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Extra Dimensions, the Cosmological Constant Problem and the LHC

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Two uncertainties define the prevailing attitude toward the LHC: uncertainty about what new physics it may find (if any); together with dissatisfaction with the "technical naturalness" arguments which (when applied to the hierarchy problem) help suggest what it should be looking for. The dissatisfaction arises because of a wide-spread despair about finding a technically natural solution to the cosmological constant problem, despite much effort spent seeking it. In this talk I describe a mechanism within supersymmetric extra-dimensional theories that allows the low-energy effective cosmological constant naturally to be of order the Kaluza-Klein scale. If this is the solution to the cosmological constant problem, then it requires extra dimensions that are both very supersymmetric and large enough to be relevant to the LHC (with the - so far successful - prediction that no MSSM particles will be discovered there, despite the low-energy supersymmetry)