Spontaneous Symmetry Breaking from an On-Shell Perspective

TL;DR

This paper demonstrates how spontaneous symmetry breaking phenomena, including the Higgs mechanism, can be derived purely from on-shell scattering amplitudes without relying on traditional Lagrangian or gauge symmetry frameworks.

Contribution

It introduces an on-shell approach to determine mass and interaction patterns from scattering amplitudes, bypassing the need for Lagrangians or vacuum expectation values.

Findings

Reproduces the Higgs mechanism from on-shell amplitudes.

Identifies the subgroup structure in symmetry breaking.

Shows the pattern of mass and interaction generation in the Standard Model.

Abstract

We show how the well known patterns of masses and interactions that arise from spontaneous symmetry breaking can be determined from an entirely on-shell perspective, that is, without reference to Lagrangians, gauge symmetries, or fields acquiring a vacuum expectation value. To do this, we review how consistent factorization of $2\rightarrow 2$ tree level scattering can lead to the familiar structures of Yang-Mills theories, and extend this to find structures of Yukawa theories. Considering only spins-$0$, $1/2$ and $1$ particles, we construct all the allowed on-shell UV amplitudes under a symmetry group $G$, and consider all the possible IR amplitudes. By demanding that on-shell IR amplitudes match onto on-shell UV amplitudes in the high energy limit, we reproduce the Higgs mechanism and generate masses for spins-$1/2$ and $1$, find that there is a subgroup $H \subseteq G$ in the IR, and other interesting relations. To highlight the results, we show the breaking pattern of the Standard Model $U(1)_{EM} \subset SU(2)_L \times U(1)_Y $, along with the generation of the masses and interactions of the particles.