Abstract
We propose a simple mechanism for stabilizing flavon fields with aligned vacuum structure in models with discrete flavor symmetry. The basic idea is that flavons are stabilized by the balance between the negative soft mass and non-renormalizable terms in the potential. We explicitly discuss how our mechanism works in A4 flavor model, and show that the field content is significantly simplified. It also works as a natural solution to the cosmological domain wall problem.
Highlights
There are many proposals that try to explain the observed pattern of neutrino masses and mixings using discrete flavor symmetry
In these classes of models, the Lagrangian is assumed to be invariant under some discrete symmetry and charged leptons and neutrinos obtain masses through vacuum expectation values (VEVs) of scalar fields which are charged under the discrete symmetry, called flavons
The inflation scale could be lower than the flavor symmetry breaking scale so that the flavor symmetry breaking occurs before inflation, but there is a flat direction in the scalar potential in the model of Ref. [10], and this solution does not work unless the inflation scale is lower than the soft supersymmetry (SUSY) breaking scale
Summary
There are many proposals that try to explain the observed pattern of neutrino masses and mixings using discrete flavor symmetry (for reviews, see Refs. [1,2,3,4]). Models with the spontaneous breakdown of discrete symmetry necessarily have several discrete degenerate vacua Such a model suffers from the cosmological domain wall problem [5]. [6] considered some possibilities that may avoid the domain wall problem in the A4 model based on the scalar potential proposed in Ref. One possibility is that (a part of) the discrete symmetry is explicitly broken so that the VEV of flat direction does not produce exactly stable domain walls.#1Ref. [6] briefly discussed a possibility that the flat direction in the scalar potential obtains a large field value during/after inflation due to the Hubble mass correction, so that domain walls are inflated away. #1Present authors (S.C. and K.N.) have shown that the effect of quantum anomaly under the color SU(3) is not enough to completely solve the degeneracy of the discrete vacua at least in many of the known discrete flavor models [8]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
