Nonperturbative bounds on scattering of massive scalar particles in d ? 2

A bstract We study two-to-two scattering amplitudes of a scalar particle mass m . For simplicity, we assume the presence ? 2 symmetry and that is odd. consider two classes amplitudes: fully nonperturbative ones effective field theory (EFT) with cut-off scale M Using primal numerical method which allows us to impose full non-linear unitarity, construct novel bounds on various observables in ? d 4 space-time dimensions for both amplitudes. show our are much stronger than obtained by using linearized unitarity or positivity only. discuss applications constraining EFTs. Finally, compare amplitude ? computed perturbatively at weak coupling, find they saturate bounds.