  New physics frameworks like the Next-to-Minimal Supersymmetric Standard Model
and the Next-to-2-Higgs-doublet Model contain three neutral CP-even Higgs
bosons. It is possible for the heavier two of these states to have masses
identical to each other, which can result in a sizeable quantum interference
between their propagators in processes they mediate. For both these models, we
study the impact of such interference on the pair-production of the lightest of
the three scalars, which we identify with the observed 125 GeV Higgs boson, in
the gluon-fusion channel at the Large Hadron Collider (LHC). We find that the
inclusion of these effects can substantially alter the cross section, compared
to its value when they are ignored, for this process. Our results illustrate
the importance of taking possible quantum interference effects into account not
only when investigating the phenomenology of extended Higgs sectors at the
future Run(s) of the LHC, but also when imposing its current exclusion bounds
on the parameter spaces of these models.
