Models used to evaluate experiments with neutrinos are surprisingly incomplete. This has now been shown in a check of the calculations using electrons.

Among the known elementary particles, neutrinos are the most difficult to observe, because the vast majority of them penetrate all matter without a trace. Extremely rarely a particle hits an atomic nucleus and produces other particles in the collision. From these, indirect conclusions can be drawn about the original properties of the invisible neutrino. Now, however, an investigation indicates that this does not work as well as expected.

Neutrinos are considered key objects for detecting weaknesses in the so-called Standard Model of particle physics. According to this model, neutrinos should theoretically have no mass at all. However, according to numerous experiments from the last decades, this is exactly the case: The three known types of neutrinos transform into each other, and such quantum mechanical “oscillations” are only possible for mass-bearing particles. More precise measurements of neutrino oscillation could provide clues to long-sought extensions of the Standard Model. Therefore, several ongoing and planned experiments should provide more precise data on how fast a neutrino of one type transforms into that of another.

A proven strategy for doing this is to produce neutrinos in large numbers at one location, such as happens as a byproduct of reactions in nuclear power plants, and capture some of them in detectors at other locations on Earth. These typically contain large quantities of highly pure substances, where the occasional impact of a neutrino on an atomic nucleus triggers a characteristic flash of light or similar signal. Such a laboratory can be built near a nuclear power plant, for example, where one can measure how many neutrinos of one kind pass through. In the same direction, one then uses a second, distant instrument to determine how many are left. The rest must have transformed into another type on the journey there.

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How well the current models work is difficult to verify

How much a neutrino oscillates between different states depends on the distance traveled as well as its energy. The former can be easily measured, but the latter can only be determined indirectly. This requires models of the interaction with an atomic nucleus, the type of particles that are created in the process, and the directions in which they fly. The sophisticated set of formulas helps to interpret the signals in the detectors and to infer the energy of the triggering neutrino.

Neutrinos are produced in a fundamentally random way during nuclear decays in a nuclear power plant, for example
But it is practically difficult to verify how well the models for a particular experiment work at all. After all, it is not possible to simply generate neutrino beams with a known energy in order to calibrate the apparatus and see how accurate the predictions of the computer programs are for precisely this energy. Rather, neutrinos are produced in a fundamentally random manner during nuclear decays in a nuclear power plant, for example. This gives rise to a wide range of energies. Under the special conditions of each experimental setup, the numerous indeterminate theoretical parameters must be adjusted until the results appear coherent. Many sources of error lurk there, causing uncertainties in the interpretation of the data.

Inferring neutrinos from electrons

It would be practical to test the limits of current models by using comparable but much easier to control and abundant particles as an alternative to neutrinos. The idea has been worked out and cleverly implemented by a group led by U.S. particle physicists Afroditi Papadopoulou and Mariana Khachatryan. In a November 2021 paper, the team now reports how they used the well-familiar electrons to test the models instead of the elusive neutrinos. Despite all the differences – electrons are charged and much heavier – the two types of particles are related, and Papadopoulou and Khachatryan were able to convert the expected interactions from neutrino to electron beams. This is because the real difficulties in applying the formulas are in the behavior of the constituents of the hit atomic nucleus. But this is mathematically similar in both cases, regardless of which member of the particle family they were bombarded with, apart from corrections for the different strength of the interactions.

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If the model correctly determines the energies of origin of neutrinos, it should also provide suitable values for electrons after careful conversions. The researchers used data from an experiment at Jefferson Lab in the US state of Virginia in which electron beams of different energies were systematically fired at atomic nuclei and the resulting particles were comprehensively measured. Helium, carbon and iron nuclei were of interest here, which are comparable to the targets in various neutrino detectors. The electron energies chosen also correspond to those of typical neutrino experiments. In addition, the physicists limited their analysis to events that were easy to interpret in order to reduce potential sources of error.

Despite the considerable effort, the results were sobering: The models performed very poorly in delivering the correct energies of the electron beams within a tolerance corridor of five percent. Overall, this was achieved in less than half of the events, in only about a third of all cases for carbon nuclei, and barely a quarter for iron.

The theoretical understanding of the interactions of neutrinos is obviously expandable even in the areas that seemed to be quite well covered so far. The exact causes of the discrepancy must now be determined so that the models become more reliable. This is especially important now, the team emphasizes, with an eye toward planned study campaigns with large-scale facilities under construction: “Now that we are entering an era of precision measurements of neutrinos, it will be crucial to make the models equally accurate and reliable.” That’s because the better the raw data from future detectors become, the more important it will be to eliminate inaccuracies in the models used to evaluate them. Otherwise, the precision we are actually aiming for will disappear under thick error bars, leaving an unnecessary amount of the already mysterious neutrinos in the dark.

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