Neutrino mass generation in asymptotically safe gravity

TL;DR

This paper investigates how neutrino masses can be generated within the framework of asymptotically safe quantum gravity, concluding that additional degrees of freedom are needed beyond the Standard Model and gravity.

Contribution

It demonstrates that the Weinberg operator cannot produce neutrino masses in asymptotic safety, and establishes bounds on the Seesaw scale and neutrino masses within this paradigm.

Findings

The Weinberg operator is incompatible with asymptotic safety.

An upper bound of 10^{14} GeV is found for the Seesaw scale.

Neutrinos could be Pseudo-Dirac in asymptotic safety.

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.