  The TeV energy region is currently being explored by both the ATLAS and CMS
experiments of the Large Hadron Collider and phenomena beyond the Standard
Model are extensively searched for. Large fractions of the parameter space of
many models have already been excluded, and the ranges covered by the searches
will certainly be increased by the upcoming energy and luminosity upgrades. If
new physics has to be discovered in the forthcoming years, the ultimate goal of
the high-energy physics program will consist of fully characterizing the
newly-discovered degrees of freedom in terms of properties such as their
masses, spins and couplings. The scope of this paper is to show how the
availability of polarized beams at high-energy proton-proton colliders could
yield a unique discriminating power between different beyond the Standard Model
scenarios. We first discuss in a model-independent way how this discriminating
power arises from the differences between polarized and unpolarized parton
distribution functions. We then demonstrate how polarized beams allow one not
only to disentangle different production mechanisms giving the same final-state
signature, but also to obtain information on the parameters of the hypothetical
new physics sector of the theory. This is illustrated in the case of a
particular class of scenarios leading to monotop production. We consider three
specific models that could produce a monotop signature in unpolarized proton
collisions, and show how they could be distinguished by means of single- and
double-spin asymmetries in polarized collisions. Our results are presented for
both the Large Hadron Collider operating at a center-of-mass energy of 14 TeV
and a recently proposed Future Circular Collider assumed to collide protons at
a center-of-mass energy of 100 TeV.
