Neutrino masses and phenomenology in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>-naturalness

In this paper, it is shown that <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>N</a:mi></a:math>-naturalness scenarios have an intrinsic mechanism to suppress neutrino masses. As in other infrared neutrino mass models like extra-dimensional theories or many species theories, the large number of mixing partners is responsible for the neutrino mass suppression. It is shown how neutrino mass matrices arise in <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>N</c:mi></c:math>-naturalness models, and the resulting neutrino mixing is analyzed. The first result is that a totally democratic coupling among the different sectors like in the original models is already ruled out by the fact that neutrinos are not massless. In the case where the sector couplings deviate from the intersector ones a tower of additional neutrino mass eigenstates appears whose difference between the squared masses, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi mathvariant="normal">Δ</e:mi><e:msubsup><e:mi>m</e:mi><e:mrow><e:mi>i</e:mi><e:mi>j</e:mi></e:mrow><e:mn>2</e:mn></e:msubsup></e:math>, is determined fully by the theory. The resulting phenomenology of such a tower is investigated, and the unique signals in neutrino oscillation experiments, neutrino mass measurements, and neutrinoless double beta decay experiments are discussed. This opens the door for terrestrial tests of <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>N</h:mi></h:math>-naturalness whose phenomenology was so far focused on cosmology.