RIKEN Seminar

The usual calculation method of field theory relies on Lagrangian under a certain symmetry. Then, one can obtain amplitudes by using Feynman rules and diagrams. In contrast, a method called "scattering amplitudes" (on-shell amplitudes, modern amplitude method, or spinor-helicity formalism) provides the amplitudes directly from symmetries without relying on Lagrangian. For example, a calculation of gluon n-point scattering amplitudes can be greatly reduced in this method. The scattering amplitude approach is expected to extract some essences in field theory, which are not obvious in the usual Feynman methods. Conventional scattering amplitude methods are the theory for massless particles, basically. In 2017, this method was generalized to involve massive particles by Nima Arkani-Hamed group. In this talk, first, I will provide a brief review of the scattering amplitudes. Next, I will introduce the scattering amplitude calculations connected with electroweak symmetry breaking, which are related to masses, vev, and longitudinal waves, by using the generalized method. In particular, we do not use Lagrangian. We derived (strictly speaking, re-derived) several equations for electroweak symmetry breaking that are supposed to be inherent in field theory. This talk is based on arXiv:1909.10551 and arXiv:2008.09652.