Abstract
If the hints for light sterile neutrinos from short-baseline anomalies are to be taken seriously, global fits indicate active-sterile mixings of a magnitude comparable to the known reactor mixing. We therefore study the conditions under which the active-sterile and reactor mixings could have the same origin in an underlying flavour model. As a starting point, we use $\mu-\tau$ symmetry in the active neutrino sector, which (for three neutrinos) yields a zero reactor neutrino angle and a maximal atmospheric one. We demonstrate that adding one sterile neutrino can change this setting, so that the active-sterile mixing and non-zero $\theta_{13}$ can be generated simultaneously. From the phenomenological perspective, electron (anti)neutrino disappearance can be easily accommodated, while muon neutrino disappearance can vanish. It is, however, difficult to reconcile the LSND results with this scenario. From the theory perspective, the setting requires the misalignment of some of the flavon vacuum expectation values, which may be achieved in an $A_4$ or $D_4$ flavour symmetry model using extra dimensions.
Highlights
While each of these observations may be interpreted by adding one extra sterile neutrino, there is a well-known tension between appearance and disappearance data in the global fits, see refs. [11, 12] for recent works
Most of the mechanisms to explain light sterile neutrino masses either rely on the principle of suppressing one sterile neutrino mass eigenvalues or on forcing the natural mass of one sterile neutrino to be zero which is lifted to a finite but small value by some correction
A certain mechanism could be used to suppress masses and mixings at the same time, and proposals include the use of the Froggatt-Nielsen mechanism [48] to explain light sterile neutrinos [49] as well as the use of exponential suppressions arising from extra spatial dimensions [50, 51]
Summary
Let us consider the 3 × 3 generic μ − τ invariant Majorana neutrino mass matrix given in [74], ABB. The step is to impose μ–τ symmetry onto the upper left 3 × 3 block of the full mass matrix Mν4×4 by requiring the two complex equations equations me2 = −me and mμ2 = mτ to hold and solving them for the remaining parameters θ14,34 and δ1,2 By this procedure, we have obtained a set of 100, 000 points which all fulfill the criteria of leading to mass matrices with the desired form of the upper left 3 × 3 block and which are phenomenologically valid except for, maybe, their value for θ13, which is exactly what we would like to investigate. No matter which data set is favoured by the reader, our general findings remain correct: it is possible to generate a sizable reactor angle from sterile neutrino contributions to the light neutrino mass matrix
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