We study I-balls/oscillons, which are long-lived, quasi-periodic, andspatially localized solutions in real scalar field theories. Contrary to thecase of Q-balls, there is no evident conserved charge that stabilizes thelocalized configuration. Nevertheless, in many classical numerical simulations,it has been shown that they are extremely long-lived. In this paper, we clarifythe reason for the longevity, and show how the exponential separation of timescales emerges dynamically. Those solutions are time-periodic with a typicalfrequency of a mass scale of a scalar field. This observation implies that theycan be understood by the effective theory after integrating out relativisticmodes. We find that the resulting effective theory has an approximate globalU(1) symmetry reflecting an approximate number conservation in thenon-relativistic regime. As a result, the profile of those solutions isobtained via the bounce method, just like Q-balls, as long as the breaking ofthe U(1) symmetry is small enough. We then discuss the decay processes of theI-ball/oscillon by the breaking of the U(1) symmetry, namely the production ofrelativistic modes via number violating processes. We show that the imaginarypart is exponentially suppressed, which explains the extraordinary longevity ofI-ball/oscillon. In addition, we find that there are some attractor behaviorsduring the evolution of I-ball/oscillon that further enhance the lifetime. Thevalidity of our effective theory is confirmed by classical numericalsimulations. Our formalism may also be useful to study condensates of ultralight bosonic dark matter, such as fuzzy dark matter, and axion stars, forinstance.
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