Mass generation via nonlinear massive solution in Higgs potential and particle creations

TL;DR

This paper explores how nonlinear classical solutions in the Higgs potential can lead to mass generation and particle creation, providing new formulas for particle production probabilities in the early universe.

Contribution

It introduces a novel approach using nonlinear massive solutions to explain mass generation and particle creation in the Higgs field, with explicit probability formulas.

Findings

Probability densities vanish at the classical vacuum

Probability densities depend on a free parameter in the solution

Behavior analyzed for three oscillating modes

Abstract

The nonlinear massive plane wave solution of the classical scalar field in the Higgs potential is revisited to study the mass generation and particle creation. In particular, by assuming that the Higgs system is in the slightly excited state in early universe and it is described by the nonlinear solution, we study the mass generation mechanism for massive vector bosons and a heavy fermion in the quantum field theory around the nonlinear massive classical field. The nonlinear massive classical solution gives the transition from the vacuum to a pair of vector bosons and fermions. We present the new formulae of the probability density of the production process for particles in the standard model of elementary particle physics. The probability densities of the particle productions vanish when the nonlinear massive solution reduces to the constant solution (the classical vacuum expectation value); while the probability densities are expressed as the function of the free parameter in the classical solution in general case. We discuss the behavior of the probability densities for the three oscillating modes in the classical solution.