Non-strongly interacting particles in supersymmetric theories - sleptons, charginos/neutralinos, and charged Higgs bosons - are difficult to detect at the Large Hadron Collider. We therefore examine the possibility of producing particles of this type in virtual γγ collisions at the LHC. Since photons can be emitted from protons which do not break up in the radiation process, very clean events can be generated, compensating to some extent for the small event numbers. Higher rates are expected, at the expense of stray hadrons, for events in which one or both protons break up.
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