  Unparticles from hidden conformal sectors provide qualitatively new
possibilities for physics beyond the standard model. In the theoretical
framework of minimal models, we clarify the relation between energy scales
entering various phenomenological analyses. We show that these relations always
counteract the effective field theory intuition that higher dimension operators
are more highly suppressed, and that the requirement of a significant conformal
window places strong constraints on possible unparticle signals. With these
considerations in mind, we examine some of the most robust and sensitive probes
and explore novel effects of unparticles on gauge coupling evolution and
fermion production at high energy colliders. These constraints are presented
both as bounds on four-fermion interaction scales and as constraints on the
fundamental parameter space of minimal models.
