Bounds on supersymmetric effective operators from heavy diphoton searches

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.