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The seventh international conference on hadron spectroscopy

Neutron lifetime disparity as a state-dependent quantum effect

Neris I. Sombillo, Denny Lane B. Sombillo

Published Dec 23, 2025• 0 citations
Publisher

Abstract

There is an ongoing tension between two neutron lifetime measurements. The so-called beam method gives a neutron lifetime of 888 seconds, while the trap (or bottle) method reports a shorter lifetime of 879 seconds. This discrepancy has sparked debates across experimental and theoretical fronts. While the intriguing possibility of a dark decay mode was initially considered, it was promptly ruled out by experimental evidence, leaving the discussion unresolved. In our work, we explore a novel approach to addressing the neutron lifetime anomaly using the quantum time operator formalism. We introduce a time operator that projects the initial system into a state evolving unitarily into a singular Dirac delta-like function, enabling localized interactions or decay. Our analysis reveals that for low-energy systems, the expectation value of this operator deviates from the classical time value due to quantum corrections. Interestingly, these corrections vanish in the classical regime of small de Broglie wavelengths. Moreover, we found that the quantum corrections are sensitive to the initial state preparation, offering a potential explanation for the observed discrepancy between the two measurement methods.

DOI
10.22323/1.500.0258

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There is an ongoing tension between two neutron lifetime measurements. The so-called beam method gives a neutron lifetime of 888 seconds, while the trap (or bottle) method reports a shorter lifetime of 879 seconds. This discrepancy has sparked debates across experimental and theoretical fronts. While the intriguing possibility of a dark decay mode was initially considered, it was promptly ruled out by experimental evidence, leaving the discussion unresolved. In our work, we explore a novel approach to addressing the neutron lifetime anomaly using the quantum time operator formalism. We introduce a time operator that projects the initial system into a state evolving unitarily into a singular Dirac delta-like function, enabling localized interactions or decay. Our analysis reveals that for low-energy systems, the expectation value of this operator deviates from the classical time value due to quantum corrections. Interestingly, these corrections vanish in the classical regime of small de Broglie wavelengths. Moreover, we found that the quantum corrections are sensitive to the initial state preparation, offering a potential explanation for the observed discrepancy between the two measurement methods.
The lifetime of the neutron, although being a fundamental quantity in particle physics, is to date still associated with a puzzle: different techniques of measurements find values of the lifetime which are mutually incompatible. While methods based on beams of neutrons find a (average) value τnbeam=888.1±2.0\tau_{n}^{\text{beam}} =888.1\pm2.0τnbeam​=888.1±2.0 s, methods based on traps obtain a shorter lifetime τntrap=879.37±0.58\tau_{n} ^{\text{trap}}=879.37\pm0.58τntrap​=879.37±0.58 s, i.e. a ∼4σ\sim 4\sigma∼4σ mismatch. This is the so-called neutron decay anomaly. We propose here a novel interpretation of this puzzle based solely on quantum mechanics (no need of physics beyond the standard model): if the measurement apparatus and the surrounding environment are able to observe the unstable system at very short (but not too short) times after the preparation of it, the so called inverse quantum Zeno (IZE) effect can take place: the IZE corresponds an increase of the decay rate through the interaction of the system with the environment. We argue that such a quantum phenomenon can be realized in the case of trap experiments but not in the case of beam experiments. There are mainly two reasons behind our interpretation of the neutron decay anomaly: (i) the intrinsic dependence of the 3-body weak decay rate on the Q value of the decay (the Sargent rule); (ii) the very peculiar setup of neutron traps, in which up to ∼108\sim 10^{8}∼108 ultra cold neutrons are confined together. This feature can help to increase the frequency of dephasing of the wave function (equivalent to the `collapse'), necessary to obtain the inverse quantum Zeno effect.
Quantum mechanics predicts that the decay rate of unstable systems could be effectively modified by the process of the measurement of the survival probability. Depending on the intrinsic properties of the unstable system and the experimental setup for the observation, one could obtain the so called (direct) quantum Zeno and inverse quantum Zeno effects corresponding to a slowing down or a speeding up of the decay, respectively. We argue that the inverse quantum Zeno effect is in principle detectable at a percent level for the neutron decay in experiments with trapped ultracold neutrons. Conversely, this effect is basically undetectable in experiments in which the neutron lifetime is measured by measuring the decays of beams of neutrons. As a test of our claim, we propose a simple qualitative correlation between the number of neutrons in the trap and the neutron lifetime: the larger the number, the faster the decay. Finally we discuss also the presently available measurements of the neutron lifetime and address the issue of the possible discrepancy that has been reported among the results obtained by the different experimental techniques.
Beam and trap methods find incompatible results for the lifetime of the neutron: the former delivers a value which is about 8.7±2.18.7\pm2.18.7±2.1 s longer than the latter. Very recently (1906.10024) it has been proposed that the inverse Zeno effect (IZE) could be responsible for the shorter lifetime in trap experiments. Here, we compare two different models of measurement, one obtained by bang-bang measurements and by a continuous measurement: the IZE turns out to be in both cases very similar, showing that the results do not depend on the details of the measurement process.
We discuss a simple and analytically solvable measurement model which describes the famous Quantum Zeno Effect (QZE) and Inverse Zeno Effect (IZE), that correspond to the slow down and to the increase of the decay rate caused by measurements (or, more in general, by the interaction of an unstable state with the detector and the environment). Within this model one can understand quite general features of the QZE and IZE: by considering an unstable quantum state, such as an unstable particle, whose decay width as function of energy is Γ(ω)=g2ωα,Γ(ω)=g^{2}ω^α,Γ(ω)=g2ωα, then -- under quite general assumptions -- the QZE occurs for α∈(0,1)α\in(0,1)α∈(0,1), while the IZE for α∈(−∞,0)∪(1,∞).α\in(-\infty,0)\cup(1,\infty).α∈(−∞,0)∪(1,∞). This result is valid also for more realistic measurement models than the one described in this work. We then apply these considerations to the decay of the neutron, for which α=5.α=5.α=5. Hence, the realization of the IZE for the neutron decay (and for the majority of weak decays) is in principle possible. Indeed, trap experiments find a lifetime that is 8.7±2.18.7\pm2.18.7±2.1 s shorter than beam experiments, suggesting that the IZE could have taken place.
Neutron time-of-flight interferometry assumes the validity of the classical time-of-flight expression in the interpretation of time-of-flight data and simultaneously assumes that the incident neutrons are de Broglie wave packets obeying the laws of quantum mechanics. A quantum-mechanical treatment of time of flight as an expected value of an appropriate time-of-arrival operator for a given initial wave-packet state shows that the size of the initial wave packet introduces measurable quantum corrections to the expected classical time of flight. Our results provide concrete testable predictions that may clarify the status of time as a quantum-dynamical observable.
Although time measurements are routinely performed in laboratories, their theoretical description is still an open problem. Correspondingly, the status of the energy-time uncertainty relation is unsettled. In the first part of this work the necessity of positive operator valued measures (POVM) as descriptions of every quantum experiment is reviewed, as well as the suggestive role played by the probability current in time measurements. Furthermore, it is shown that no POVM exists, which approximately agrees with the probability current on a very natural set of wave functions; nevertheless, the choice of the set is crucial, and on more restrictive sets the probability current does provide a good arrival time prediction. Some ideas to experimentally detect quantum effects in time measurements are discussed. In the second part of the work the energy-time uncertainty relation is considered, in particular for a model of alpha decay for which the variance of the energy can be calculated explicitly, and the variance of time can be estimated. This estimate is tight for systems with long lifetimes, in which case the uncertainty relation is shown to be satisfied. Also the linewidth-lifetime relation is shown to hold, but contrary to the common expectation, it is found that the two relations behave independently, and therefore it is not possible to interpret one as a consequence of the other. To perform the mentioned analysis quantitative scattering estimates are necessary. To this end, bounds of the form ∥1Re−iHtψ∥22≤Ct−3\|1_Re^{-iHt}ψ\|_2^2 \leq C t^{-3}∥1R​e−iHtψ∥22​≤Ct−3 have been derived, where ψψψ denotes the initial state, HHH the Hamiltonian, RRR a positive constant, and CCC is explicitly known. As intermediate step, bounds on the derivatives of the SSS-matrix in the form $\|1_K S^{(n)}\|_\infty \leq C_{n,K} $ have been established, with n=1,2,3n=1,2,3n=1,2,3, and the constants Cn,KC_{n,K}Cn,K​ explicitly known.