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arXiv:1005.4817 · Modern Physics Letters A

DEVIATION FROM THE EXPONENTIAL DECAY LAW IN RELATIVISTIC QUANTUM FIELD THEORY: THE EXAMPLE OF STRONGLY DECAYING PARTICLES

Francesco Giacosa, Giuseppe Pagliara

Published Sep 5, 2011• 35 citations
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Abstract

We show that a short-time regime, in which a deviation from the exponential decay law occurs, exists also in the framework of a superrenormalizable relativistic quantum field theory. This, in turn, implies the possibility of a quantum Zeno effect also for elementary decays. The attention is then focused on the typical order of magnitude of strong decay rates of mesons: for these particles, strong deviations from the exponential decay law are present during a period of time comparable with their mean lifetime. As a concrete example, the case of the ρ meson is studied.

DOI
10.1142/s021773231103670x

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We show that a short-time regime, in which a deviation from the exponential decay law occurs, exists also in the framework of a superrenormalizable relativistic quantum field theory. This, in turn, implies the possibility of a quantum Zeno effect also for elementary decays. The attention is then focused on the typical order of magnitude of strong decay rates of mesons: for these particles, strong deviations from the exponential decay law are present during a period of time comparable with their mean lifetime. As a concrete example, the case of the ρ meson is studied.
The quantum Zeno effect--suppression of decay by frequent measurements--was believed to occur only when the response of the detector is so quick that the initial tiny deviation from the exponential decay law is detectable. However, we show that it can occur even for exactly exponentially decaying systems, for which this condition is never satisfied, by considering a realistic case where the detector has a finite energy band of detection. The conventional theories correspond to the limit of an infinite bandwidth. This implies that the Zeno effect occurs more widely than expected thus far.
After reviewing the description of an unstable state in the framework of nonrelativistic Quantum Mechanics (QM) and relativistic Quantum Field Theory (QFT), we consider the effect of pulsed, ideal measurements repeated at equal time intervals on the lifetime of an unstable system. In particular, we investigate the case in which the ‘bare’ survival probability is an exact exponential (a very good approximation in both QM and QFT), but the measurement apparatus can detect the decay products only in a certain energy range. We show that the Quantum Zeno Effect can occur in this framework as well.
The short-time behavior of an unstable particle is examined in a realistic field theoretical model. The onset of linear decreasing of the nondecay probability is shown to be extremely rapid, so rapid as to exclude any relevance of regimes quadratic in time (``Zeno'' quantum paradox). The result applies to super-renormalizable, renormalizable, and nonrenormalizable cases, particularly to the proton decay problem. We discuss also the deviations from the exponential decay law in small-Q-value decays.
After reviewing the description of an unstable state in the framework of nonrelativistic Quantum Mechanics (QM) and relativistic Quantum Field Theory (QFT), we consider the effect of pulsed, ideal measurements repeated at equal time intervals on the lifetime of an unstable system. In particular, we investigate the case in which the ‘bare’ survival probability is an exact exponential (a very good approximation in both QM and QFT), but the measurement apparatus can detect the decay products only in a certain energy range. We show that the Quantum Zeno Effect can occur in this framework as well.
After reviewing the description of an unstable state in the framework of nonrelativistic Quantum Mechanics (QM) and relativistic Quantum Field Theory (QFT), we consider the effect of pulsed, ideal measurements repeated at equal time intervals on the lifetime of an unstable system. In particular, we investigate the case in which the `bare' survival probability is an exact exponential (a very good approximation in both QM and QFT), but the measurement apparatus can detect the decay products only in a certain energy range. We show that the Quantum Zeno Effect can occur in this framework as well.
The time evolution of quantum states for unstable particles can be conveniently divided into three domains: the very short time where Zeno's paradox is relevant, the intermediate interval where the exponential decay holds more or less, and the very long time where the decay is governed by a power law. In this work, we reexamine several questions relating to the deviations from the simple exponential decay law. On the basis of general considerations, we demonstrate that deviations from exponential decay near t=0t=0t=0 are inevitable. We formulate general resonance models for the decay. From analytic solutions to specific narrow-width models, we estimate the time parameters T1{T}_{1}T1​ and T2{T}_{2}T2​ separating the three domains. The parameter T1{T}_{1}T1​ is found to be much much less than the lifetime ${\ensuremath{\Gamma}}^{\ensuremath{-}1}$, while T2{T}_{2}T2​ is much greater than the lifetime. For instance, for the charged pion decay, ${T}_{1}\ensuremath{\sim}\frac{{10}^{\ensuremath{-}14}}{\ensuremath{\Gamma}}$ and ${T}_{2}\ensuremath{\sim}\frac{190}{\ensuremath{\Gamma}}$. A resolution of Zeno's paradox provided by the present consideration and its limitaions are discussed.