Naturally small neutrino mass from asymptotic safety

We consider the dynamical generation of an arbitrarily small neutrino Yukawa coupling in two scenarios embedded in trans-Planckian asymptotic safety: first the Standard Model with right-handed neutrinos, then the gauged $B-L$ model. We show that this mechanism is more in line with existing theoretical calculations in quantum gravity when it is applied to the $B-L$ model. Interestingly, this scenario can accommodate, in full naturalness and without extensions, the possibility of purely Dirac, pseudo-Dirac, and Majorana neutrinos with any see-saw scale. We investigate eventual distinctive signatures of these cases in the detection of gravitational waves from first-order phase transitions.