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Prospects are examined for the detection of a slow decay of the lightestneutralino (or any other longlived particles) at the CERN LHC and at Very LargeHadron Collider (VLHC). We first point out that such hadron colliders willbecome the ``neutralino factory'' producing 10^6--10^9 neutralinos/yr, ifgluinos and/or squarks actually exist below O(1) TeV. The lightest neutralino(\neu), usually assumed to be stable, will be unstable if lightersuperparticles such as the gravitino (\gra) or axino (\axi) exist, or R-parityis not conserved. The decay signal would, however, be missed in usual colliderexperiments, particularly when the decay mostly occurs outside the detector. Inorder to search for such a slow decay of \neu, we propose a dedicatedexperiment where the collision products are dumped by a thick shield, which isfollowed by a long decay tunnel. The decay product of \neu can be detected by adetector located at the end of the tunnel. The slow arrival time and the largeoff angle (to the direction of the interaction point) of the decay product willprovide a clear signature of slowly decaying \neu's. One can explore the decaylength (c\tau) in a wide range, i.e., 0.2 m to 1x10^5 km for \mneu=25 GeV and 1m to 2 km for \mneu=200 GeV at the LHC. This corresponds to the range of theSUSY breaking scale \rtF=2x10^5 to 2x10^7 GeV in case of the \neu\to\gamma\gradecay predicted in gauge-mediated SUSY breaking models. At VLHC, one can extendthe explorable range of \mneu up to 1000 GeV, and that of \rtF up to 1x10^8GeV. In case of the \neu\to\gamma\axi decay, the Peccei- Quinn symmetrybreaking scale F_a can be explored up to 5x10^11 GeV. The mass of the decayingparticle can be determined by using the correlation between the energy and thearrival time of the decay product.Comment: 44 pages (LaTeX) including 26 figures, one reference adde

Hadron colliders as the “neutralino factory”: Search for a slow decay of the lightest neutralino at the CERN LHC