Neutrino mass generation in asymptotically safe gravity

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msup><a:mn>10</a:mn><a:mn>14</a:mn></a:msup><a:mtext> </a:mtext><a:mtext> </a:mtext><a:mi>GeV</a:mi></a:mrow></a:math> for this bound when neglecting neutrino mixing for a visible mass of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:msup><c:mn>10</c:mn><c:mrow><c:mo>−</c:mo><c:mn>10</c:mn></c:mrow></c:msup><c:mtext> </c:mtext><c:mtext> </c:mtext><c:mi>GeV</c:mi></c:mrow></c:math>. 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 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:msup><e:mn>10</e:mn><e:mrow><e:mo>−</e:mo><e:mn>15</e:mn></e:mrow></e:msup><e:mtext> </e:mtext><e:mtext> </e:mtext><e:mi>GeV</e:mi></e:mrow></e:math>. Third, we explore whether neutrinos could also be pseudo-Dirac neutrinos in asymptotic safety and find that this possibility can be accommodated.