On longevity of l-ball/oscillon

We study I-balls/oscillons, which are long-lived, quasi-periodic, and spatially localized solutions in real scalar field theories. Contrary to the case of Q-balls, there is no evident conserved charge that stabilizes the localized configuration. Nevertheless, in many classical numerical simulations, it has been shown that they are extremely longlived. In this paper, we clarify the reason for the longevity, and show how the exponential separation of time scales emerges dynamically. Those solutions are time-periodic with a typical frequency of a mass scale of a scalar field. This observation implies that they can be understood by the effective theory after integrating out relativistic modes. We find that the resulting effective theory has an approximate global U(1) symmetry reflecting an approximate number conservation in the non-relativistic regime. As a result, the profile of those solutions is obtained via the bounce method, just like Q-balls, as long as the breaking of the U(1) symmetry is small enough. We then discuss the decay processes of the I-ball/oscillon by the breaking of the U(1) symmetry, namely the production of relativistic modes via number violating processes. We show that the imaginary part is exponentially suppressed, which explains the extraordinary longevity of I-ball/oscillon. In addition, we find that there are some attractor behaviors during the evolution of I-ball/oscillon that further enhance the lifetime. The validity of our effective theory is confirmed by classical numerical simulations. Our formalism may also be useful to study condensates of ultra light bosonic dark matter, such as fuzzy dark matter, and axion stars, for instance.