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Extending the Higgs sector of the MSSM by triplets alleviates the little hierarchy problem and naturally allows for enhancements in the diphoton decay rate of the lightest CP-even Higgs h.
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See e.g. Conference talks in ”Fourth International Workshop in Prospects for Charged Higgs Discovery at Colliders”, Uppsala University, Sweeden, 8-11 October 2012, http://www.grid.tsl.uu.se/chargedhiggs2012/
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