Neutrino mass generation in asymptotically safe gravity

Abstract

There exist several distinct phenomenological models to generate neutrino masses. We explore, which of these models can consistently be embedded in a quantum theory of gravity and matter. We proceed by invoking a minimal number of degrees of freedom beyond the Standard Model. Thus, we first investigate whether the Weinberg operator, a dimension-five-operator that generates neutrino masses without requiring degrees of freedom beyond the Standard Model, can arise in asymptotically safe quantum gravity. We find a negative answer with far-reaching consequences: new degrees of freedom beyond gravity and the Standard Model are necessary to give neutrinos a mass in the asymptotic-safety paradigm. Second, we explore whether the type-I Seesaw mechanism is viable and discover an upper bound on the Seesaw scale. The bound depends on the mass of the visible neutrino. We find a numerical value of $10^{14}\, \rm GeV$ for this bound when neglecting neutrino mixing for a visible mass of $10^{-10}\, \rm GeV$. Conversely, for the most ``natural" value of the Seesaw scale in a quantum-gravity setting, which is the Planck scale, we predict an upper bound for the neutrino mass of the visible neutrino of approximately $10^{-15}\, \rm GeV$. Third, we explore whether neutrinos could also be Pseudo-Dirac-neutrinos in asymptotic safety and find that this possibility can be accommodated.