  We propose a simple mechanism for copiously producing heavy Higgs bosons with
enhanced decay rates to two photons at the LHC, within the context of the
Minimal Supersymmetric extension of the Standard Model (MSSM). In the
CP-conserving limit of the theory, such a diphoton resonance may be identified
with the heavier CP-even $H$ boson, whose gluon-fusion production and decay
into two photons are enhanced by loops of the lightest supersymmetric partner
of the top quark $\tilde{t}_1$ when its mass $m_{\tilde{t}_1}$ happens to be
near the $\tilde{t}^*_1\tilde{t}_1$ threshold, i.e.~for
$m_{\tilde{t}_1}\!\simeq \!\frac12 M_H$. The scenario requires a relatively low
supersymmetry-breaking scale $M_S\stackrel{<}{{}_\sim} 1$ TeV, but large values
of the higgsino mass parameter, $\mu \stackrel{>}{{}_\sim} 1$ TeV, that lead to
a strong $H \tilde{t}^*_1 \tilde{t}_1$ coupling. Such parameters can
accommodate the observed mass and standard-like couplings of the 125 GeV $h$
boson in the MSSM, while satisfying all other constraints from the LHC and dark
matter searches. Additional enhancement to the diphoton rate could be provided
by Coulombic QCD corrections and, to a lesser extent, by resonant contributions
due to $\tilde{t}_1^* \tilde{t}_1$ bound states. To discuss the characteristic
features of such a scenario, we consider as an illustrative example the case of
a diphoton resonance with a mass of approximately 750 GeV, for which an excess
was observed in the early LHC 13 TeV data and which later turned out to be
simply a statistical fluctuation.
