The BMSSM framework is an effective theory approach that encapsulates a variety of extensions beyond the MSSM with which it shares the same field content. The lightest Higgs mass can be much heavier than in the MSSM without creating a tension with naturalness or requiring superheavy stops. The phenomenology of the Higgs sector is at the same time much richer. We critically review the properties of a Higgs with mass around 125GeV in this model. In particular, we investigate how the rates in the important inclusive 2 photons channel, the 2 photons + 2 jets and the ZZ to 4 leptons (and/or WW) can be enhanced or reduced compared to the standard model and what kind of correlations between these rates are possible. We consider both a vanilla model where stops have moderate masses and do not mix and a model with large mixing and a light stop. We show that in both cases there are scenarios that lead to enhancements in these rates at a mass of 125GeV corresponding either to the lightest Higgs or the heaviest CP-even Higgs of the model. In all of these scenarios we study the prospects of finding other signatures either of the 125GeV Higgs or those of the heavier Higgses. In most cases the $oo{tau}tau$ channels are the most promising. Exclusion limits from the recent LHC Higgs searches are folded in our analyses while the tantalising hints for a Higgs signal at 125GeV are used as an example of how to constrain the BMSSM and/or direct future searches.
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