Assessing Perturbativity and Vacuum Stability in High-Scale Leptogenesis

We consider the requirements that all coupling constants remain perturbative and the electroweak vacuum metastable up to the Planck scale in high-scale thermal leptogenesis, in the context of a type-I seesaw mechanism. We find a large region of the model parameter space that satisfies these conditions in combination with producing the baryon asymmetry of the Universe. We demonstrate these conditions require ${\rm Tr}[Y_N^\dagger Y_N] \lesssim 0.66$ on the neutrino Yukawa matrix. We also investigate this scenario in the presence of a large number $N_F$ of coloured Majorana octet fermions in order to make quantum chromodynamics asymptotically safe in the ultraviolet.