Abstract
We derive analytic necessary and sufficient conditions for the vacuum stability of the left-right symmetric model by using the concepts of copositivity and gauge orbit spaces. We also derive the conditions sufficient for successful symmetry breaking and the existence of a correct vacuum. We then compare results obtained from the derived conditions with those from numerical minimization of the scalar potential. Finally, we discuss the renormalization group analysis of the scalar quartic couplings through an example study that satisfies vacuum stability, perturbativity, unitarity and experimental bounds on the physical scalar masses.
Highlights
Shows that λh becomes negative at a scale of around 1010 GeV for experimentally measured value of the Higgs mass [10]
The current bounds on mass limits are from LHC 13 TeV run data [38, 39], which largely depends on charged lepton flavors involved in the decay process: MH1±± (770–870) GeV MH2±± (660–760) GeV Parameter space for quartic couplings can be further squeezed by requiring tree-level unitarity to be preserved in a variety of scattering process
We develop a method to extract necessary and sufficient conditions to ensure vacuum stability in Left-Right Symmetric model (LRSM) by using the application of gauge orbit parameters in two-Higgs fields case
Summary
For the stability of the vacuum state, the potential should be bounded in all field directions. In the large-field limit, terms with dimension d < 4 can be ignored as they are negligible in comparison to the quartic terms (denoted by V4(φi)) in the potential. Requiring V4(φi) > 0 as field values φi → ∞ is a strong condition for boundedness. This criterion is termed as Bounded From Below (BFB) condition. For obtaining conditions for vacuum stability of a scalar potential using BFB criterion, concepts of copositivity criteria and gauge orbit spaces can help greatly simplify the analysis
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