Elliptically Oscillating Classical Solution in Higgs Potential and the Effects on Vacuum Transitions

TL;DR

This paper explores oscillating solutions in the Higgs potential using elliptic functions, analyzing their quantum fluctuations and implications for vacuum transition probabilities.

Contribution

It introduces a novel perturbation method around oscillating solutions in the Higgs field, extending the understanding of quantum effects beyond the vacuum state.

Findings

Finite transition probability between vacuum and multi-quanta states

Classified classical solutions using Jacobian elliptic functions

Perturbation theory reduces to standard form at vacuum

Abstract

We investigate oscillating solutions of the equation of motion for the Higgs potential. The solutions are described by Jacobian elliptic functions. Classifying the classical solutions, we evaluate a possible parameter-space for the initial conditions. In order to construct the field theory around the oscillating solutions quantum fluctuations are introduced. This alternative perturbation method is useful to describe the non-trivial quantum theory around the oscillating state. This perturbation theory reduces to the standard one if we take the solution at the vacuum expectation value. It is shown that the transition probability between the vacuum and multi-quanta states is finite as long as the initial field configuration does not start from the true vacuum.