Bootstrapping the $a$-anomaly in $4d$ QFTs: Episode II

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.