Mass Deformed Exact S-parameter in Conformal Theories

We use the exact expression for the S parameter in the perturbative region of the conformal window to establish its dependence on the explicit introduction of fermion masses. We demonstrate that the relative ordering with which one sends to zero either the fermion mass or the external momentum leads to drastically different limiting values of S. Our results apply to any fermion matter representation and can be used as benchmark for the determination of certain relevant properties of the conformal window of any generic vector like gauge theory with fermionic matter. We finally suggest the existence of a universal lower bound on the opportunely normalized S parameter and explore its theoretical and phenomenological implications. Our exact results constitute an ideal framework to correctly interpret the lattice studies of the conformal window of strongly interacting theories.