We study gapped 4d quantum field theories (QFTs) obtained from a relevant deformation of a UV conformal field theory (CFT). For simplicity, we assume the existence of a \mathbb{Z}_2 symmetry and a single \mathbb{Z}_2-odd stable particle and no \mathbb{Z}_2-even particles at low energies. Using unitarity, crossing and the assumption of maximal analyticity we compute numerically a lower bound on the value of the a-anomaly of the UV CFT as a function of various non-perturbative parameters describing the two-to-two scattering amplitude of the particle.
