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There are lots of models of gravity mediated SUSY breaking with various spectra as well as various general gauge mediation models. Are there any "smoking gun" experimental singnatures that could definitely distinguish between the two scenarios? Would this be possible to do at the LHC or would we need an ILC-type machine to do that?

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They differ by the scale where SUSY is primarily broken, which is reflected in the gravitino mass etc. They have different predictions for the spectrum etc. I won't give you a full-fledged answer today but instead, let me recommend a brand new - today - lectures on SUSY from the top to down by Mike Dine: arxiv.org/abs/1102.3386 –  Luboš Motl Feb 17 '11 at 7:13
    
Thank you @Luboš Motl ! I think I've found a good reference here: prl.aps.org/abstract/PRL/v76/i19/p3494_1 –  stringpheno Feb 17 '11 at 16:41
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I just noticed this question. It's a good one without a clear answer. There are sum rules that arise in GMSB (but maybe in other scenarios too), and collider signatures that might most plausibly be interpreted as decays to gravitinos (but which can be faked by other models, even plausible ones). The two scenarios also tend to have fairly different cosmologies, although getting an experimental handle on the relevant things will be difficult. I might try to write a detailed answer at some point, but the short version is that it's an open question (one I've been thinking a lot about lately.) –  Matt Reece Mar 10 '11 at 3:12
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