Renormalizable quartic couplings among new particles are typical of supersymmetric models. Their detection could provide a test for Supersymmetry, discriminating it from other extensions of the Standard Model. Quartic couplings among squarks and sleptons, together with the SU(3) gauge couplings for squarks, allow the production of a pair of sleptons through gluon fusion, at the one-loop level. The corresponding cross section, however, is at most of O(1) fb for slepton and squark masses of O(100) GeV. Our investigation is then extended to the gluon-fusion production of sleptons through the exchange of Higgs bosons. The cross section is even smaller, of O(0.1) fb, if the exchanged Higgs boson has mass considerably below the slepton-pair threshold, but it is enhanced when it is resonant. It can reach the O(10) fb mark for the production of sleptons of same chirality, and it can exceed it for the production of T̄'s of opposite chirality, even when the chirality-mixing terms in the squark sector are vanishing. The cross section may be further enhanced if these mixing terms are nonnegligible, providing therefore a potentially interesting probe of the Higgs sector, in particular of μ, tan β, and the trilinear soft Supersymmetry-breaking couplings, also for more realistic sfermion spectra.
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