Time dilation in the oscillating decay laws of moving two-mass unstable quantum states

Abstract

The decay of a moving system is studied in case the system is initially prepared in a superposition of two, approximately orthogonal, unstable quantum states. The survival probability is evaluated over short and long times in the reference frame where the unstable system moves with constant linear momentum p. The mass distribution densities, which describe the two unstable states of the superposition, exhibit thresholds near the non-vanishing lower bounds and of the mass spectra. If these lower bounds coincide, the long-time survival probability shows a dominant inverse-power-law decay and is approximately related to the survival probability at rest via a time dilation. The scaling factor reads . If the lower bounds and differ, damped oscillations of the survival probability appear over long times and the scaling relation is lost. These oscillations are enveloped in an inverse-power-low profile which is determined by the thresholds. By changing reference frame, the period T0 of the oscillations at rest transforms in the longer period Tp according to a factor which is the weighted mean of the factors and , with non-normalized weights and . The oscillations tend to vanish in the ultrarelativistic limit.