  As recently shown, the a-anomaly of the UV fixed point of 4d quantum field
theories, can be constrained by studying scattering amplitudes. The basic idea
is to couple the QFT to a dilaton and impose unitarity of the scattering
amplitudes of physical particles and probe dilatons. In this work we find new
lower bounds on the $a$-anomaly in several gapped QFTs containing different
numbers of stable scalar particles.
