Non-unitary neutrino mixing and CP violation in the minimal inverse seesaw model

We propose a simplified version of the inverse seesaw model, in which only two pairs of the gauge-singlet neutrinos are introduced, to interpret the observed neutrino mass hierarchy and lepton flavor mixing at or below the TeV scale. This minimal inverse seesaw scenario (MISS) is technically natural and experimentally testable. In particular, we show that the effective parameters describing the non-unitary neutrino mixing matrix are strongly correlated in the MISS, and thus, their upper bounds can be constrained by current experimental data in a more restrictive way. The Jarlskog invariants of non-unitary CP violation are calculated, and the discovery potential of such new CP-violating effects in the near detector of a neutrino factory is discussed.

The standard oscillation formalism then yields the vacuum transition probability in the form:

Non-unitary Lepton Mixing in Neutrino Oscillations
Suppose the neutrinos entering the charged current (CC) interactions are in general not a mere unitary admixture of three light mass eigenstates. There can be other components present which do not enter charged currents.
Assuming the extra states are dynamically inaccessible one can effectively consider only three light mass eigenstates are relevant for oscillations of the three flavours. Technically, one has to canonically normalize the light fields when the heavy sector effectively decouples.
is a (small) hermitean matrix characterizing the departure from a unitary , which can be at leading order parametrized by means of the measured neutrino mixing parameters.

Type-III seesaw:
In the canonical type-I seesaw, the non-unitarity effects are suppressed because the same structure ( ) that makes the light neutrino masses to fall into the sub-eV region enters : In the canonical type-II seesaw there is nothing extra that could admix into the flavour eigenstates.
The situation is analogous to the type-I case.
since is to be kept around the electroweak scale (being a Dirac mass) there is another virtue in scenarios with potentially large (%) non-unitary effects -a heavy sector in few TeV range, perhaps observable at the LHC (?) Expected bonus: Thus, the non-unitarity due to the quasi-decoupled heavy sector is tiny unless one invokes a fine-tuning. Minkowski 1977Yanagida 1979Glashow 1979 Thus, there is a need to disentangle the lightness of the neutrino masses from the typical magnitude of the structure.

Virtues of the ISS:
+ Naturalness of the setting + Similarity to the type-I/III, but very different in the amount of lepton number violation + Non-unitarity effects not suppressed by the smallness of the neutrino masses, simple form of gives rise to correlations between various entries (better than mere Schwarz inequality) + LFV effects also not suppressed, non-vanishing even for zero neutrino masses

Inverse seesaw scenario (ISS)
Due to the presence of an extra singlet sector, the traditional 6x6 neutrino mass matrix is enlarged, typically to a 9x9 structure.
The RH sector is arranged to be pseudo-Dirac with a tiny mass difference providing the only source of lepton number violation. Light neutrino masses are driven by an interplay of two different scales.
One can keep the right-handed sector sizably admixed into the flavour eigenstates entering the CC by keeping relatively large (at the %-level) whilst dynamically decoupling the light neutrinos from the heavy ones so that the three mass-eigenstate mixing approximation makes sense. In other words, the mixing (driving the non-unitarity parameters) is potentially large due to the proximity of and the electroweak scale, while the light neutrino mass scale is suppressed due to an extra freedom in choosing .
Thus, ISS is a very plausible framework providing accessible (at least in principle) new physics without unnatural fine-tunning In particular, one typically obtains a structure like Thus, only the off-diagonal can be sizeable, yielding a specific pattern of would-be extra CP violation entering the oscillation formulae, c.f. Figure 1.
Moreover, CP effects can be sizeable only for normal hierarchy, see Figure.2. ISS in the usual formulation is not very predictive, but it is not minimall either, one can have even simpler model, yet compatible with the oscillation data.

Minimal Inverse Seesaw Scenario (MISS) η µτ
Future experimental sensitivity to : There is a certain chance to observe an effect at future facilities like a neutrino factory only before the standard oscillations take over (note the different dependence on the oscillation length). An OPERA-like near detector within few tens of kilometers would be an ideal tool to do that, see Figure 3.