Abstract: We study a class of 4d quantum field theories (QFTs) which are defined as a relevant deformation of a UV conformal field theory (CFT) and which can be characterized by a single Z2 odd asymptotic state at low energies. Using unitarity, crossing and assumption of maximal analyticity we compute numerically a lower bound on the value of the a-anomaly describing the UV CFT as a function of various non-perturbative parameters describing the two-to-two scattering of the asymptotic state.