  We identify the bounds on supersymmetric effective operators beyond MSSM,
from heavy diphoton resonance ($X$) negative searches at the LHC, where $X$ is
identified with the neutral CP-even (odd) $H$ ($A$) or both (mass degenerate).
While minimal supersymmetric models (MSSM, etc) comply with the data, a leading
effective operator of $d=6$ can contribute significantly to diphoton production
$\sigma\sim 1$ fb, well above its MSSM value and in conflict with recent data.
Both the $b\bar b$ and $gg$ production mechanisms of $H$ and $A$ can contribute
comparably to this. We examine the dependence of the diphoton cross section
$\sigma$ on the values of $m_X$, $\Lambda$ and $\tan\beta$, under the
experimental constraints from the SM-like higgs couplings $hgg$ and
$h\gamma\gamma$ (due to mixing) and from the $b\bar b$ and $t\bar t$ searches.
These give $\Lambda$ larger than $\sim 5$ TeV for $m_X$ in the range $0.5-1$
TeV. We show how to generate the $d=6$ effective operator from microscopic
(renormalizable) models. This demands the presence of vector-like states beyond
the MSSM spectrum (and eventually but not necessarily a gauge singlet), of mass
near $\Lambda$ and thus outside the LHC reach.
