Not yet dead end... Neutrino Oscillation (I)

In 1998, at SuperK experiment, we confirmed the fact that neutrinos oscillate, which means the flavour of neutrino changes according its energy and travel distance. The flavour of neutrinos is about which kind of charged lepton we observe in the detector when it interacts with the detector material. The flavour of neutrinos can be electron neutrinos, muon neutrinos, and tauon neutrinos. Of course, they have their anti particles. The anti neutrinos interact with detector material with the daughter particle, which is just the CP conjugate particle to that for neutrinos, e.g. after an electron neutrino interact with material, an electron goes out; then an anti electron neutrino generates an anti electron (which we call 'positron').

The neutrino oscillations are the aftermath of the neutrino mixing and the non-equal mass size of neutrinos. The neutrino mixing is the mismatch between neutrino flavour states and neutrino mass states, which are the eigenstates when neutrino travel in vacuum. Neutrino mixing is described by a 3-time-3 matrix. Usually, we use PMNS parametrisation to describe it with 3 mixing angles: theta12 𝜃₁₂, theta13 (𝜃₁₃) and theta23 (𝜃₂₃), and a Dirac CP phase: delta (𝛿). The non-equal mass size bring the phase difference of the plane wave between any two of mass states. These phase differences are characterised by the mass-square differences: the 21 mass-square difference (𝝙m²₂₁) and the 31 mass-square difference (𝝙m²₃₁), the mass square difference between the 2 and 1 mass states and between the 3 and 1 mass states, respectively. So far we well understand the value of 𝜃₁₂, 𝜃₁₃, 𝝙m²₂₁. Some problems left are the sign of 𝝙m²₃₁ (𝝙m²₃₁>0 or 𝝙m²₃₁<0), if 𝜃₂₃ is larger or smaller than 45º, if CP is violated in neutrino sector, and if CP is really violated, what the value of 𝛿 is. The first of three problems will be resolved by the next generation experiments, like JUNO, DUNE and T2HK...etc. However, the uncertainty of 𝛿 will not satisfy us.

We will not talk about 1𝞂 any more. If we set the aim that we need the precision of leptonic mixing as how we have done in the quark sector. Then, probably we need to talk the precision at 90% C.L. at least. In the prediction, we expect the precision of 1𝞂 precision for 𝛿 is about 10-15º, depending on what the true value of 𝛿 is. It is much poorer for the higher statistics sensitivity. This expectation is equilibrium to 10% for the 1𝞂 precision for 𝛿, which is similar to what we have for the other parameters right now. These precision level is of course far from 0.1% at . If in quark sector, we cannot find new physics at such precision level, in the parallel it is hard to find any new physics in the present precision for neutrino sector.

We have used twenty years to complete the knowledge of neutrino oscillations. We almost have a complete understanding on neutrino oscillations. By far, it is less possible to measure all parameters in only one neutrino oscillation parameters. This is mainly because of the uncertainty, for example the energy resolution, etc. In the other word, we need multiple experiments to complete the picture of neutrino oscillations. Combining analysis with the published data then pictures it out. These combine analysis are call 'the global fit'. There are several 'the global fit' groups, for example, nufit, etc. Though comparing results from different groups can be a cross check, experimental details affects the final results. These global-fit working group do not belong to any experiments. As a result, the working members can only reproduce the experimental result by released data with proper but not precise assumption. How big the systematics is is question, while we are tracing for the high precision.

Except for the uncertainty control, the multi-channel strategy is also required for measuring all parameters in one experiment. In that sense, we need the neutrino beam contains more then one flavour and good ability of flavour separation for the detector. We may need more than one detectors, depending on the neutrino beam energy. This beam design can be realised by the proposed muon-decay facility projects, such as neutrino factory, NuSTORM, and MOMENT, etc. These configurations are aiming to produce clean electron- and muon-flavour neutrino beams with high intensity without contamination from the meson decay. Furthermore, these experiments will not only work for neutrino physics, but also be a pavement for muon colliders.

Next generation oscillation experiments, DUNE, T2HK, JUNO of course will extend our knowledge of neutrino oscillation physics. But after then? Surely, muon-decay facilities will be told. It will be a long way to see it's launching, especially if we stop and are fully satisfied by the old-fashioned techniques.