Abstract
We study the electroweak vacuum stability in Type I seesaw models for 3 generations of neutrinos in scenarios where the right-handed neutrinos have explicit bare mass terms in the Lagrangian and where these are dynamically generated through the mechanism of spontaneous symmetry breaking. To best highlight the difference of the two cases we concentrate on the absolute stability of the scalar potential. We observe that for the first scenario, the scale at which the scalar potential becomes unstable is lower from that within the Standard Model. In addition the Yukawa couplings $\mathbf{Y}_\nu$ are constrained such that $\Tr{[\mathbf{Y}^{\dagger}_\nu \mathbf{Y}_{\nu}}] \lesssim10^{-3}$. In the second scenario the electroweak stability can be improved in a large region of parameter space. However, we found that the scalar used to break the lepton number symmetry cannot be too light and have a large coupling to right-handed neutrinos in order for the seesaw mechanism to be a valid mechanism for neutrino mass generation. In this case we have $\Tr [\mathbf{Y}^\dagger_{\nu} \mathbf{Y}_\nu]\lesssim 0.01$.
Highlights
I seesaw models for three generations of neutrinos in scenarios where the right-handed neutrinos have explicit bare mass terms in the Lagrangian and where these are dynamically generated through the mechanism of spontaneous symmetry breaking
From the figures it is clear that a large λS Mhigh aids a lot at stabilizing the Higgs potential for small values of YN Mhigh. This is due to the positive contribution to the running of λH, which together with the tree-level threshold effect help increase the stability of the scalar potential compared to YN Mhigh increases, the effect from the tree-level threshold effect shift remains fairly constant since λS goes to zero near
We find that Tr[Yν†Yν] 10−3 in order for the standard model (SM) electroweak vacuum stability not be worsened
Summary
Despite its spectacular success the SM cannot be the complete theory of nature. We have convincing evidence that neutrinos have small but finite masses. Our study is carried out using the RGEs outlined in [24] and where to one-loop order, the running of λH , Tr Yν†Yν and the diagonal elements of the neutrino Yukawa coupling matrix are approximately given by dλH dt. Beyond a Majorana mass scale of ∼ 1010 GeV the value of λH (MN ) is negative and high-scale seesaw models break down if the scalar potential were to remain stable as we require. We conclude that for the current preferred value of αs, electroweak stability would lead to seesaw scales approximately six orders of magnitude lower than the Grand Unified theory scale with neutrino Yukawa couplings of order O 10−2. We focus on the effects of a complex scalar gauge singlet on the electroweak vacuum stability captured by the simple majoron model and compare the results with the explicit mass case studied above.
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