# Energy of unstable states at long times - High Energy Physics - Phenomenology

Abstract: An effect generated by the nonexponential behavior of the survival amplitudeof an unstable state in the long time region is considered. In 1957 Khalfinproved that this amplitude tends to zero as $t\to\infty$ more slowly than anyexponential function of $t$. For a time-dependent decay rate $\gammat$Khalfin-s result means that this $\gammat$ is not a constant for large $t$but that it tends to zero as $t\to\infty$. We find that a similar conclusioncan be drawn for the instantaneous energy of the unstable state for a largeclass of models of unstable states: This energy tends to the minimal energy ofthe system ${\cal E} {min}$ as $t\to\infty$ which is much smaller than theenergy of this state for $t$ of the order of the lifetime of the consideredstate. Analyzing the transition time region between exponential andnon-exponential form of the survival amplitude we find that the instantaneousenergy of a considered unstable state can take large values, much larger thanthe energy of this state for $t$ from the exponential time region. Taking intoaccount results obtained for a model considered, it is hypothesized that thispurely quantum mechanical effect may be responsible for the properties of broadresonances such as $\sigma$ meson as well as having astrophysical andcosmological consequences.

Author: K. Urbanowski, J. Piskorski

Source: https://arxiv.org/