Abstract
We discuss vacuum stability in Froggatt-Nielsen (FN) models. One concern in FN models is that for large flavon VEVs the running of the quartic Higgs coupling is enhanced what might lead to a more severe instability compared to the Standard Model (SM). We study this issue using the renormalization-group improved scalar potential. Another issue is that the mixing between the Higgs and the flavon can potentially destabilize the potential. However, taking current bounds on the flavon phenomenology into account, we find that both effects do not lead to an instability that is more severe than in the SM.
Highlights
First two generations (θ12 ∼ ) and the smallness of the mixing angles involving the third generation (θ13 ∼ 2, θ23 ∼ 3)
If the Yukawa couplings are considered to be dependent on the flavon VEV, y( S /M ), all Yukawa couplings will be of order unity for large flavon VEVs, S ∼ M
We studied the vacuum stability of Froggatt-Nielsen models
Summary
The complex flavon field S contains a pseudo-scalar degree of freedom a that would be massless after the spontaneous breaking of the (global) U(1)FN symmetry We will neglect this particle in our analysis and assume that it obtains a soft mass term through an explicitly U(1)FN-breaking term that is above all relevant scales that we aim to study. The second effect is the stabilizing effect caused by mixing of the flavor eigenstates which does not depend on the sign of λm This effect can overturn the negative contribution from the extended fermion sector in h-direction. In general the barrier in s-direction is high and large in case of ms ∼ M mh This reduces the tunneling amplitude calculation effectively to a 1D path problem in h-direction (with a fixed flavon VEV). Once M and mσ are decoupled, one should do proper RG-running between the scales
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