On Longevity of I-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 long-lived. 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.
