In Gildener-Weinberg models the 125 GeV Higgs self-coupling is about twice the Standard Model value, making double-Higgs production hard to see, while new charged and neutral Higgs bosons should be light enough for the LHC to find.
Symmetry Breaking and Scalar Bosons,
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Phenomenology of the new light Higgs bosons in Gildener-Weinberg model
In Gildener-Weinberg models the 125 GeV Higgs self-coupling is about twice the Standard Model value, making double-Higgs production hard to see, while new charged and neutral Higgs bosons should be light enough for the LHC to find.