Exotic decay channels are not the cause of the neutron lifetime anomaly

Since long neutron lifetimes measured with a beam of cold neutrons are significantly different from lifetimes measured with ultracold neutrons bottled in a trap. It is often speculated that this"neutron anomaly"is due to an exotic dark neutron decay channel of unknown origin. We show that this explanation of the neutron anomaly can be excluded with a high level of confidence when use is made of new data on neutron decay parameters. Furthermore, data from neutron decay now compare well with Ft data derived from nuclear \b{eta} decays.


Introduction
Neutron β decay plays a key role in several fields of physics and astrophysics [1], [2], [3], [4]. On one hand, all semileptonic processes in nature, which involve both first-generation quarks and leptons, require neutron decay data for the calculation of their cross sections or rates. On the other hand, neutron data are increasingly used for sensitive searches of new physics beyond the standard model (SM). Rigorous bounds on parameters beyond the SM can be derived from low-energy processes like neutron, pion, or nuclear weak decays, and from high-energy processes like e d u e  in pp reactions at the LHC.
On the quark level, the latter reaction has the same Feynman diagram as neutron decay e d u e  . With effective field theory [5], these high-and low-energy processes can be linked and data compared with each other. In many cases the low-energy data lead to better constraints, in particular for processes beyond the SM involving left-handed (SM-)neutrinos. In contrast, high-energy data from LHC give better limits on processes involving right-handed neutrinos, see [6], [7], [8], and references therein.
Over the years the precision of neutron decay data has seen considerable progress. In the past three decades, errors of the neutron lifetime have diminished by a factor of ten, and errors of the β decay asymmetry by a factor of twenty, see the previous editions of the Particle Data Group's reviews (PDG) [9]. At the same time, these data have become more reliable: the corrections required to obtain the neutron lifetime from the raw data have dropped from hundreds of seconds to one quarter of a second, and the leading corrections to the β asymmetry diminished more than tenfold, as found in the corresponding literature.
So everything seems to proceed well, but there is a rather longstanding problem. The neutron lifetime can be measured with two different methods, and since many years, the lifetimes derived from these differ significantly [9], [10], [11], [12]. Most lifetime experiments nowadays use the decay of ultracold neutrons (UCN) stored in a trap, as pioneered by W. Mampe et al. [13]. In these "bottle" experiments, the exponential decrease of the number of stored UCN is registered. In the "beam" experiments, a beam of cold neurons is used, and the decay products emitted from a well-defined beam volume are counted. Today, the average bottle lifetime, derived from eight measurements on five different instruments, is by four standard deviations shorter than the average beam lifetime, the latter being obtained from two runs of one instrument.
It is frequently speculated that this "neutron anomaly" might be due to an exotic neutron decay into a dark fermion. Such a decay channel would be visible in the total decay rate of the bottle experiments, but not in the beam experiments. Various possible dark decay channels have been discussed in very recent papers, of which we give an incomplete list: Investigated were exotic decays that are completely dark, or with the dark fermion accompanied either by visible particles such as γ or e + e - [14], or by invisible  pairs [15] or dark photons [16]. The disappearance of neutrons via neutron mirror-neutron oscillations was proposed in [17], [18], and the role of neutron-antineutron oscillations in dark neutron decay investigated in [19]. In Ref. [20] it is pointed out that a Fierz term of size b = 1.44% would enhance the branching ratio of dark decays, allowed by existing neutron data, to the level required to explain the neutron lifetime anomaly. This in turn, however, leads to some tension with the experimental limit on b from [21]. The detection of neutron dark decays via nuclear decays was discussed in [22], [23], and detection by electro-disintegration of the deuteron in [24]. According to [25], such dark decays could also solve problems in the small-structure formation in cosmology.
However, neutron dark decays would lead to problems with observed neutron star masses [26], [27], [28]. Dark neutron decays that are accompanied by γ [29] or e + eemission [30], [31] were experimentally excluded as cause of the neutron anomaly for most of the relevant energy range. It would be desirable to verify or to exclude dark neutron decays on a more general basis. Since several years, the neutron anomaly has also reached the popular science sector, see [32], [33], and others. Due to this, the public is aware of the neutron anomaly, but not of the strong progress made in neutron decay.
In the SM, the neutron lifetime   for the decay e n pe    and its axial-vector coupling constant gA are linked to each other in a well-known way. A recent letter [34] suggested to use this link to test the hypothesis of dark neutron decay. However, the lifetime and gA were not known with sufficient precision for this purpose. Therefore, the authors made an educated guess on "favored" values for lifetime and gA that would satisfy this link and provide a bound on the branching ratio for dark neutron decays.
In the present letter we show that we can now test the hypothesis of a dark branch in neutron decay, like in Ref. [34], though slightly modified, and based not on favored values but on measured data that include all experimental results on neutron decay. This has become possible by including new results on the β decay asymmetry not yet listed in PDG-2018. In the following, we first explain the method in some detail, and then discuss the new data base and its consequences for the neutron anomaly.

The method
In the beam experiments on the neutron lifetime, cold neutrons in a beam are absorbed in a neutron detector within milliseconds after they have entered the decay volume.
In the bottle experiments, the UCN remaining in the trap decay via both channels, allowed and exotic, as with the partial decay rate and for decay into dark channels X, The above-mentioned link between   and gA is given by the so-called SM master formula [34], which allows calculating the neutron lifetime expected in the SM, 2 2 4908.6(1.9) s This result is consistent with that of Ref. [34], but the ingredients on the right-hand side of Eq. (6) -The value of λ can in principle be derived from lattice theory, but presently only with a precision of 1% [37], which is by far not sufficient for our purpose.
-Experimentally, the value of λ is derived from neutron decay correlation coefficients, which in the SM all depend only on λ. The coefficients most sensitive to λ are the β decay asymmetry A and the electron-antineutrino correlation a, because both coefficients respond to the deviation of λ from -1.
-The PDG-2018 average derived from these equations is -The three new bottle lifetimes [38], [39], [40] confirm earlier bottle measurements; the corresponding preprints are already cited in Ref. [34]. -The new electron-antineutrino value from aSPECT [41] has a four times lower error than previous a-values, but is preliminary and therefore not used here, but its inclusion would not significantly change the conclusion of our analysis.
-The new β asymmetry measurements are crucial for our discussion.

 
, with a considerably smaller error).

Consequences for the dark-decay hypothesis
Inserted into Eq. (6), our , as one would expect if the neutron anomaly was due to an exotic branch. We emphasize that the results from PERKEO III, UCNA, and UCNτ that enter Fig. 2 are derived from blinded data. This leaves not much room for a dark channel in neutron decay. Like the other publications on the neutron anomaly, we assume that the parameters entering the analysis, in particular the nuclear Ft-values whose average is used in Eq. (6) , are not affected by the exotic process in question. But even if they were, it would require some fine-tuning to shift    to beam  . In addition for most nuclei, nuclear dark decays are forbidden due to energy constraints, see [22] and [23]. To add a very unlikely possibility: should the difference between    and beam  be merely a statistical outlier of probability 6×10 -5 , then this probability is not much higher than the probability of 4×10 -5 that the neutron anomaly itself is due to a statistical error.
We can also calculate a new bound on BRX. Like in Ref. [34], we calculate one-sided bounds with 95% C.L. In addition, we use truncated distributions to account for the upper constraint BR ≤ 100%, which increases all bounds slightly, for instance the guessed bound in Ref. [34] from 0.27%, to 0.32%. We use the updated values for bottle  and λ in Eq. (12) of Ref. [34] and find the new bound BRX < 0.28%. This bound is 3.3 times better than the bound BRX < 0.92% derived from the data of PDG-2018 alone, which latter is still compatible with the value BRX = 1.0(0.2)% from Eq. (4). When we discard the three λ values from the past century, as was done in Ref. [34], our bound drops to BRX < 0.14%.
We conclude that the discussions of dark neutron decays (interesting as they are) should no longer be pursued in the context of the neutron anomaly.

The Ft value for neutron decay
We use the occasion to point out that, with the new neutron decay data cited in this article, the neutron-derived Ft-value becomes competitive with the Ft-values of superallowed nuclear 0 + →0 + β decays [36], which latter is with nuclear half-lives t and phase space factors f. In this equation, R   and δNS are the nuclear transition-dependent radiative corrections, and δC is the isospin correction. R   is a function only of nuclear charge Z and β energy E, independent of nuclear structure, and typically close to 1.5%; δNS and δC are in most cases a fraction of 1%, see Table X in [36].
Under CVC, Eq. (8) holds also for the vector part of neutron decay, with an additional spin factor ½. For the neutron, nuclear-structure dependent corrections are absent, δNS = δC = 0. The neutron's branching ratio for Fermi transitions equals 1/(1+3λ 2 ), and we need λ as additional parameter (likewise, for β transitions to different nuclear levels, separately measured branching ratios are needed to obtain Ft0+→0+). The vector part of the neutron Ft-value is therefore  , which is fortunate because a recent calculation suggests [46], [47] that the last word on its value may not yet have been spoken.

Conclusion
It is often speculated that the neutron decay anomaly may be due to dark neutron decay channels. Our analysis, based on all neutron decay data, excludes such an explanation, cf. Fig. 2, and lowers the bound on the dark branching ratio from BRX < 0.92% (95% C.L.), based on the data of PDG-2018, to BRX < 0.28%, based on our update of PDG-2018. We also show, Fig. 3, that neutron decay data nowadays compare well with Ft-data derived from nuclear β decays.