On the utility and implication of convex effective potential for the Higgs particles

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It is suggested that within the effective potential approach, convexity and spontaneous symmetry breaking(SSB) make the Higgs modes (elementary or effective) complicated in that the normal final states (experimentally identifiable) for Higgs modes could not be analytically defined. This observation might have some nontrivial consequences for the Standard Model (SM) and particle physics.
10 pages, LaTex, no figure, revised version

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