Searching for the $N$-naturalness tower of neutrinos

Abstract

We present the first experimental search for the $N$-naturalness tower of neutrinos using a global analysis of publicly available neutrino data. As a potential solution to the hierarchy problem, the $N$-naturalness model employs a varying Higgs mass parameter among $N$ dark sectors and encodes the required fine-tuning of the placement of the sectors in a parameter $r$. We report exclusion limits on the parameter space ($r$, $N$), for normal and inverted ordering and in case the neutrino is Majorana or Dirac. In the case of a Majorana neutrino, we can rule out $N\le 10^4$ sectors with $r\ge 0.1$. This is particularly exciting as it shows that a gauge and gravitational unification around $M_{GUT}$, which is a benchmark scenario of the $N$-naturalness framework with $N=10^4$ without fine-tuning, is ruled out by neutrino experiments.