Quantum Corrections to the Decay Law in Flight

TL;DR

This paper provides analytical expressions for relativistic quantum decay probabilities, revealing how decay laws deviate from exponential behavior in flight and depend on the Lorentz factor, with implications for understanding particle decay in relativistic regimes.

Contribution

It introduces analytical formulas for survival probabilities of moving particles, detailing quantum corrections to decay laws and their dependence on relativistic effects, supported by realistic decay calculations.

Findings

Critical transition times depend on Lorentz factor γ.

Quantum corrections cause deviations from classical time dilation.

NE region size increases with particle velocity.

Abstract

The deviation of the decay law from the exponential is a well known effect of quantum mechanics. Here we analyze the relativistic survival probabilities, $S(t,p)$, where $p$ is the momentum of the decaying particle and provide analytical expressions for $S(t,p)$ in the exponential (E) as well as the nonexponential (NE) regions at small and large times. Under minimal assumptions on the spectral density function, analytical expressions for the critical times of transition from the NE to the E at small times and the E to NE at large times are derived. The dependence of the decay law on the relativistic Lorentz factor, $\gamma = 1/\sqrt{1 - v^2/c^2}$, reveals several interesting features. In the short time regime of the decay law, the critical time, $\tau_{st}$, shows a steady increase with $\gamma$, thus implying a larger NE region for particles decaying in flight. Comparing $S(t,p)$ with the well known time dilation formula, $e^{-\Gamma t/\gamma}$, in the exponential region, an expression for the critical $\gamma$ where $S(t,p)$ deviates most from $e^{-\Gamma t/\gamma}$ is presented. This is a purely quantum correction. Under particular conditions on the resonance parameters, there also exists a critical $\gamma$ at large times which decides if the NE region shifts backward or forward in time as compared to that for a particle at rest. All the above analytical results are supported by calculations involving realistic decays of hadrons and leptons.