Probing axino LSP from diphotons events with large missing transverse energy

In a supersymmetry model with an axino as the lightest supersymmetric particle (LSP) and a Bino as the next LSP (NLSP), supersymmetry particles produced in pair at a high energy collider end up with including two Binos, followed by each Bino's decay into a photon and an axino. Final states are diphoton with large missing energy. We have comprehensively studied the implication of $\gamma\gamma+$MET data from the ALEPH, CDF II, and recent ATLAS and CMS experiments. No excess over the standard model backgrounds can be explained in this model if the NLSP Bino decays outside the detector, which happens when the axino decay constant $f_a$ is large enough. The ALEPH and CDF II data put a very strong bound on $f_a$ for light Bino case with $m_{\tilde{B}} < 150$ GeV: the narrow hadronic axion window around $f_a \sim 10^6$ GeV is completely closed. In the case where the gluino mass is smaller than about 776 GeV, the recent ATLAS data limit $f_a > 10^5$ GeV for the Bino mass below 700 GeV. This is already stronger than the previous laboratory bounds.