relativistic field theories
From the theoretical point of view, the decay rate for a process φi → φj þ φk can be defined in general terms as [1]
It is easy to find that massless particles of a beam cannot decay into other massive species because the energy-momentum conservation for asymptotic states is never fulfilled.[1]
Summary
The decay of a particle into other species is one of the simplest and most relevant effects in relativistic field theories. This reasoning is valid as long as the assumption of asymptotic final states is correct or at least when it is a good approximation Following this recipe, it is easy to find that massless particles of a beam cannot decay into other massive species because the energy-momentum conservation for asymptotic states is never fulfilled.[1] More general, this recipe based on the asymptotic state assumption forbids any decay process for which the total mass of the produced particles exceeds the mass of the decaying particles. Eq (2) is meaningless and the energy-momentum conservation as well as the decay rate should be accounted in a different way This motivates us to explore the possibility that processes ( decays) forbidden by the asymptotic final state assumption are allowed. As very intense fields play an important role in this subjects, we suggest that these effects should be something to look at
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