Comultiplication in link Floer homology and transversely non-simple links

For a word w in the braid group on n-strands, we denote by T_w the corresponding transverse braid in the rotational symmetric tight contact structure on S^3. We exhibit a map on link Floer homology which sends the transverse invariant associated to T_{ws_i} to that associated to T_w, where s_i is one of the standard generators of B_n. This gives rise to a "comultiplication" map on link Floer homology. We use this to generate infinitely many new examples of prime topological link types which are not transversely simple.Comment: 16 pages, 10 figure

Electroweak Vacuum Stability and the Seesaw Mechanism Revisited

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