Consistent origin of neutrino mass and freeze-in dark matter in large N theories

Most of what we concern in beyond standard phenomenology are the existence of tiny numbers. The well-defined principle for protecting the tiny number to be large from quantum correction is supersymmetry. However, such a nice framework is challenged by the non-observation of superpartners at LHC. Instead, we propose a new principle to realize a natural framework to explain the smallness of feebly interaction dark matter coupling and neutrino mass. The scalar sector as well as gauge sector must be extended to include $N$ copies as a price. It is found in this paper that the yukawa coupling $y$ as well as quartic coupling $\lambda$ scales with inverse power of $N$ to maintain perturbativity. In terms of the scaling behavior of couplings, the freeze-in dark matter becomes compatible with neutrino mass requirement. The biggest observation is that $y$ has to be evaluated by $1/N^{3/2}$ in type-I seesaw mechanism in order to obtain a large $N$ suppressed neutrino mass. The intrinsic hierarchy between $1/\sqrt{N}$ and $1/N^{3/2}$ for yukawa coupling $y$ can be improved if we focus on the loop generated neutrino mass which can be relaxed to be $1/N$. The underlying reason for not use $1/\sqrt{N}$ is that freeze-in dark matter provides a lower bound for the scaling. Therefore the only choice of scaling for yukawa coupling is left to be $1/N$. Based on this simple scaling, we realiza an unified framework for explaining FIMP and neutrino mass.