  In the scenario where only superpartners were produced at the Large Hadron
Collider, how one could determine whether the supersymmetric model pointed out
is 4-dimensional or higher-dimensional ? We propose and develop a series of
tests for discriminating between a pure supersymmetry (SUSY) and a SUSY
realized within the well-motivated warped geometry a la Randall-Sundrum (RS).
Two of these tests make use of some different patterns arising in the
squark/slepton mass spectrum. The other distinctive RS SUSY feature is the
possibly larger (even dominant) Higgs boson decay branching ratios into
sleptons, compared to pure SUSY. Techniques for pinning up the presence of soft
SUSY breaking terms on the TeV-brane are also suggested, based on the analysis
of stop pair production at the International Linear Collider. For all these
phenomenological studies, we had first to derive the 4-dimensional (4D)
effective couplings and mass matrices of the sfermions and Higgs bosons in RS
SUSY. The localization of Higgs bosons, characteristic of RS, leads to
singularities in their couplings which are regularized by the exchange
contribution of infinite towers of Kaluza-Klein (KK) scalar modes with
Dirichlet-Dirichlet boundary conditions. A general method is provided for this
regularization, based on the completeness relation. The sfermion masses are
obtained either from integrating out those specific KK towers or by treating
their mixing effects. Finally, we show at the one-loop level how all quadratic
divergences in the Higgs mass cancel out for any cut-off, due to 5D SUSY and to
5D anomaly cancellation; the analytical way followed here also allows a
justification of the infinite KK summation required for the so-called KK
regularization in 5D SUSY, which has motivated a rich literature.
