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Vacuum structure of the left-right symmetric model
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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 useful 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 a small part of the parameter space with good vacua. Consequences for some scalar masses are also discussed.
Forward citations
Cited by 6 Pith papers
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Loop-Level Lepton Flavor Violation and Diphoton Signals in the Minimal Left-Right Symmetric Model
Recasting axion limits onto the one-loop H3 couplings of the minimal left-right symmetric model excludes the right-handed scale up to 2×10^9 GeV and could eventually probe 6×10^11 GeV.
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Decaying scalar dark matter in the minimal left-right symmetric model
The lightest neutral scalar of the SU(2)_R triplet in the minimal left-right model can serve as a long-lived decaying dark matter candidate in the keV to multi-MeV mass range, provided the left-right scale exceeds abo...
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Theorem on vacuum stability
A type-I (Higgs-only VEV) local minimum is lower than every type-0 and type-III extremum in the restricted scalar potentials considered, by a proof using homogeneous-function identities.
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Gravitational Waves as a Probe of Left-Right Symmetry Breaking
With one scalar coupling tuned to about 10^-3, the minimal left-right symmetric model predicts a first-order phase transition whose gravitational waves could be seen by LISA and other planned space interferometers.
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Machine Learning Left-Right Breaking from Gravitational Waves
An ML-guided scan combined with a high-precision effective field theory finds a small region of the minimal Left-Right Symmetric Model where the first parity-breaking phase transition yields gravitational waves detect...
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The Alternative Left-Right Scenario: Unitarity, Vacuum Stability and RG Evolution
Renormalization group evolution in the Alternative Left-Right Model restricts the allowed quartic couplings and yields upper bounds on extended Higgs scalar masses for theoretical consistency up to 10^16 GeV.
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