Open Questions

The past two decades have revolutionised our picture of neutrino physics, but many questions remain unanswered:

1. Is the CP-violating phase δ non-zero, and if so, what is its value?
2. Is the neutrino mass hierarchy “normal” (mass state 1, dominated by the electron neutrino, is the lightest) or “inverted” (mass state 3 is lighter than mass state 1)?
3. Are there any sterile neutrino states, and if so, how many, and how do their masses compare to those of the “active”, Standard Model, states?
4. What is the absolute neutrino mass scale?

T2K is the first of a new generation of experiments which aim to answer these questions over the next decade or so.  Here we present a brief look at some of these current and future experiments: for more details of the T2K physics programme, go to “About T2K”.

The CP-violating Phase δ

In the PMNS matrix, the phase δ always appears in conjunction with θ₁₃, and therefore its value can only be measured if we are sensitive to θ₁₃.  Since CP violation, by definition, corresponds to a difference between particles and antiparticles, one might expect that a measurement of δ would require comparing results from neutrino and antineutrino beams, which is inconvenient (antineutrino beams are harder to make, and antineutrino interaction cross-sections are lower, so if we need comparable statistics with both neutrinos and antineutrinos it more than doubles the running time).  In fact, this is not strictly true: for a long-baseline experiment, the value of δ modifies the pattern of oscillations as a function of neutrino energy, so even an experiment running only neutrinos (not antineutrinos) can in principle measure δ – though comparing neutrinos and antineutrinos is undoubtedly the most elegant method.

Unfortunately, optimising an experiment for sensitivity to θ₁₃ does not optimise its ability to measure δ: the sensitivity of T2K to δ is therefore rather limited, though recent results have been promising.  The near-future experiment with the best sensitivity to δ is probably NOνA, which has been deliberately designed with this goal in mind.  However, as there are ambiguities between δ and θ₁₃ (i.e. the values determined by a single experiment are usually highly correlated), the best sensitivity will be obtained by combining results from several experiments.  At present there is some tension between the T2K result and NOνA in the normal ordering case.

The next-generation experiments Hyper-Kamiokande and DUNE (formerly LBNE) have excellent prospects for measuring δ, but will not start taking data until the 2020s.

The Mass Hierarchy

In cases where only one oscillation need be considered, neutrino oscillations in a vacuum are proportional to sin² (1.267 Δm² L/E) (where Δm² is measured in eV², L in km, and E in GeV), and are therefore insensitive to the sign of Δm².  As a consequence, for θ₂₃ (mixing between muon and tau neutrinos) we do not know whether mass state 2 is lighter or heavier than mass state 3.  In contrast, matter-enhanced mixing (the MSW effect) is sensitive to the sign of the mass difference, because normal matter has a high electron density (not mu or tau density). Neutrino experiments with baselines of order 1000 km or more can therefore disentangle the mass hierarchy: electron-neutrino appearance is enhanced for normal hierarchy (m₁ < m₃) but suppressed for inverted hierarchy (m₁ > m₃).  This effect is very small for T2K, with a baseline of “only” 295 km, but is significant for NOνA (baseline 810 km), and even more so for the DUNE experiment between Fermilab and Homestake (1300 km) .  Note that it only works for θ₁₃, not for the larger θ₂₃ mixing: only mixings which involve the electron neutrino (recall that θ₂₃ describes mixing between muon and tau neutrinos) are affected by a high density of electrons.

Sterile Neutrinos

Sterile neutrinos are neutrinos that do not interact via the weak interaction, and are thus essentially invisible to all neutrino experiments.  A sterile neutrino that oscillates into one or more of the known, “active”, neutrino states can be identified by one of two signatures in oscillation experiments:

1. oscillations with a value of Δm² inconsistent with the known results for solar and atmospheric mixing;
2. a disappearance signal in neutral current interactions (which are sensitive to all types of active neutrino, and therefore do not “see” oscillations between active flavours).

As discussed in the Neutrino Oscillations page, evidence for an inconsistent value of Δm² has been presented by the LSND experiment and the MiniBooNE antineutrino experiment (though not by the MiniBooNE neutrino experiment).  As this is potentially the first discovery of a particle completely unexpected in the Standard Model and its usual extensions (such as supersymmetry), it is extremely important, and urgently requires confirmation and explanation.  The MiniBooNE result is based on quite low statistics as yet: assuming that it persists when more data are available, it will become very important to study this sector.  Long-baseline experiments can address this issue by studying neutral-current reactions such as ν + p → ν + p + π⁰: the signature of sterile neutrinos would be a deficit in such reactions in the far detector compared to the near detector.  It is inconvenient that the signal is so far observed only in antineutrinos: most long-baseline experiments run, at least initially, with neutrino beams, which are easier to make and easier to detect (neutrinos have higher interaction cross-sections than antineutrinos).  Note that the presence of the signal in antineutrinos and not in neutrinos suggests that this is a CP-violating process, which makes it doubly interesting.

The Absolute Mass Scale

Neutrino oscillation experiments only ever provide information on squared mass differences, and are thus unable to shed light on the absolute neutrino mass scale: for example, a squared mass difference of 7.6×10^–5 eV² could correspond to masses of 0 and 0.0087 eV, 0.1 and 0.10038 eV, 1 and 1.000038 eV, etc.  There are basically two direct and one indirect way to measure absolute neutrino masses:

1. the endpoint of the energy spectrum of electrons from radioactive beta decay (usually tritium) – a non-zero neutrino mass will lower the endpoint and suppress the yield of very high-energy electrons;
2. the observation of neutrinoless double beta decay – this process only happens if the electron neutrino is not massless and is a Majorana particle;
3. the observation of a hot-dark-matter component of the Universe as derived from studies of the cosmic microwave background – this would give a measure of the sum of all neutrino masses (including any sterile neutrinos).

This topic is discussed further in the page on Neutrinos Beyond the Standard Model.  A number of current and near-future experiments aim to address this topic, especially via neutrinoless double beta decay.

Summary: Current and Near-Future Neutrino Experiments

The measurement of θ₁₃ represents a significant milestone in neutrino physics, but the above list shows that many questions remain to be answered. In addition,
there are further open questions in the field of neutrino astrophysics: what astrophysical objects are the sources of high-energy cosmic rays (and hence high-energy neutrinos), what exactly is the role of neutrinos in core-collapse supernovae, and can we detect neutrinos from the annihilation of supersymmetric dark matter? Fortunately, there are many experiments aiming to address these questions. A list, not necessarily exhaustive, of present and future neutrino experiments can be found on Wikipedia.