Nonperturbative bounds on scattering of massive scalar particles in d ≥ 2
Abstract
We study two-to-two scattering amplitudes of a scalar particle of mass m. For simplicity, we assume the presence of &Z;2 symmetry and that the particle is &Z;2 odd. We consider two classes of amplitudes: the fully nonperturbative ones and effective field theory (EFT) ones with a cut-off scale M. Using the primal numerical method which allows us to impose full non-linear unitarity, we construct novel bounds on various observables in 2 ≤ d ≤ 4 space-time dimensions for both classes of amplitudes. We show that our bounds are much stronger than the ones obtained by using linearized unitarity or positivity only. We discuss applications of our bounds to constraining EFTs. Finally, we compare our bounds to the amplitude in ϕ4 theory computed perturbatively at weak coupling, and find that they saturate the bounds.
- Publication:
-
Journal of High Energy Physics
- Pub Date:
- December 2022
- DOI:
- 10.1007/JHEP12(2022)092
- arXiv:
- arXiv:2207.12448
- Bibcode:
- 2022JHEP...12..092C
- Keywords:
-
- Field Theories in Higher Dimensions;
- Field Theories in Lower Dimensions;
- Nonperturbative Effects;
- Scattering Amplitudes;
- High Energy Physics - Theory
- E-Print:
- 38 pages + appendices, 23 figures