Abstract
The left-right symmetric model (LRSM), originally proposed to explain parity violation in low energy processes, has since emerged as an attractive framework for light neutrino masses via the seesaw mechanism. The scalar sector of the minimal LRSM consists of an SU(2) bi-doublet, as well as left- and right-handed weak isospin triplets, thus making the corresponding vacuum structure much more complicated than that of the Standard Model. In particular, the desired ground state of the Higgs potential should be a charge conserving, and preferably global, minimum with parity violation at low scales. We show that this is not a generic feature of the LRSM potential and happens only for a small fraction of the parameter space of the potential. We also analytically study the potential for some simplified cases and obtain sufficient conditions (though not necessary) to achieve successful symmetry breaking. We then carry out a detailed statistical analysis of the minima of the Higgs potential using numerical minimization and find that for a large fraction of the parameter space, the potential does not have a good vacuum. Imposing the analytically obtained conditions, we can readily find the small part of the parameter space with good vacua. Consequences for some scalar masses are also discussed.
Highlights
It is known that for certain ranges of the parameters, a desired vacuum is obtained
Eq (2.10) is what we need to successfully achieve spontaneous symmetry breaking in the left-right symmetric model (LRSM), for general values of the parameters, the scalar potential does not necessarily lead to this vacuum expectation values (VEVs) alignment
With further developed algorithms, we can make the program capable of identifying the zero entries in eq (2.10). In this way we can find out all possible VEV alignments that can be obtained in the LRSM potential
Summary
The LRSM [7–9] extends the SM gauge group GSM ≡ SU(3)c ⊗ SU(2)L ⊗ U(1)Y to GLR ≡ SU(3)c ⊗SU(2)L ⊗SU(2)R ⊗U(1)B−L. Eq (2.10) is what we need to successfully achieve spontaneous symmetry breaking in the LRSM, for general (arbitrary) values of the parameters, the scalar potential does not necessarily lead to this VEV alignment. With further developed algorithms (see the details presented in section 5), we can make the program capable of identifying the zero entries in eq (2.10) In this way we can find out all possible VEV alignments that can be obtained in the LRSM potential. While the potential for such cases may be too complicated to repeat the analytical calculations given here, our numerical method can be implemented to analyze the vacuum structures of such models We leave these studies for future work
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